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UBC Theses and Dissertations

The drying of lumber in a fluidized bed of inert solids Veljkovic, Maja 1976

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THE DRYING OF LUMBER IN A F L U I D I Z E D I BED OF I N E R T S O L I D S b y MAJA V E L J K O V I C B . A . S c , University of Belgrade, 1972 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF THE R E Q U I R E M E N T S FOR THE DEGREE OF MASTE R OF A P P L I E D S C I E N C E i n t h e D e p a r t m e n t o f C H E M I C A L E N G I N E E R I N G We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H C O L U M B I A J a n u a r y 1 9 7 6 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depa r t m e n t The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 D a t e hotel? 2.h, W76 ABSTRACT T h e u s e o f f l u i d i z e d b e d s o f h o t i n e r t s o l i d s f o r d r y -i n g w o o d i s a r e l a t i v e l y new c o n c e p t . R e c e n t i n v e s t i g a t i o n s o n f l u i d i z e d b e d d r y i n g o f t h i n v e n e e r ( 1 , 2 ) h a v e s h o w n t h a t m o r e r a p i d d r y i n g c a n b e a c h i e v e d b y t h i s m e t h o d t h a n b y c o n v e n t i o n a l m e a n s . I n t h e p r e s e n t w o r k , b l o c k s o f W e s t e r n H e m l o c k w o o d , 2 i n . x 4 i n . x 1 f t . c o n t a i n i n g 7 0 % t o 1 0 0 % m o i s t u r e ( d r y -b a s i s ) w e r e d r i e d i n a f l u i d i z e d b e d o f -20 +30 m e s h s a n d a t f o u r l e v e l s o f b e d t e m p e r a t u r e ( 1 7 5 , 1 9 0 , 2 0 4 , a n d 2 1 7 ° F ) a n d t h r e e a i r v e l o c i t i e s . T h e d r y i n g t i m e r e q u i r e d t o r e a c h 1 5 % m o i s t u r e c o n t e n t ( M . C . ) was 1 4 - 1 5 h r s . f o r l u m b e r d r i e d a t 2 0 4 ° F a s a g a i n s t t w o o r more days g e n e r a l l y t a k e n i n K i l n d r y -i n g . T h e q u a l i t y o f t h e w o o d d r i e d a t b e d t e m p e r a t u r e s o f 2 0 4 ° F a n d b e l o w was n o t a d v e r s e l y a f f e c t e d . B e d t e m p e r a t u r e h a d a s t r o n g i n v e r s e e f f e c t on d r y i n g t i m e , w h i l e t h e f l u i d i z -i n g a i r f l o w r a t e h a d l i t t l e e f f e c t . T h e d i f f u s i o n e q u a t i o n was e m p l o y e d t o d e s c r i b e t h e m o v e m e n t o f m o i s t u r e d u r i n g t h e f a l l i n g - r a t e p e r i o d o f d r y -i n g a n d t h e h e a t c o n d u c t i o n e q u a t i o n t o d e s c r i b e t h e u n s t e a d y -s t a t e m o v e m e n t o f h e a t i n s i d e t h e d r y i n g b l o c k o f w o o d . M a t h e m a t i c a l l y , d r y i n g was t r e a t e d b o t h as a o n e a n d a t w o -d i m e n s i o n a l p r o b l e m . T h e r e s u l t i n g e q u a t i o n s w e r e s o l v e d o n a d i g i t a l c o m p u t e r t o p r e d i c t t h e a v e r a g e m o i s t u r e c o n t e n t i i a n d t h e a v e r a g e t e m p e r a t u r e o f t h e d r y i n g b l o c k o f w o o d , e a c h a s a f u n c t i o n o f t i m e . T h e d i s t r i b u t i o n o f m o i s t u r e c o n t e n t w i t h i n t h e d r y i n g b l o c k was a l s o c o m p u t e d . T h e c a l c u l a t e d r e s u l t s s h o w e d a g o o d a g r e e m e n t w i t h e x p e r i m e n t a l d a t a . T h e e c o n o m i c s o f f l u i d i z e d b e d d r y i n g w e r e e s t i m a t e d a n d c o m p a r e d w i t h t h e c o s t o f K i l n d r y i n g . T h e r e s u l t s - s h o w e d t h a t t h e c a p i t a l c o s t o f t h e f l u i d i z e d bed s y s t e m i s c o n s i -d e r a b l y l o w e r w h i l e t h e o p e r a t i n g c o s t i s s i m i l a r t o t h a t f o r k i l n d r y i n g . T A B L E OF C O N T E N T S P a g e ABSTRACT" i i L I S T OF T A B L E S v i i L I S T OF F I G U R E S \ v i i i A CKNOWLEDGEMENTS x C h a p t e r 1 I N T R O D U C T I O N . . 1 2 BACKGROUND AND P R E V I O U S WORK 4 2.1 D r y i n g M e c h a n i s m f o r Wood 4 1 . D e f i n i t i o n o f d r y i ng 4 2. M o i s t u r e m o v e m e n t i n d r y i n g 4 3. P e r i o d s o f d r y i n g 7 4. C o n s t a n t - r a t e p e r i o d 9 5. F a l l i n g - r a t e p e r i o d 11 A . D i f f u s i o n t h e o r y . 11 B. C a p i l l a r y t h e o r y 14 C. M o v i n g b o u n d a r y t h e o r y 16 D. O t h e r m o d e l s 17 2.2 F l u i d i z e d B e d D r y i n g 18 1 . D r y i ng o f w o o d 18 2. H e a t t r a n s f e r b e t w e e n a f l u i d i z e d b e d a n d a s u b m e r g e d o b j e c t 24 i v C h a p t e r P a g e 3 T H E O R E T I C A L A N A L Y S I S OF D R Y I N G IN F A L L I N G - R A T E P E R I O D . 25 3.1 D e f i n i t i o n o f t h e P r o b l e m 25 3.2 S e l e c t i o n o f a M o d e l . . . 25 3.3 A s s u m p t i o n s 27 3.4 T h e o r e t i c a l A n a l y s i s 27 1 . H e a t t r a n s f e r 28 2. M a s s t r a n s f e r 32 3.5 S o l u t i o n o f t h e M a s s a n d H e a t T r a n s f e r E q u a t i o n s 35 1 . M a s s t r a n s f e r 35 2. H e a t t r a n s f e r 44 3.6 C a l c u l a t i o n P r o c e d u r e 46 1. C o m p u t e r p r o g r a m 47 2. M a s s t r a n s f e r 47 3 . H e a t t r a n s f e r 49 4. E X P E R I M E N T A L STUDY 53 4.1 E q u i p m e n t 53 4.2 P r o c e d u r e 56 4.3 R e s u l t s ... 65 5. D I S C U S S I O N OF R E S U L T S 84 5.1 C o n t r o l l i n g M e c h a n i s m . . . . . 8 4 5.2 E f f e c t o f O p e r a t i n g V a r i a b l e s 85 1. B e d t e m p e r a t u r e 8 5 2 . A i r f 1 ow r a t e 86 v C h a p t e r P a g e 3. F l u i d i z e d b e d - d r y i n g v s . a i r -d r y i n g 86 5.3 Q u a l i t y T e s t s 87 5.4 T h e o r y v e r s u s E x p e r i m e n t 88 1 . M a s s t r a n s f e r 8 8 2 . H e a t t r a n s f e r 91 3. D i s t r i b u t i o n o f m o i s t u r e d u r i n g d r y i n g 92 6 COMPARISON WITH K I L N DRYING " 9 4 6.1 D r y i n g T i m e 9 4 6.2 E c o n o m i c s 9 4 7., C O N C L U S I O N S . 99 NOMENCLATURE 101 R E F E R E N C E S 1 0 8 A P P E N D I C E S A D I G I T A L COMPUTER PROGRAMS I l l B SUMMARY OF E X P E R I M E N T A L AND T H E O R E T I C A L R E S U L T S OF A V E R A G E M.C. V S . T I M E , AND AVERAGE WOOD TE M P . V S . T I M E 125 C C A L I B R A T I O N CHARTS FOR A I R - F L O W ROTAMETER AND FOR E L E C T R I C M O I S T U R E METER 141 D M O I S T U R E D I S T R I B U T I O N V S . T I M E CURVES 144 v i L I S T OF T A B L E S T a b l e P a g e 1 A c c u r a c y o f m o i s t u r e m e t e r 56 2 A v e r a g e m o i s t u r e c o n t e n t f r o m E q . ( 8 0 ) v s . v a l u e s m e a s u r e d a t 2 / 5 " f r o m s u r f a c e 61 3 S u m m a r y o f e x p e r i m e n t a l r e s u l t s 66 4 P r o p e r t i e s o f t h e f l u i d i z e d b e d 77 5 P r o p e r t i e s o f W e s t e r n H e m l o c k 78 6 F l u i d i z e d b e d - - t o - s u r f a c e h e a t t r a n s f e r c o e f f i c i e n t s h , c a l c u l a t e d b y E q . ( 7 9 ) . . . . . . 78 7 V a l u e s o f e f f e c t i v e m a s s d i f f u s i v i t y ( D ) a n d t h e r m a l d i f f u s i v i t y ( a ) f o u n d b y l e a s t s q u a r e f i t o f t h e o r e t i c a l a n d e x p e r i m e n t a l d r y i n g c u r v e s 80 8 R e s u l t s o f q u a l i t y t e s t s o n f l u i d i z e d b e d d r i e d w o o d 88 9 C o m p a r i s o n b e t w e e n e x p e r i m e n t a l ( M . C . y z ) a n d c a l c u l a t e d m o i s t u r e c o n t e n t s f o r b e d t e m p . = 2 1 7 ° F a n d U = 1.2 U m f 91 10 F l u i d i z e d b e d v s . k i l n d r y i n g o f H e m l o c k . . . . • 9 5 11 E c o n o m i c s o f f l u i d i z e d b e d d r y i n g o f l u m b e r . 97 \ v i i L I S T OF F I G U R E S F i g u r e P a g e 1 M a g n i f i e d t h r e e - d i m e n s i o n a l s k e t c h o f a s o f t w o o d 6 2 M o i s t u r e c o n t e n t v s . t i m e ,.. 8 3 D r y i n g r a t e v s . m o i s t u r e c o n t e n t 8 4 F l u i d i z e d b e d d r y i n g m o d e l o f Wen a n d L o o s . . 21 5 G e o m e t r y o f b l o c k 28 6 A d s o r p t i o n - D e s o r p t i on i s o t h e r m 34 7 A v e r a g e w o o d t e m p e r a t u r e v s . t i m e c a l c u -l a t e d b y E q . ( 7 6 ) u s i n g d i f f e r e n t t i m e i n t e r v a l s 51 8 D i a g r a m o f e q u i p m e n t 54 9 L o c a t i o n o f t h e r m o c o u p l e s a n d e l e c t r o d e s . . . . 55 10 P o s i t i o n o f s a m p l e i n f l u i d i z e d b e d 58 11 S t r e s s c o n d i t i o n s i n d r y i n g w o o d l e a d i n g t o c a s e h a r d e n i ng d e f e c t 63 12 S u r f a c e c h e c k s 63 13 H o n e y c o m b d e f e c t 63 14 C a s e h a r d e n i ng t e s t 6 4 15 M o i s t u r e c o n t e n t v s . t i m e i n t w o - d i m e n s i o n a l d r y i n g 67 16 M o i s t u r e c o n t e n t v s . t i m e i n t w o - d i m e n s i o n a l d r y i n g 6 8 17 M o i s t u r e c o n t e n t v s . t i m e i n o n e - d i m e n s i o n a l d r y i n g ( y d i r e c t i o n ) 69 18 M o i s t u r e c o n t e n t v s . t i m e i n o n e - d i m e n s i o n a l d r y i n g ( z d i r e c t i o n ) 70 v i i i F i g u r e P a g e 19 M o i s t u r e c o n t e n t v s . t i m e f o r d r y i n g i n d i f f e r e n t d i r e c t i o n s 71 20 E f f e c t o f b e d t e m p e r a t u r e on d r y i n g r a t e i n t w o - d i m e n s i o n a l d r y i n g 7 2 21 D r y i n g r a t e s w i t h a n d w i t h o u t f l u i d i z e d b e d ( t w o - d i m e n s i o n a l d r y i n g ) 73 22 D r y i n g t i m e f o r m o i s t u r e r a n g e (-90 t o 1 5 % ) v s . b e d t e m p e r a t u r e ( t w o - d i m e n s i o n a l d r y -i n g ) . . . . 74 23 T e m p e r a t u r e h i s t o r y o f l u m b e r d u r i n g t w o -d i m e n s i o n a l d r y i n g 75 24 A v e r a g e w o o d t e m p e r a t u r e v s . t i m e i n t w o -d i m e n s i o n a l d r y i n g 76 25 D i f f u s i o n c o e f f i c i e n t s f r o m l i t e r a t u r e ( 3 7 , F i g . 5) a n d d i f f u s i o n c o e f f i c i e n t s f o u n d i n t h i s w o r k v s . d r y i n g t e m p e r a t u r e . . . 81 26 S e n s i t i v i t y o f M.C. v s . t i m e p r e d i c t i o n t o v a l u e s o f d i f f u s i v i t y 82 27 S e n s i t i v i t y o f a v e r a g e w o o d t e m p . v s . t i m e p r e d i c t i o n t o v a l u e s o f t h e r m a l d i f f u s i v i t y . 83 28 Q u a l i t y t e s t s . 89 29 D i s t r i b u t i o n o f m o i s t u r e i n w o o d a f t e r o n e h o u r o f d r y i n g 9 3 30 D i s t r i b u t i o n o f m o i s t u r e i n w o o d a f t e r t w o h o u r s o f d r y i n g 9 3 i x ACKNOWLEDGEMENTS T h e a u t h o r w o u l d l i k e t o e x p r e s s h e r a p p r e c i a t i o n t o h e r r e s e a r c h a d v i s o r D r . K.B. M a t h u r f o r h i s a d v i c e a n d e n c o u r a g e m e n t i n t h i s w o r k . T h e a u t h o r i s a l s o g r a t e f u l t o D r s . A. M e i s e n a n d N. E p s t e i n f o r t h e i r h e l p w i t h t h e t h e o r e t i c a l a s p e c t s o f t h e w o r k a n d t o D r s . P. W a t k i n s o n a n d R.M.R. B r a n i o n f o r u s e f u l d i s c u s s i o n s . A l s o a c k n o w l e d g e d i s t h e w o r k d o n e b y t h e s t a f f o f t h e w o r k s h o p o f t h e C h e m i c a l E n g i n e e r i n g D e p a r t m e n t . T h e a u t h o r i s i n d e b t e d t o D r . J . W i l s o n a n d o t h e r m e m b e r s o f t h e F a c u l t y o f t h e U . B . C . D e p a r t m e n t o f F o r e s t r y . S p e c i a l t h a n k s a r e d u e t o D r . V. M a t h u r o f M a c M i l l a n B l o e d e l R e s e a r c h L t d . f o r s u p p l y i n g and t e s t i n g wood sampl e s , and f o r many h e l p f u l d i s c u s s i o n s . F i n a l l y , t h e a u t h o r w o u l d l i k e t o a c k n o w l e d g e t h e a d v i c e a n d e n c o u r a g e m e n t b y h e r s t u d e n t c o l l e a g u e s , a n d s p e c i a l l y f o r t h e a s s i s t a n c e w i t h c o m p u t e r p r o g r a m m i n g g i v e n b y B. B o w e n and w i t h t h e a p p a r a t u s by S. Tarn. \ X C H A P T E R 1 I N T R O D U C T I O N T h e a i m o f t h i s i n v e s t i g a t i o n was t o a s s e s s t h e f e a s -i b i l i t y o f d r y i n g l u m b e r i n a b e d o f i n e r t s o l i d s f l u i d i z e d w i t h h o t a i r . I t i s known t h a t h e a t c a n be t r a n s f e r r e d r a p i d l y a n d e v e n l y f r o m a f l u i d i z e d b e d t o a n o b j e c t i m m e r s e d i n t h e b e d . One o f t h e r e m a r k a b l e f e a t u r e s o f t h e f l u i d i z e d b e d i s i t s t e m p e r a t u r e u n i f o r m i t y i n b o t h r a d i a l a n d a x i a l d i r e c t i o n s w i t h e f f e c t i v e t h e r m a l c o n d u c t i -v i t y o f up t o o n e h u n d r e d t i m e s t h a t o f s i l v e r , ( 3 , p . 2 6 5 ) . T h e h i g h r a t e o f b e d - t o - o b j e c t h e a t t r a n s f e r i s d u e t o t h e b u b b l e - i n d u c e d v i g o r o u s m i x i n g o f t h e s o l i d p h a s e w h i c h a l s o c a u s e s p r a c t i c a l l y i s o t h e r m a l c o n d i t i o n s i n t h e b e d ( 4 ) . Z i e g l e r e t a l . ( 5 ) , who s t u d i e d s i m u l t a n e o u s h e a t a n d m a s s t r a n s f e r f r o m t h e s u r f a c e o f a w e t s p h e r e i n a g a s s t r e a m a n d a g a s f l u i d i z e d b e d , f o u n d t h a t t h e p r e s e n c e o f s o l i d p a r t i c l e s i n t h e f l u i d i z e d s t a t e i n c r e a s e d t h e r a t e o f m a s s t r a n s f e r s e v e r a l t i m e s a n d o f h e a t t r a n s f e r 10 t o 20 t i m e s . I n d r y i n g e x p e r i m e n t s L o o s ( 1 ) f o u n d t h a t t h e d r y i n g t i m e r e q u i r e d t o d r y 1 / 1 0 " g r e e n l o b l o l l y p i n e v e n e e r f r o m v 1 0 7 . 3 % M.C. down t o 5% M.C. i n a f l u i d i z e d b e d o f s a n d a t 4 0 0 ° F was 1 3/4 m i n u t e s . T h e h i g h e s t d r y i n g r a t e s o b t a i n e d i n t h i s s t u d y w e r e t h r e e t i m e s f a s t e r f o r a f l u i d i z e d b e d 1 2 o f s a n d t h a n t h o s e f o r j e t d r y e r s r u n a t t h e s a m e t e m p e r a -t u r e s . S i m i l a r r e s u l t s h a v e b e e n r e p o r t e d b y B a b a i l o v ( 2 ) who f o u n d t h a t t h e d r y i n g t i m e r e q u i r e d t o d r y 0 . 0 6 " t h i c k p e e l e d v e n e e r f r o m 8 0 % M.C. t o 6% M.C. i n a f l u i d i z e d b e d o f m e t a l l u r g i c a l s l a g a t 2 9 3 ° F was 1 m i n u t e . F l u i d i z e d b e d d r y i n g a p p e a r s t o h a v e s e v e r a l a d v a n t -a g e s o v e r c o n n e c t i v e d r y i n g w i t h h o t a i r , w h i c h c a n b e s u m m a r i z e d a s f o l l o w s . 1. A u n i f o r m a n d c l o s e l y c o n t r o l l a b l e t e m p e r a t u r e t h r o u g h o u t t h e b e d . 2. S h o r t e r d r y i n g t i m e t h a n i n o t h e r t y p e s o f d r y e r s , o w i n g t o t h e h i g h r a t e s o f h e a t a n d m a s s t r a n s f e r b e t w e e n t h e b e d a n d a n o b j e c t i m m e r s e d i n i t . 3. T h e c a p i t a l c o s t i s e x p e c t e d t o be l o w e r t h a n f o r o t h e r t y p e s o f d r y e r s s i n c e w i t h t h e h i g h d r y i n g r a t e s a t t a i n a b l e , t h e d r y e r W o u l d b e r e l a t i v e l y s m a l l . H e a v y b u i l d i n g s a n d f o u n d a t i o n s w o u l d t h e r e f o r e n o t b e n e e d e d f o r h o u s i n g t h e d r y e r . 4. T h e o p e r a t i o n a n d m a i n t e n a n c e o f t h e d r y e r i s r e l a t i v e l y s i m p l e , a s i t i s o f s i m p l e c o n s t r u c t i o n w i t h no m o v i n g p a r t s . T h e o p e r a t i o n c a n b e a u t o -m a t e d w i t h o u t d i f f i c u l t y . P r e l i m i n a r y e x p e r i m e n t s done by Tarn on d r y i n g o f 2" x 4" p i e c e s o f W. Hemlock i n a f l u i d i z e d bed o f sand showed t h e d r y i n g t o be much f a s t e r t h a n i n t h e a b s e n c e o f t h e sand bed ( 4 2 ) , The work r e p o r t e d i n t h i s t h e s i s c o v e r s f u r t h e r e x p e r i m e n t s on d r y i n g o f samples o f Western Hemlock immersed i n a f l u i d i z e d bed 3 o f -20 + 30 mesh s a n d , f o r m u l a t i o n o f a t h e o r e t i c a l , model t o d e s c r i b e t h e s i m u l t a n e o u s h e a t and mass t r a n s f e r p r o c e s s e s i n v o l v e d and f i n a l l y an economic a s s e s s m e n t o f f l u i d i z e d bed d r y i n g v e r s u s k i l n d r y i n g o f lumber. The work has been c a r r i e d o u t i n c o n s u l t a t i o n w i t h M a c M i l l a n B l o e d e l R e s e a r c h L t d . C H A P T E R 2 BACKGROUND AND P R E V I O U S WORK 2.1 D r y i n g M e c h a n i s m f o r Wood 1. D e f i n i t i o n o f d r y i n g D r y i n g i s d e f i n e d a s t h e r e m o v a l o f a r e l a t i v e l y s m a l l a m o u n t o f l i q u i d m o i s t u r e f r o m a w e t s o l i d b y e v a p o r a t i o n . I n t h e e v a p o r a t i o n p r o c e s s h e a t h a s t o be s u p p l i e d t o t h e m a t e r i a l s o t h a t s i m u l t a n e o u s t r a n s f e r o f h e a t a n d m a s s o c c u r . T h e e v a p o r a t i n g m o i s t u r e i s u s u a l l y c a r r i e d a w a y b y m e a n s o f a n e x t e r n a l d r y i n g m e d i u m c i r c u l a t e d o v e r t h e d r y -i n g s o l i d . O f t e n t h i s m e d i u m c o n s i s t s o f d r y a i r , w h i c h may b e h e a t e d t o a c t a s t h e h e a t t r a n s f e r m e d i u m . 2. M o i s t u r e m o v e m e n t i n d r y i n g W a t e r o c c u r s i n w o o d a s f r e e w a t e r i n c e l l c a v i t i e s a n d a s a d s o r b e d o r b o u n d w a t e r w h i c h i s h e l d w i t h i n t h e s t r u c t u r e o f c e l l w a l l s . F r e e w a t e r p r e s e n t i n c e l l c a v i t i e s a b o v e t h e f i b e r - s a t u r a t i o n p o i n t ( F . S . P . - t h e m o i s t u r e c o n -t e n t a t w h i c h t h e c e l l w a l l s a r e s a t u r a t e d w i t h w a t e r b u t t h e r e i s no f r e e w a t e r i n c e l l c a v i t i e s ) , d o e s n o t a f f e c t t h e p r o p e r t i e s o f w o o d o t h e r t h a n w e i g h t . T h e b o u n d - w a t e r , h o w e v e r , d o e s a f f e c t w o o d p r o p e r t i e s , i t i s m o r e d i f f i c u l t t o r e m o v e a n d r e q u i r e s a d d i t i o n a l e n e r g y f o r i t s r e m o v a l 4 5 ( b o n d i n g e n e r g y ) . A c c o r d i n g t o Stamm ( c i t e d i n r e f . 3 5 ) , t h e r e a r e t h r e e w a y s i n w h i c h a d s o r b e d w a t e r may b e h e l d w i t h i n c e l l w a l l s : (1) a s w a t e r o f c o n s t i t u t i o n t h a t c a n n o t b e r e m o v e d f r o m w o o d w i t h o u t c a u s i n g c h e m i c a l c h a n g e i n t h e n a t u r e o f c e l l w a l l s , ( 2 ) a s s u r f a c e - b o u n d w a t e r , a n d ( 3 ) a s c a p i l l a r y - c o n d e n s e d w a t e r i n t h e t r a n s i e n t c e l l - w a l l c a p i l l -a r i e s . . T h e r e m o v a l o f w a t e r p r e s e n t i n t h e l a s t t w o f o r m s d o e s n o t c a u s e a n y c h e m i c a l c h a n g e i n t h e w o o d . A b o v e t h e f i b e r s a t u r a t i o n p o i n t , t h e c e l l w a l l s a r e s a t u r a t e d w i t h w a t e r a n d no u n b a l a n c e d f o r c e e x i s t s w h i c h w o u l d t e n d t o c a u s e d i f f u s i o n f r o m r e g i o n s o f h i g h c o n c e n t r a -t i o n t o t h o s e o f l o w c o n c e n t r a t i o n . H o w e v e r , t h e c e l l c a v i -t i e s c o n t a i n v a r y i n g a m o u n t s o f w a t e r , a n d t h a t w a t e r m o v e s b y c a p i l l a r y a c t i o n . B e l o w t h e f i b e r - s a t u r a t i o n p o i n t , w a t e r o c c u r s i n w o o d a s l i q u i d i n c e l l w a l l s a n d a s w a t e r v a p o r i n c e l l c a v i t i e s , a n d m o v e s b y d i f f u s i o n d u e t o d i f f e r -e n c e s i n m o i s t u r e c o n t e n t a n d v a p o r p r e s s u r e r e s p e c t i v e l y . M o i s t u r e c a n move w i t h i n s o f t w o o d by v a r i o u s m e c h a n i s m s . A c c o r d i n g t o B r o w n ( 6 , p . 2 6 ) t h e r e a r e f i v e m a i n p a t h s o f t r a v e l ( s e e F i g . 1 ) , 1. t h r o u g h t h e c a v i t i e s o f t r a c h e i d s 2. t h r o u g h t h e p i t s 3. t h r o u g h t h e w o o d r a y c e l l s 4. t h r o u g h t h e i n t e r c e l l u l a r s p a c e s , i . e . , b e t w e e n t h e t r a c h e i d s w h i c h do n o t a c t u a l l y r e s t a g a i n s t e a c h o t h e r a n d 5. t h r o u g h t h e t r a n s i t o r y c e l l - w a l l p a s s a g e s , w h i c h 6 Fig.i.Magnified three-dimensional sketch of a softwood t t : e n d - g r a i n s u r f a c e ; t g : t a n g e n t i a l s u r f a c e ; rr: r a d i a l s u r f a c e ; t r : t r a c h e i d ; w n w o o d r a y ; p : p i t s j c : c e l l c a v i t y ; s p : s p r i n g w o o d ; s m i s u m m e r w o o d ; a r : a n n u | a r r i n g 7 e x i s t w i t h i n t h e c e l l w a l l o n l y w hen l i q u i d s e p a -r a t e s t h e s u b m i c r o s c o p i c c o m p o n e n t s o f t h e w a l l , a n d w h i c h d i s a p p e a r w h e n t h e l i q u i d i s r e m o v e d . T h e a v a i l a b l e s p a c e f o r m o i s t u r e m o v e m e n t i s s a i d t o be f r o m 25 t o 8 5 % o f t h e t o t a l v o l u m e o f w o o d ( 6 ) , t h e a v a i l a b l e s p a c e f o r w o o d o f h i g h s p e c i f i c g r a v i t y ( b o n e - d r y w t . o f w o o d * / w t . o f a n e q u a l v o l u m e o f w a t e r ) b e i n g l e s s . O f t h e t o t a l m o v e m e n t a r e a , t h e r a y c e l l s r e p r e s e n t o n l y 2 % , a n d t h e i n t e r c e l l u l a r s p a c e s e v e n l e s s ( 6 , p . 2 6 ) . H e n c e , t h e m a i n a r e a s a v a i l a b l e f o r m o v e m e n t o f m o i s t u r e ( i n a n y f o r m ) a r e : c e l l c a v i t i e s , p i t s , a n d t h e t r a n s i t o r y c e l l w a l l p a s s a g e s . 3. P e r i o d s o f d r y i n g T h e r e a r e two p e r i o d s o f d r y i n g i n w h i c h t h e p a t t e r n o f d r y i n g r a t e i s r a d i c a l l y d i f f e r e n t : t h e " c o n s t a n t - r a t e p e r i o d " a n d t h e " f a l l i n g - r a t e p e r i o d " . F r o m d a t a o b t a i n e d d u r i n g d r y i n g o f s o l i d s , a c u r v e o f m o i s t u r e c o n t e n t ( d r y b a s i s ) a s a f u n c t i o n o f t i m e ( F i g . 2) may b e p l o t t e d . T h e v a r i a t i o n o f d r y i n g r a t e w i t h m o i s t u r e c o n t e n t c a n b e b e t t e r s e e n i f t h e M.C. v e r s u s t i m e c u r v e i s g r a p h i c a l l y o r n u m e r i c -a l l y d i f f e r e n t i a t e d a n d p l o t t e d a s dm/de v s . m, ( s e e F i g . 3 ) w h e r e m p e r c e n t a g e m o i s t u r e c o n t e n t , d r y - b a s i s , i s g i v e n b y t h e f o l l o w i n g e q u a t i o n : B o n e - d r y w e i g h t o r o v e n - d r y w e i g h t i s d e f i n e d a s t h e w e i g h t o b t a i n e d on d r y i n g w o o d t o c o n s t a n t w e i g h t i n a n o v e n a t 2 1 2 ° F . 8 t i m e ©-(hrs) Fig.2 MOISTURE CONTENT vs. TIME m o i s t u r e c o n t e n t ( % ) F i „ 3 DRYING RATE vs. MOISTURE CONTENT 9 m = ( O r i g i n a l w e i g h t ) - ( b o n e - d r y w e i g h t ) 1 Q 0  111 ( b o n e - d r y w e i g h t ) T h e c o n s t a n t - r a t e p e r i o d o n e a c h c u r v e i s r e p r e s e n t e d b y s e c t i o n B C , a n d t h e f a l l i n g - r a t e p e r i o d b y CE w h i c h b e g i n s w h e n t h e m o i s t u r e c o n t e n t r e a c h e s t h e c r i t i c a l v a l u e ( p o i n t C ) . T h e s e c t i o n CD i s u s u a l l y c a l l e d t h e f i r s t f a l l i n g r a t e p e r i o d d u r i n g w h i c h t h e s o l i d s u r f a c e i s no l o n g e r f u l l y c o v e r e d w i t h m o i s t u r e . As m o r e a n d m o r e o f t h e s u r f a c e b e c o m e s d r y , t h e d r y i n g r a t e d e c r e a s e s . T h e p o r t i o n DE i s t h e s e c o n d f a l l i n g - r a t e p e r i o d d u r i n g w h i c h t h e s o l i d s u r -f a c e i s a s s u m e d t o b e c o m p l e t e l y d r y . 4. C o n s t a n t - r a t e p e r i o d I n t h e f i r s t d r y i n g p e r i o d ( c o n s t a n t - r a t e ) t h e r a t e o f d r y i n g d e p e n d s e n t i r e l y o n e x t e r n a l p a r a m e t e r s s u c h a s t h e v e l o c i t y , f l o w p a t t e r n , t e m p e r a t u r e a n d h u m i d i t y o f . t h e d r y i n g a i r . D u r i n g t h i s p e r i o d , t h e r e s i s t a n c e t o i n t e r n a l t r a n s f e r o f m o i s t u r e t o t h e s u r f a c e i s . s m a l l c o m p a r e d t o th'e e x t e r n a l r e s i s t a n c e t o r e m o v a l o f m o i s t u r e f r o m t h e s u r -f a c e . H e n c e , t h e e v a p o r a t i o n r a t e o f l i q u i d a t t h e s o l i d s u r f a c e c o n t r o l s t h e d r y i n g r a t e . I f t h e e x t e r n a l c o n d i t i o n s a r e k e p t c o n s t a n t , t h e n t h e d r y i n g r a t e i n t h i s p e r i o d i s N c o n s t a n t . D u r i n g t h i s p e r i o d , t h e s o l i d h a s a c o n t i n u o u s f i l m o f l i q u i d o v e r t h e e n t i r e d r y i n g s u r f a c e . I t i s a l s o k nown t h a t i f a l l t h e h e a t f o r e v a p o r a t i o n o f w a t e r i s s u p p l i e d i n t h e d r y i n g a i r ( c o n v e c t i v e d r y i n g ) , t h e t e m p e r a -t u r e o f t h e s o l i d w i l l e q u i l i b r a t e a t o r c l o s e t o t h e w e t -10 b u l b t e m p e r a t u r e o f a i r . T h e e q u i l i b r i u m b e t w e e n h e a t t r a n s -f e r t o t h e s o l i d s u r f a c e a n d m a s s t r a n s f e r f r o m t h e s a t u r a t e d s u r f a c e o f t h e s o l i d , w h i c h e x i s t s d u r i n g t h i s p e r i o d o f d r y -i n g , c a n b e e x p r e s s e d a s f o l l o w s (7), A U A T k„AP dmx _ hAT _ g c so so a s s u m i n g no c h a n g e i n s o l i d v o l u m e d u r i n g d r y i n g , w h e r e AT = T - T ( ° F ) g s c ' T g = g a s d r y - b u l b t e m p . ( ° F ) T = s u r f a c e t e m p , d u r i n g e v a p o r a t i o n ( ° F ) AP = P • - P n ( a t m . ) s c g Pg = p a r t i a l p r e s s u r e o f w a t e r i n t h e g a s ( a t m . ) pc r • = v a p o r p r e s s u r e o f w a t e r a t T ( a t m . ) h = h e a t t r a n s f e r c o e f f i c i e n t ( B T U / f t . 2 n r . ° F ) A = l a t e n t h e a t o f v a p o r i z a t i o n ( B T U / l b m . ) k g = m a s s t r a n s f e r c o e f f i c i e n t ( l b m . / f t . h r . a t m . ) p s o = S ° 1 1 C ' d e n s i t y ( l b m . / f t . ) o f d r y wood I = h a l f t h i c k n e s s o f s o l i d ( f t . ) 2 A = s u r f a c e a r e a ( f t . ) /dm\ _ d r y i n g r a t e d u r i n g t h e c o n s t a n t - r a t e p e r i o d d8 c /Ibm. w a t e r \ M b m . b o n e - d r y wood, h r s . 11 A f t e r t h e c r i t i c a l M.C. i s r e a c h e d t h e f a l l i n g r a t e p e r i o d o f d r y i n g b e g i n s . 5. F a l l i n g - r a t e p e r i o d S i n c e t h e r e i s no l o n g e r a n y f r e e m o i s t u r e on t h e s o l i d s u r f a c e , a n a d d i t i o n a l r e s i s t a n c e t o m o i s t u r e t r a n s f e r a r i s e s , i n s i d e t h e m a t e r i a l b e i n g d r i e d . T h e d r y i n g r a t e t h e r e f o r e d e c r e a s e s a n d b e c o m e s g o v e r n e d b y t h e r a t e o f m o i s -t u r e m o v e m e n t w i t h i n t h e s o l i d . T h e i n t e r n a l m a s s t r a n s f e r r a t e d e p e n d s on t h e i n t e r n a l p h y s i c a l n a t u r e o f t h e s o l i d a n d i t s m o i s t u r e c o n t e n t . I n a d d i t i o n , t h e s o l i d s u r f a c e i s no l o n g e r a t t h e w e t b u l b t e m p e r a t u r e s , s o t h a t i t b e c o m e s n e c e s s a r y t o t a k e i n t o a c c o u n t b o t h t e m p e r a t u r e a n d m o i s t u r e c o n t e n t d i s t r i b u t i o n s w i t h i n t h e b o d y . M o s t o f t h e v a r i o u s t h e o r e t i c a l m o d e l s w h i c h h a v e b e e n p r o p o s e d f o r i n t e r p r e t a t i o n o f m o i s t u r e d i s t r i b u t i o n a n d r a t e o f m o i s t u r e m o v e m e n t i n s i d e p o r o u s s o l i d s f a l l i n t o t h e f o l l o w i n g c a t e g o r i e s : A. D i f f u s i o n t h e o r y B. C a p i l l a r y t h e o r y a n d t h e m o s t r e c e n t o n e C. M o v i n g b o u n d a r y t h e o r y . A. D i f f u s i o n t h e o r y T h i s t h e o r y , w h i c h a s s u m e s t h a t l i q u i d m o i s t u r e m o v e s t h r o u g h t h e s o l i d b o d y a s a r e s u l t o f c o n c e n t r a t i o n d r i v i n g f o r c e , was f i r s t p r o p o s e d b y S h e r w o o d ( 9 ) a n d Newman ( 1 0 ) . 1 2 T h e y u s e d F i c k ' s s e c o n d l a w o f d i f f u s i o n , w h i c h h a s a m a t h e -m a t i c a l f o r m a n a l o g o u s t o D a r c y ' s l a w a n d F o u r i e r ' s h e a t -c o n d u c t i o n l a w t o d e s c r i b e t h e r a t e o f m o i s t u r e m o v e m e n t i n s i d e t h e d r y i n g s o l i d . F i c k ' s s e c o n d l a w o f d i f f u s i o n i s w r i t t e n a s f o l l o w s : 2 dm n d m w h e r e y i s t h e t h i c k n e s s o f t h e s o l i d i n t h e d i r e c t i o n o f d i f f u s i o n a n d D i s t h e d i f f u s i o n c o e f f i c i e n t . S h e r w o o d (9) a n d Newman (10) f o u n d a c o m p l e x s o l u t i o n f o r t h i s e q u a t i o n f o r t h e d r y i n g o f a s l a b i n t h e f a l l i n g - r a t e p e r i o d . T h e a s s u m p t i o n s u s e d i n d e r i v i n g t h i s e q u a t i o n w e r e : 1 . S u r f a c e has a c o n s t a n t m o i s t u r e c o n t e n t . 2 . E v a p o r a t i o n t a k e s p l a c e a t t h e s u r f a c e . 3. T h e d i f f u s i o n c o e f f i c i e n t D i s c o n s t a n t . F o r t h e s e c o n d i t i o n s t h e s o l u t i o n o f t h e d i f f u s i o n e q u a t i o n f o r a s l a b g i v e n b y Newman (10) i s a s f o l l o w s : D6TT 2 9D9TT 2 _ 2 5 D 9 7 T 2 X = J L [ e " « * 2 + l e " 4 * 2 + ^ e " ^ ~ + ...] IT w h e r e D = d i f f u s i o n c o e f f i c i e n t I = h a l f - t h i c k n e s s 9 = t i m e X = t h e f r a c t i o n a l a m o u n t o f m o i s t u r e unremoved 1 3 C 0 0 D v a r i e s w i t h m o i s t u r e c o n t e n t a s w e l l a s w i t h t e m p e r a t u r e b u t o v e r s m a l l r a n g e s o f m o i s t u r e c o n t e n t a n d t e m p e r a t u r e , t h e a s s u m p t i o n o f c o n s t a n c y o f D i s a g o o d a p p r o x i m a t i o n , a n d i s o f t e n u s e d . F o r l o n g d r y i n g t i m e s , E q . ( 3 ) s i m p l i f i e s t o a l i m i t -i n g f o r m o f t h e d i f f u s i o n e q u a t i o n a s f o l l o w s : v 8 - D 6 I T 2 / 4 £ 2 , n VX = —j e J . I E q . ( 3 . 1 ) may b e d i f f e r e n t i a t e d t o g i v e t h e d r y i n g r a t e a s 2 dm _ . - I T D / _ \ o o _ _ _ ( m _ m J 3 . 2 rim w h e r e d r y i n g r a t e , 1 b . / ( h r . ) ( 1 b . d r y s o l i d ) . m,m .m^ a v e r a g e m o i s t u r e c o n t e n t ( d r y b a s i s ) a t . °° a n y t i m e 0, a t t h e s t a r t o f t h e f a l l i n g -r a t e p e r i o d , a n d a t t h e s u r f a c e , r e s p e c t i v e l y , l b . / l b . T h e d i f f u s i o n m o d e l h a s b e e n w i d e l y a c c e p t e d f o r d r y i n g o f p o r o u s s o l i d s . C e a g l s k e a n d H o u g e n ( 1 2 ) b e l i e v e d t h a t t h e d i f f u s i o n e q u a t i o n was a p p l i c a b l e t o t h e d r y i n g o f a s o l i d h a v i n g a f i n e u n i f o r m f i b r o u s s t r u c t u r e , s u c h as w o o d , b e c a u s e t h e c a p i l l a r y t e n s i o n , w h i c h c a u s e s t h e f l o w o f l i q u i d v a r i e s d i r e c t l y w i t h t h e d e g r e e o f s a t u r a t i o n o f t h e s o l i d . T h e y 14 s u g g e s t e d t h a t t h e m o v e m e n t o f w a t e r i n f i b r o u s m a t e r i a l s s u c h a s t e x t i l e s , w o o d , p a p e r a n d s t a r c h t a k e s p l a c e b y d i f f u s i o n r a t h e r t h a n b y g r a v i t y , c a p i 1 1 a r i t y o r e x t e r n a l p r e s s u r e . . ' * On t h e o t h e r h a n d , i t i s e v i d e n t t h a t t h e r e i s a d i f f e r -e n c e b e t w e e n t h e b o u n d w a t e r d i f f u s i o n d u r i n g d r y i n g o f w o o d a n d t h e F i e k i a n d i f f u s i o n d e s c r i b e d b y t h e d i f f u s i o n m o d e l ( 1 1 ) . I n t h e f o r m e r o n l y v e r y s m a l l t e m p e r a t u r e d e p e n d e n t p o r t i o n o f w a t e r m o l e c u l e s m i g r a t e a t a n y t i m e s ( i . e . , w a t e r m o l e c u l e s b o u n d e d t o t h e i r s o r p t i o n s i t e s m i g r a t e t o new s i t e s w h en t h e y r e c e i v e e n e r g y i n e x c e s s o f t h e b o n d i n g e n e r g y ) w h e r e a s i n t h e l a t t e r a l l w a t e r m o l e c u l e s m i g r a t e a t a l l t i m e s . T h i s l e a d s t o t h e c o n c l u s i o n t h a t s t r i c t l y s p e a k i n g F i c k ' s s e c o n d l a w d o e s n o t n e c e s s a r i l y h o l d t r u e f o r b o u n d w a t e r d i f f u s i o n . N e v e r t h e l e s s , t h e d i f f u s i o n e q u a t i o n h a s b e e n f o u n d t o g i v e r e a s o n a b l e a g r e e m e n t w i t h e x p e r i m e n t a l d a t a a n d c a n b e u s e d w i t h i n t h e l i m i t s i m p o s e d b y t h e a s s u m p t i o n s l i s t e d e a r l i e r i n t h i s s e c t i o n . B. C a p i l l a r y t h e o r y T h e c a p i l l a r y f l o w t h e o r y ( 7 , 8 , 1 3 , 1 4 , 1 5 , 1 6 ) a s s u m e s t h a t l i q u i d m o i s t u r e i n a p o r o u s s o l i d m o v e s t h r o u g h a v e r y l a r g e n u m b e r o f c a p i l l a r i e s e x t e n d i n g i n a l l d i r e c t i o n s b y l i q u i d - s o l i d m o l e c u l a r a t t r a c t i o n . I t p o s t u l a t e s t h a t d u r -i n g t h e c o n s t a n t - r a t e p e r i o d , t h e r e i s a w a t e r f i l m on t h e s o l i d s u r f a c e s i n c e t h e c a p i l l a r i e s a r e f u l l . A s w a t e r e v a p o r a t e s f r o m t h e s u r f a c e , some u n s a t u r a t e d s u r f a c e p o r t i o n s 15 a p p e a r a n d w a t e r s t a r t s t o f l o w f r o m t h e l a r g e c a p i l l a r i e s i n t o t h e s m a l l e r c a p i l l a r i e s a n d t o t h e s u r f a c e . I n t h i s w a y , some c a p i l l a r i e s a r e d r a i n e d o u t a n d m o r e d r y s u r f a c e a p p e a r s . As a r e s u l t o f t h e r e d u c e d m a s s t r a n s f e r a r e a a t t h e s u r f a c e , t h e r a t e o f d r y i n g d e c r e a s e s . F o r t h i c k s o l i d s w i t h l o n g c a p i l l a r i e s , a n i n t e r n a l f l o w r e s i s t a n c e i s a l s o p o s t u l a t e d . T h e m a i n a s s u m p t i o n s i n v o l v e d i n t h i s m o d e l a r e : 1. l i q u i d m o i s t u r e m o v e s o n l y b y c a p i l l a r y m o t i o n 2. e v a p o r a t i o n t a k e s p l a c e o n l y a t t h e s u r f a c e 3. s u r f a c e t e m p e r a t u r e e q u a l s w e t - b u l b t e m p e r a t u r e a t t h e c r i t i c a l p o i n t , a n d i n c r e a s e s up t o t h e d r y b u l b t e m p e r a t u r e a s t h e e q u i l i b r i u m M.C. i s r e a c h e d 4. e f f e c t o f m a s s t r a n s f e r o n h e a t t r a n s f e r i s n e g l i g i b l e . T h e f a l l i n g - r a t e , a s s u g g e s t e d b y P e r r y ( r e f . 7; s e e F i g . 3) c a n be e x p r e s s e d w i t h f a i r a c c u r a c y o v e r t h e r e q u i r e d r a n g e o f m o i s t u r e c o n t e n t s b y a n e q u a t i o n s i m i l a r t o E q . ( 3 . 2 ) ; t h u s w h e r e i s r e l a t e d t o t h e d r y i n g r a t e o v e r t h e c o n s t a n t -r a t e p e r i o d a s f o l l o w s : dm _ /dm d0 ^d8 f a l 1 i n g - r a t e = K,(m-m m) 4 K ( d m / d e ) c 5 16 S u b s t i t u t i n g ( d m / d e ) c f r o m E q . ( 1 ) i n t o E q : ( 5 ) , a n d p u t t i n g K-| i n t o Eq . ( 4 ) g i v e s : d e p A£ (m -m ) s c 00 T h i s t h e o r y o f m o i s t u r e m o v e m e n t c o u l d o n l y b e a p p l i c a b l e f o r l i q u i d w a t e r ( f r e e a n d c a p i l l a r y c o n d e n s e d ) moving c o n - , t i n u o u s l y i n c a p i l l a r i e s t h r o u g h f i b e r c a v i t i e s , p i t c h a m b e r s , p i t m e m b r a n e s a n d o t h e r v o i d s b y m a s s f l o w . H o w e v e r , a p a r t o f t h e b o u n d w a t e r i n w o o d i s s u r f a c e b o u n d w a t e r a n d i t s m o v e m e n t t h r o u g h c e l l w a l l s c a n n o t b e n e g l i g i b l e . , - ^ T h i s v i e w i s s u p p o r t e d b y e x p e r i m e n t a l d a t a w h i c h , i n g e n e r a l , s h o w a n o n - l i n e a r r e l a t i o n s h i p b e t w e e n d r y i n g r a t e a n d m o i s t u r e c o n t e n t ( e . g . , F i g . 2 0 ) r a t h e r t h a n t h e l i n e a r r e l a t i o n s h i p a s s u m e d i n w r i t i n g E q . ( 4 ) . C. M o v i n g b o u n d a r y m o d e l T h i s i s t h e m o s t r e c e n t m o d e l f o r i n t e r p r e t a t i o n o f m o i s t u r e d i s t r i b u t i o n i n s i d e a p o r o u s s o l i d d u r i n g d r y i n g , w i d e l y a c c e p t e d i n t h e e a s t e r n w o r l d ( 1 4 , 1 7 , 1 8 ) . T h e s o l i d i s c o n s i d e r e d t o h a v e a w e t z o n e a n d a d r y z o n e . E v a p o r a -t i o n t a k e s p l a c e a t t h e i n t e r f a c e b e t w e e n t h e w e t a n d d r y z o n e s w h i c h m o v e s i n w a r d s d u r i n g d r y i n g . A c c o r d i n g t o t h i s m o d e l , t h e i n t e r f a c e a n d t h e d r y z o n e o f f e r t h e m a i n r e s i s t -a n c e t o t h e f l o w o f m o i s t u r e , t h e r e s i s t a n c e o f t h e w e t z o n e b e i n g n e g l i g i b l e i n c o m p a r i s o n . M o i s t u r e m o v e m e n t i n t h e 17 w e t z o n e i s c o n s i d e r e d t o b e b y c a p i l l a r y m o t i o n a n d i n t h e d r y z o n e b y v a p o r d i f f u s i o n . M o r e d e t a i l e d d i s c u s s i o n o f t h i s m o d e l i s g i v e n i n S e c t i o n 2 . 2 . D. O t h e r m o d e l s I t i s i m p o r t a n t t o a d d t h a t o v e r 30 y e a r s a g o L y k o v ( c i t e d i n r e f . 13) f o u n d t h a t m o i s t u r e c a n move t h r o u g h a w e t m a t e r i a l d u e t o t e m p e r a t u r e g r a d i e n t ( k n o w n a s t h e r m o -d i f f u s i o n a l e f f e c t ) . T h i s e f f e c t a c c o r d i n g t o L y k o v was t h e r e s u l t o f t h e r m o d y n a m i c c o u p l i n g o f t h e h e a t a n d m a s s t r a n s -f e r p r o c e s s e s . V a l c h a r ( 1 9 ) s u g g e s t e d t h a t l i q u i d m o i s t u r e m o v e m e n t may b e e f f e c t e d b y c h a n g e s i n c o n c e n t r a t i o n o f v a p o r m o i s -t u r e , a s a r e s u l t o f c o u p l i n g o f h e a t a n d m a s s t r a n s f e r p r o c e s s e s . T h e r e h a v e b e e n a f e w a t t e m p t s t o g e n e r a l i z e t h e p r o -b l e m , f o r e x a m p l e b y K r i s c h e r a n d h i s s c h o o l ( 2 0 ) ( c i t e d i n r e f . 1 3 ) . T h e y w r o t e t h e d i f f e r e n t i a l m a s s a n d h e a t e q u a -t i o n s , a s s u m i n g t h a t m o i s t u r e may m o v e b y t w o m e c h a n i s m s : c a p i l l a r i t y c h a r a c t e r i z e d b y a " m o i s t u r e c o n d u c t i v i t y c o -e f f i c i e n t " a n d d i f f u s i o n c h a r a c t e r i z e d b y a " m o i s t u r e d i f f u s i -v i t y c o e f f i c i e n t " . T h e t w o m e c h a n i s m s may a c t i n s e r i e s , i n p a r a l l e l , o r i n s e r i e s a n d p a r a l l e l c o m b i n a t i o n s . T h e t w o c o e f f i c i e n t s a r e f u n c t i o n s o f t h e n a t u r e o f t h e s o l i d , i t s m o i s t u r e c o n t e n t a n d t e m p e r a t u r e , s o t h a t K r i s c h e r ' s a n a l y s i s l e a d s t o d i f f e r e n t i a l e q u a t i o n s w i t h v a r i a b l e c o e f f i c i e n t s . H e n c e , a c o m p l i c a t e d c a l c u l a t i o n p r o c e d u r e i s i n v o l v e d i n 18 d e t e r m i n i n g t h e r a t e o f i n t e r n a l m o i s t u r e t r a n s f e r . On t h e b a s i s o f K r i s c h e r ' s h y p o t h e s i s , L y k o v e t a l . ( 2 7 ) ( c i t e d i n r e f . 1 3 ) m o d i f i e d t h e i r o r i g i n a l c o n c e p t a n d a p p l i e d t h e m e t h o d s o f t h e r m o d y n a m i c s o f i r r e v e r s i b l e p r o -c e s s e s t o t h e i n t e r n a l h e a t a n d m a s s t r a n s f e r p r o c e s s e s i n d r y i n g . A c c o r d i n g t o t h e m , m o i s t u r e t r a n s f e r o c c u r s d u e t o a m o i s t u r e t r a n s f e r d r i v i n g f o r c e ( w h i c h t a k e s i n a l l p o s s i b l e m e c h a n i s m s o f m o i s t u r e t r a n s f e r ) c h a r a c t e r i z e d b y a m o i s t u r e d i f f u s i v i t y c o e f f i c i e n t , a n d d u e t o a t e m p e r a t u r e g r a d i e n t , w h i c h i s c h a r a c t e r i z e d b y a t h e r m o - g r a d i e n t c o e f f i c i e n t . V a l u e s o f b o t h t h e c o e f f i c i e n t s a r e d e p e n d e n t o n m o i s t u r e c o n t e n t a n d t e m p e r a t u r e , a s w e l l a s o n t h e n a t u r e o f s o l i d . ' I t s h o u l d b e n o t e d t h a t i n t h i s a p p r o a c h t h e L y k o v " m o i s t u r e d i f f u s i v i t y " a t t e m p t s t o i n c l u d e b o t h o f K r i s c h e r ' s c o -e f f i c i e n t s i n o n e p a r a m e t e r b y u s i n g a g e n e r a l i z e d d r i v i n g f o r c e i n s t e a d o f t w o s e p a r a t e d r i v i n g f o r c e s ( d i f f u s i o n a l a n d c a p i 1 1 a r y ) . A l t h o u g h t h e c o n c e p t o f m o i s t u r e m o v e m e n t o c c u r r i n g s i m u l t a n e o u s l y b y o n e o r m o r e m e c h a n i s m s i s v e r y r e a l i s t i c , t h e m a t h e m a t i c s i n v o l v e d b e c o m e s v e r y c o m p l e x a n d t h e r e f o r e s u c h m o d e l s h a v e n o t b e e n a p p l i e d i n p r a c t i c e . 2.2 F l u i d i z e d B e d D r y i n g 1 . D r y i ng o f w o o d T h e u s e o f f l u i d i z e d b e d s o f i n e r t p a r t i c l e s t o d r y w o o d i s a r e l a t i v e l y new c o n c e p t . L o o s ( 1 ) d r i e d g r e e n p i n e v e n e e r 19 i n f l u i d i z e d b e d s o f s a n d a n d C e r a s p h e r e s ( h o l l o w c e r a m i c s p h e r e s -10 +30 m e s h ) , u s i n g t w o v e n e e r t h i c k n e s s e s ( 1 / 1 0 i n c h a n d 3/16 i n c h ) , t h r e e b e d t e m p e r a t u r e s ( 2 5 0 , 3 2 5 , a n d 4 0 0 ° F ) a n d t w o a i r v e l o c i t i e s ( 3 0 a n d 60 c f m ) . T h e s h o r t e s t d r y i n g t i m e t o r e a c h 5% M . C , s t a r t i n g f r o m 1 0 7 . 3 % M.C. was f o u n d t o b e 1 3/4 m i n u t e s f o r t h e t h i c k e r v e n e e r . T h e m a x i -mum d r y i n g r a t e s o b t a i n e d w e r e t h r e e t i m e s f a s t e r w i t h s a n d b e d s a n d t w o t i m e s f a s t e r w i t h C e r a s p h e r e b e d s t h a n t h o s e f o r a j e t d r i e r a t t h e s a m e t e m p e r a t u r e . I n c r e a s i n g t h e b e d t e m p e r a t u r e h a d t h e g r e a t e s t e f f e c t o n d r y i n g r a t e . A i r f l o w r a t e h a d a n e f f e c t o n d r y i n g r a t e o n l y a t l o w b e d t e m p e r a t u r e s a n d w i t h t h e s l o w e r d r y i n g r a t e m e d i u m ( C e r a -s p h e r e s ) , b u t h a d n e g l i g i b l e e f f e c t a t h i g h e r t e m p e r a t u r e s a n d w i t h s a n d b e d s . B a b a i l o v a n d P e t r i ( 2 ) h a v e r e c e n t l y r e p o r t e d s i m i l a r w o r k o n d r y i n g o f p e e l e d v e n e e r o f t h i c k n e s s e s 1.9 mm, 1.45 mm, 1.1 mm i n c h a n d 0 . 6 5 mm, i n a f l u i d i z e d b e d o f m e t a l -l u r g i c a l s l a g ( p a r t i c l e s i z e , 0 . 5 1 5 - 1 . 1 2 5 mm), f r o m 8 0 % M.C. t o 6% M.C. a t s e v e r a l t e m p e r a t u r e s a n d a i r v e l o c i t i e s . T h e y f o u n d t h a t t h e d r y i n g t i m e f o r 1.45 mm t h i c k v e n e e r d e c r e a s e d b y a f a c t o r o f 6.5 as t h e b e d t e m p e r a t u r e i n c r e a s e d f r o m 105 t o 2 8 0 ° C ; h o w e v e r , f o r b e d t e m p e r a t u r e i n c r e a s e f r o m 2 6 0 ° C t o 2 8 0 ° C , t h e d r y i n g t i m e d e c r e a s e d v e r y l i t t l e . T h e y a l s o f o u n d t h a t t h e v e l o c i t y o f g a s d i d n o t p l a y a n i m p o r t a n t r o l e i n v e n e e r d r y i n g . B a b i l o v a n d P e t r i r e p o r t e d t h e f o l l o w i n g l i n e a r r e l a t i o n s h i p b e t w e e n d r y i n g t i m e ( T ) a n d t h e t h i c k n e s s o f v e n e e r ( S . , ) : 20 x = k-| S-j - b i 7 w h e r e c o e f f i c i e n t s a n d b^ a r e b e d t e m p e r a t u r e ( T ) d e p e n d e n t k 1 = 1.98 x 1 0 7 x t " 2 , 6 3 + 7 . 7 8 8 b 1 = 1 1 . 9 x 1 0 7 x t ~ 3 , 2 9 + 1 .41 9 w h e r e S-j i s i n m i l l i m e t e r s , t i n d e g r e e s c e n t i g r a d e a n d x i s i n s e c o n d s . F r o m a c o m p a r i s o n b e t w e e n f l u i d i z e d b e d d r y e r s a n d o t h e r t y p e s o f d r y e r s ( c o n v e c t i v e d r y e r , c o n t a c t d r y e r a n d r o t a r y d r y e r ) , B a b a i l o v a n d P e t r i s h o w e d t h a t d r y i n g t i m e i n t h e f l u i d i z e d b e d i s much s h o r t e r . A m a t h e m a t i c a l m o d e l f o r c a l c u l a t i n g t h e r a t e o f v e n e e r o r w o o d d r y i n g i n a f l u i d i z e d b e d h a s b e e n p r e s e n t e d b y Wen a n d L o o s ( 2 2 ) . T h e s y m b o l s u s e d i n t h i s m o d e l a n d t h e i r p h y s i c a l r e l a t i o n s h i p t o t h e d r y i n g v e n e e r a r e s h o w n i n F i g . ( 4 ) . 21 FLUIDIZED BED DRYING MODEL Fig.4 OF WEN AND LOOS d s d s = b e d t e m p e r a t u r e ( ° F ) = s u r f a c e t e m p e r a t u r e o f d r y l a y e r ( ° F ) = t e m p e r a t u r e o f i n t e r f a c e b e t w e e n w e t a n d d r y l a y e r s ( ° F ) = v a p o r p r e s s u r e o f w a t e r i n b e d ( a t m . ) = v a p o r p r e s s u r e o f w a t e r a t T j s ( a t m . ) P.p = v a p o r p r e s s u r e o f w a t e r a t i n t e r f a c e ( a t m . ) L, = t h i c k n e s s o f w o o d ( f e e t ) AL, = t h i c k n e s s o f d r y l a y e r ( f e e t ) . 22 F r o m h e a t t r a n s f e r e q u a t i o n <• - h<VTds»= fe<Tds-Tf> a n d m a s s t r a n s f e r e q u a t i o n t h e y d e r i v e d 8D M n • - D a n d 8ksi ,T T w 6 * 4 ksi ( 1 - x ) = I F 7 t ( W ^ ' - r , 10 Nw - y v v -"Uf- • T U T * , 1 1 12 13 2 w h e r e q = f l u x o f h e a t t r a n s f e r , B T U / ( f t . ) ( h r . ) T = a v e r a g e t e m p e r a t u r e i n t h e w o o d , ° F h = h e a t t r a n s f e r c o e f f i c i e n t a c r o s s g a s f i l m , B T U / ( h r . ) ( f t . 2 ) ( ° F ) k = e f f e c t i v e t h e r m a l c o n d u c t i v i t y o f w o o d , S 1 B T U / ( h r . ) ( f t . ) ( ° F ) k = m a s s t r a n s f e r c o e f f i c i e n t a c r o s s g a s f i l m , 9 1 l b . m o l e s / ( h r . ) ( f t . 2 ) ( a t m . ) D = e f f e c t i v e d i f f u s i v i t y o f w a t e r v a p o r t h r o u g h d r y w o o d l a y e r , f t . 2 / h r . 23 R = g a s c o n s t a n t , ( a t m . ) ( f t . 6 ) I ( 1 b . m o l e s ) ( ° F ) X = f r a c t i o n o f w a t e r r e m a i n i n g i n w o o d A = l a t e n t h e a t o f v a p o r i z a t i o n o f w a t e r , B T U / l b . M, = m o l e c u l a r w t . o f w a t e r , l b s . w p = i n i t i a l w t . o f w a t e r p e r u n i t v o l . o f wood, l b m . / f t . w 6 = t i m e , h r s . ' 0 P l o t s o f 1-X v s . u s i n g e x p e r i m e n t a l d a t a a t a b e d t e m p e r a t u r e o f 2 5 0 ° F g a v e s t r a i g h t l i n e s a n d w e r e u s e d t o c a l c u l a t e k , ,D , h , a n d k . a s s u m i n g i n E q . ( 1 3 ) t o b e s i ' e g i J f n t h e b o i l i n g p o i n t o f w a t e r ( 2 1 2 ° F ) a n d P f i n E q . ( 1 2 ) t o b e o n e a t m o s p h e r e . H o w e v e r , a t b e d t e m p e r a t u r e s o f 3 0 0 ° F a n d a b o v e , t h e p l o t s d i d n o t g i v e s t r a i g h t l i n e s , a n d t h e d a t a s h o w e d t h e r a t e o f d r y i n g a b o v e 2 5 0 ° F t o b e a w e a k e r f u n c t i o n o f b e d t e m p e r a t u r e t h a n i n d i c a t e d b y E q . ( 1 2 ) . T h e a s s u m p -t i o n t h a t t h e t e m p e r a t u r e a t t h e i n t e r f a c e b e t w e e n t h e d r y a n d w e t l a y e r s i s t h e b o i l i n g t e m p e r a t u r e o f w a t e r i s a n a r b i t r a r y o n e a n d a p p a r e n t l y b e c o m e s i n v a l i d a t h i g h b e d t e m p e r a t u r e s . I t w o u l d a l s o n o t a p p l y a t b e d t e m p e r a t u r e s l o w e r t h a n 2 1 2 ° F . A m o r e r e a s o n a b l e a s s u m p t i o n f o r T ^ w o u l d a p p e a r t o b e t h e w e t b u l b t e m p e r a t u r e . H o w e v e r , p l o t s o f 1-X v s . 6/1-X u s i n g e x p e r i m e n t a l d a t a o b t a i n e d i n t h i s w o r k 1 d i d n o t g i v e s t r a i g h t l i n e s . T h e m o d e l d e s c r i b e d a b o v e i s t h e r e f o r e c o n s i d e r e d t o be o f l i m i t e d v a l i d i t y . 24 2. H e a t t r a n s f e r b e t w e e n a f l u i d i z e d b e d a n d a s u b m e r g e d o b j e c t H e a t t r a n s f e r b e t w e e n a f l u i d i z e d b e d a n d a s u r f a c e i n c o n t a c t w i t h i t i s much m o r e r a p i d t h a n i n s i n g l e - p h a s e g a s f l o w , o r i n a f i x e d b e d . B e d - t o - o b j e c t h e a t t r a n s f e r c o e f f i c i e n t s i n g a s f l u i d i z e d b e d s h a v e b e e n f o u n d t o b e 20 t o 40 t i m e s t h o s e f o r g a s e s a l o n e ( 5 , 3 ) . P o s s i b l e e x p l a n a -t i o n s f o r g o o d h e a t t r a n s f e r i n f l u i d i z e d b e d s h a v e b e e n s u m m a r i z e d b y Z i e g l e r e t a l . ( 5 ) a s f o l l o w s : 1. T h e i n c r e a s e i n h e a t t r a n s f e r i s a c o n s e q u e n c e o f t h e s c r u b b i n g a c t i o n o f p a r t i c l e s a g a i n s t t h e t r a n s -f e r s u r f a c e . T h i s a c t i o n d i s t u r b s t h e g a s f i l m , d e c r e a s e s i t s r e s i s t a n c e t o t h e f l o w o f h e a t a n d s o i n c r e a s e s h e a t t r a n s f e r c o e f f i c i e n t ( 2 3 , 2 4 , 2 5 ) . 2. F l u i d i z e d p a r t i c l e s m o v e i n p o c k e t s f r o m t h e c o r e o f t h e b e d t o t h e h e a t t r a n s f e r s u r f a c e , a b s o r b i n g o r g i v i n g up h e a t b y u n s t e a d y s t a t e c o n d u c t i o n a n d r e t u r n i n g t o t h e c o r e o f t h e b e d ( 2 7 , 2 8 ) . T h e g a s s e r v e s a s a s t i r r i n g a g e n t a n d a l s o a s a h e a t t r a n s f e r m e d i u m b e t w e e n t h e p a r t i c l e s a n d t h e s u r -f a c e . T h e p r e s e n c e o f t h e f l u i d i z e d p a r t i c l e s c a u s e s t h e h e a t c a p a c i t y o f t h e p o c k e t s t o b e h i g h t h e r e b y g i v i n g f a s t e r h e a t t r a n s f e r t h a n w i t h a g a s a l o n e . S e v e r a l e q u a t i o n s f o r c a l c u l a t i n g h e a t t r a n s f e r c o -e f f i c i e n t s p r o p o s e d b y d i f f e r e n t i n v e s t i g a t o r s , a r e g i v e n i n t h e b o o k b y K u n i i a n d L e v e n s p i e l ( 3 , p . 2 6 8 ) . C H A P T E R 3 T H E O R E T I C A L A N A L Y S I S OF D R Y I N G IN F A L L I N G - R A T E P E R I O D 3.1 D e f i n i t i o n o f t h e P r o b l e m T h e p r o b l e m i s t o f o r m u l a t e a m a t h e m a t i c a l m o d e l f o r d r y i n g i n t h e f a l l i n g - r a t e p e r i o d w h i c h c a n b e u s e d t o p r e -d i c t d i s t r i b u t i o n o f m o i s t u r e a n d t e m p e r a t u r e i n s i d e t h e w o o d d u r i n g d r y i n g w i t h a f i n i t e e x t e r n a l r e s i s t a n c e t o h e a t a n d m a s s t r a n s f e r . T h e m o d e l w i l l b e r e s t r i c t e d t o t h e d r y i n g o f a u n i f o r m l y w e t s l a b o f w o o d w i t h h e a t a n d m a s s t r a n s f e r o c c u r r i n g i n o n e d i m e n s i o n a n d i n t w o d i m e n s i o n s . 3.2 S e l e c t i o n o f a M o d e l T h e v a r i o u s m o d e l s f o r m o i s t u r e t r a n s f e r i n s i d e w e t b o d i e s d i s c u s s e d i n t h e p r e v i o u s s e c t i o n s w e r e e x a m i n e d , a n d t h e l i q u i d d i f f u s i o n m o d e l was s e l e c t e d f o r t h e f o l l o w i n g r e a s o n s : 1. T h e c a p i l l a r y t h e o r y o f m o i s t u r e m o v e m e n t i s a p p l i c -a b l e o n l y t o t h a t f r a c t i o n o f w a t e r w h i c h m o v e s t h r o u g h c a p i l l a r i e s b y m a s s f l o w ( f r e e a n d c a p i l l -a r y c o n d e n s e d w a t e r ) b u t n o t t o s u r f a c e b o u n d m o i s -t u r e w h o s e m o v e m e n t b y m o l e c u l a r d i f f u s i o n c a n n o t b e n e g l i g i b l e , e s p e c i a l l y a t l o w m o i s t u r e c o n t e n t s . 2. T h e m o v i n g b o u n d a r y m o d e l a s s u m e s t h a t t h e t e m p e r a -25 t u r e a t t h e i n t e r f a c e b e t w e e n t h e d r y a n d w e t z o n e s i s t h e b o i l i n g t e m p e r a t u r e o f w a t e r . T h i s i s a n a r b i t r a r y a s s u m p t i o n a n d a p p a r e n t l y b e c o m e s i n v a l i d a t b e d t e m p e r a t u r e s h i g h e r t h a n , a s w e l l a s l o w e r t h a n , 2 1 2 ° F . A m o r e r e a s o n a b l e a s s u m p t i o n f o r t h e i n t e r f a c e t e m p e r a t u r e w o u l d a p p e a r t o be t h e w e t b u l b t e m p e r a t u r e , b u t p l o t s o f ( 1 - X ) v s . 0 / ( 1 - X ) u s i n g t h e e x p e r i m e n t a l d a t a o b t a i n e d i n t h i s w o r k d i d n o t g i v e t h e e x p e c t e d s t r a i g h t l i n e . T h i s m o d e l i s t h e r e f o r e c o n s i d e r e d t o b e o f l i m i t e d v a l i d i t y . B e s i d e s , t h e c o n c e p t o f h a v i n g a c o m p l e t e l y d r y z o n e a n d a w e t z o n e d o e s n o t s e e m t o b e r e a l i s t i c . 3. T h e d i f f u s i o n m o d e l on t h e o t h e r h a n d o f f e r s a m o r e r e a s o n a b l e m e c h a n i s m f o r t h e m o v e m e n t o f b o u n d w a t e r d u r i n g d r y i n g , a n d i s a m e n a b l e t o m a t h e -m a t i c a l a n a l y s i s . I t h a s , t h e r e f o r e , r e c e i v e d a c c e p t a n c e i n t h e l i t e r a t u r e ( 7 ) . S h e r w o o d ( 9 ) a n d Newman ( 1 0 ) h a v e t h o r o u g h l y i n v e s t i -g a t e d t h e p r o b l e m o f d i f f u s i o n i n p o r o u s s o l i d s w h e n t h e m a s s t r a n s f e r c o e f f i c i e n t t h r o u g h t h e g a s f i l m i s i n f i n i t e ( i . e . , z e r o s u r f a c e r e s i s t a n c e t o m a s s t r a n s f e r ) . I n t h e a n a l y s i s p r e s e n t e d h e r e , t h e i r s o l u t i o n s a r e e x t e n d e d t o i n c l u d e t h e m o r e g e n e r a l b o u n d a r y c o n d i t i o n w h e r e t h e s u r f a c e m a s s t r a n s -f e r c o e f f i c i e n t i s f i n i t e . I n a d d i t i o n , t h e t h e o r y d e v e l o p e d i s c a p a b l e o f y i e l d i n g t h e d i s t r i b u t i o n o f m o i s t u r e w i t h i n t h e s o l i d a s a f u n c t i o n o f t i m e , w h i l e Newman's d i f f u s i o n m o d e l p r o v i d e s o n l y a v e r a g e v a l u e s o f m o i s t u r e c o n t e n t o f 27 w o o d d u r i n g d r y i n g . 3.3 A s s u m p t i o n s 1. T h e e f f e c t i v e d i f f u s i v i t y D a n d t h e r m a l d i f f u s i -- v i t y a a r e a s s u m e d t o r e m a i n c o n s t a n t d u r i n g t h e c o u r s e o f a d r y i n g r u n . 2. L i q u i d e v a p o r a t e s o n l y f r o m t h e s u r f a c e . 3. T h e s u r r o u n d i n g a i r i s d r y ( m b - 0 ) . 4. T h e s o c a l l e d " r a d i a t i o n " b o u n d a r y c o n d i t i o n e x i s t s ( 3 0 ) . T h i s b o u n d a r y c o n d i t i o n d e s c r i b e s t h e s i t u a -t i o n w h e r e t h e f l u x o f h e a t o r m a s s a c r o s s t h e s u r -f a c e i s p r o p o r t i o n a l t o t h e t e m p e r a t u r e o r p a r t i a l p r e s s u r e g r a d i e n t s b e t w e e n t h e s u r f a c e a n d t h e s u r r o u n d i n g m e d i u m ( i . e . , f i n i t e s u r f a c e r e s i s t a n c e t o h e a t a n d m a s s t r a n s f e r ) . 3.4 T h e o r e t i c a l A n a l y s i s I n t h e f o l l o w i n g a n a l y s i s , t h e d r y i n g o f a b l o c k o f w o o d i s t r e a t e d a s a t w o - d i m e n s i o n a l p r o b l e m , a s s u m i n g t h a t t e m p e r a t u r e a n d m o i s t u r e g r a d i e n t s i n t h e x - d i r e c t i o n ( a l o n g t h e g r a i n ) ( s e e F i g . 5) c a n b e n e g l e c t e d . T h i s a s s u m p t i o n i s v a l i d f o r d r y i n g o f a l o n g p i e c e o f l u m b e r ( 2 " x 4 " x l 2 " ) , a n d was s a t i s f i e d i n t h e e x p e r i m e n t a l w o r k b y i n s u l a t i n g t h e t w o e n d s o f t h e b l o c k f o r b o t h h e a t a n d m a s s t r a n s f e r . N o t e t h a t y d i r e c t i o n i s a r a d i a l d i r e c t i o n ( a c r o s s t h e g r o w t h z o n e s ) a n d z i s a t a n g e n t i a l d i r e c t i o n ( p a r a l l e l 28 F ie .5 GEOMETRY OF BLOCK t o t h e g r o w t h z o n e s ) . When a b l o c k o f w e t w o o d i s s u b j e c t e d t o c o n v e c t i v e t h e r m a l d r y i n g , two p r o c e s s e s o c c u r s i m u l t a n e o u s l y , 1. T r a n s f e r o f h e a t t o t h e s u r f a c e b y c o n v e c t i o n a n d t h e n i n t o t h e i n t e r i o r o f t h e b l o c k b y c o n d u c t i o n . 2. T r a n s f e r o f m a s s a s l i q u i d f r o m t h e i n t e r i o r t o t h e s u r f a c e b y d i f f u s i o n a n d a s v a p o r f r o m t h e s u r -f a c e t o t h e s u r r o u n d i n g s b y c o n v e c t i o n . 1. H e a t t r a n s f e r An e l e m e n t a r y h e a t b a l a n c e i n s i d e t h e b l o c k g i v e s : 2 9 i i 36 w h e r e a = ( s u b s c r i p t s r e f e r s t o s o l i d p r o p e r t i e s ) 2 - ( T b - T ) T = jj—T—r ' d i m e n s i o n l e s s t e m p e r a t u r e 3 u b ~ V k g = t h e r m a l c o n d u c t i v i t y ( B T U / f t . h r . ° F ) , a s s u m e d c o n s t a n t C p s = s p e c i f i c h e a t ( B T U / l b m . ° F ) P s 0 = d e n s i t y (1 bm . / f t . 3 ) o f d r y wood T = t e m p e r a t u r e a t a n y p o i n t i n s i d e b l o c k ( ° F ) T b = t e m p e r a t u r e o f f l u i d i z e d b e d ( ° F ) T Q = i n i t i a l t e m p e r a t u r e o f b l o c k ( ° F ) a t t h e b e g i n n i n g o f t h e f a l l i n g - r a t e p e r i o d , assumed c o n s t a n t t h r o u g h o u t t h e b l o c k 8 = t i m e ( h o u r s ) o a = t h e r m a l d i f f u s i v i t y ( f t . / h r . ) , . ( a v e r a g e v a l u e o v e r t h e d r y i n g p e r i o d ) . E q u a t i o n (1) m u s t s a t i s f y t h e f o l l o w i n g i n i t i a l a n d b o u n d a r y c o n d i t i o n s . ilhi t i a l . c o n d ' i t i on 6 = 0 , f o r a l l y , z : T = T n o r T = 1 4 30 F i n a l c o n d i t i o n 6 °°, f o r a l l y , z : T -*• o r T •*• 0 B o u n d a r y ^ c o n d i t i o n s • . B > .0, y = Jt. - L < Z < L: ks l y - A % > l y = « T „ - T . ) w h e r e A = l a t e n t h e a t o f v a p o r i z a t i o n o f w a t e r ( B T U / l b m . ) m = m a s s o f w a t e r / m a s s o f d r y w o o d ( l b m . / l b m . ) p h = e x t e r n a l h e a t t r a n s f e r c o e f f i c i e n t ( B T U / f t . h r . ° F ) D = d i f f u s i v i t y o f w a t e r i n w o o d ( a v e r a g e v a l u e o v e r t h e d r y i n g p e r i o d ) ( f t . 2 / h r . ) . L e t M = w h e r e mg ( a s s u m e d c o n s t a n t t h r o u g h o u t t h e b l o c k ) a n d mro a r e t h e m o i s t u r e c o n t e n t s o f t h e w o o d a t 9 = 0, ( a t t h e b e g i n n i n g o f t h e f a l l i n g - r a t e p e r i o d ) and e •+ », r e s p e c t i v e l y . S u b s t i t u t i o n from Eqs. (3.) and (7) i n t o Eq. (6) g i v e s - M W & " ADPso'm0-"-> l y " » « ( T B - T 0 ) T 8 o r 31 3T A D p s o ( m Q - m ° o ) SM , _ h _ ^ P u t t i ng ADp (m^-iTi ) so 0 00 v_  B a 1 Q a n d f = b 11 K s i n E q . ( 9 ) , g i v e s 9 T a ' ! 4 "bT 12 ay sy T h e b o u n d a r y c o n d i t i o n s f o r t h e o t h e r t h r e e s u r f a c e s c a n b e f o u n d i n a s i m i l a r m a n n e r . T h u s f o r 6 > 0, y = -Jl, a n d - L < Z < L + I I + A |H = b T 13 • ay ay F o r 6 > 0, z = L , a n d -Jl < y < £ , aT a aM _ h T " a T " a a T " b T 14 32 F o r 6 > 0, z = - L , a n d -I < y < J l , , 3T . a 3M _ h T • 1 R 2. M a s s t r a n s f e r A s i m p l e m a t e r i a l b a l a n c e o n a n e l e m e n t i n s i d e t h e b l o c k g i v e s -8 9 3 y 2 3 z 2 T h e i n i t i a l , f i n a l , and boundary c o n d i t i o n s a r e : 6 = 0 , f o r a l l y , z : M = 1 17 ( 6 -> °°, f o r a l l y , z : M -*• 0 ) 18 F o r 6 > 0, y = l% - L < Z < L - Dp = k (P -P. ) 19 s 0 3 y g x s b w h e r e k = e x t e r n a l m a s s t r a n s f e r c o e f f i c i e n t ( l b m . / f t . 9 h r . a t m . ) 2 P = p a r t i a l p r e s s u r e o f w a t e r v a p o r a t t h e s u r f a c e ( a t m . ) P. = p a r t i a l p r e s s u r e o f w a t e r v a p o r i n t h e b e d ( a t m . ) 33 I f we a s s u m e t h a t t h e w a t e r v a p o r c o n c e n t r a t i o n i n t h e s u r r o u n d i n g i s z e r o , i . e . , P b = 0, a n d t h e p a r t i a l p r e s ^ s u r e o f w a t e r v a p o r a t t h e s u r f a c e i s g i v e n b y P = P -S" 1-m 20 s v p s w h e r e P y p i s t h e v a p o r p r e s s u r e a t th.e s u r f a c e , a n d S i s t h e s l o p e o f t h e d e s o r p t i o n i s o t h e r m c u r v e f o r W e s t e r n H e m l o c k ( F i g . 6 ) r e p r e s e n t i n g t h e r e l a t i o n s h i p b e t w e e n m o i s t u r e c o n -t e n t {%) a n d r e l a t i v e h u m i d i t y ( % ) , t h e b o u n d a r y c o n d i t i o n ( i . e . , E q . ( 1 9 ) ) b e c o m e s : D p s K - ^ - f y = k g p v P s " 1 { ( m o - m ~ ) M + m ~ } 2 1 H o w e v e r , s i n c e rn - 0, E q . ( 2 1 ) b e c o m e s k P <;" 1 M = g VP . M 22 ^ D P S 0 L e t t i ng k P s " ^  9 V = C 23 °Pso E q . ( 2 2 ) b e c o m e s 24 i g 6 ADSORPTION AND DESORPTION ISOTHERMS AT f o r w e s t e r n h e m l o c k (ref 30) t 1 1 1 0 245°F 1 1 1 1 1 1 f*. 5.0 30.0 40J0 50.0 60.0 70.0 80-0 90.0 r e l a t i v e h u m i d i t y (%) 34 30X 35 In a s i m i l a r way, f o r 9 > 0 , y = -I, -L < Z < L + § = CM 25 f o r 9 > 0 , z ' = L , ' - A < y < A 9M_ 9z = CM 26 f o r 9 > 0 , z = - L , -SL < y < I + I T = CM _ 27 a Z 3.5 S o l u t i o n of the Mass and Heat T r a n s f e r E q u a t i o n s The mass t r a n s f e r boundary c o n d i t i o n s r e p r e s e n t e d by E q . ' s ( 2 4 ) , ( 2 5 ) , (26) and (27) a re i ndependen t o f t e m p e r a -t u r e , hence i t i s a p p r o p r i a t e to s o l v e the mass t r a n s f e r e q u a t i o n s f i r s t . The e q u a t i o n s a re l i n e a r and can t h e r e f o r e be s o l v e d by s e p a r a t i o n o f v a r i a b l e s ( 39 , p. 3 6 3 ) . 1. Mass t r a n s f e r L e t us assume t h a t the s o l u t i o n o f Eq. (16) i s o f the f o rm: M = ^ 1 ( 6 ) ^ 2 ( y ) i p 3 ( z ) 28 i . e . , the i n d e p e n d e n t v a r i a b l e s can be s e p a r a t e d , ty^ , ij^, ^ 36 b e i n g f u n c t i o n s o f 9 , y , z , r e s p e c t i v e l y . S u b s t i t u t i n g ( 1 6 ) i n t o ( 2 8 ) a n d r e a r r a n g i n g g i v e s : l = D { ^ _ + 29 i p 1 \l>2 i>3 T h e l e f t h a n d s i d e ( L H S ) i s o n l y a f u n c t i o n o f 9 w h e r e a s t h e r i g h t h a n d s i d e ( R H S ) i s a f u n c t i o n o f y a n d z . T h i s c o n d i t i o n c a n o n l y be m e t i f - j — — = D { ~ - + ——} = c o n s t a n t 30 * 1 ^2 *3 2 L e t t h e c o n s t a n t b e d e n o t e d b y -DX s o t h a t : V 2 a n d _ i _ + - ± - = . x d .32 ^2 ^3 T h e s o l u t i o n o f E q . ( 3 1 ) i s *-| - e 33 37 o m i t t i n g t h e c o n s t a n t o f i n t e g r a t i o n m u l t i p l y i n g t h e RHS o f E q . ( 3 3 ) . F r o m E q . ( 3 2 ) we h a v e V V 2 L = _ . A.. _ \ 34 *2 *3 O n c e a g a i n t h e LHS a n d RHS o f E q . ( 3 4 ) a r e f u n c t i o n s o f d i f f e r e n t i n d e p e n d e n t v a r i a b l e s s o t h a t V 2 T ^ - = - 3 35 *2 a n d V 2 2 j i T - - X = - 3^ 36 v 3 T h e g e n e r a l s o l u t i o n o f E q . ( 3 5 ) i s ^ 2 = A ' s i n ( 3 y ) + B ' c o s ( 3 y ) 37 w h e r e A 1 a n d B' a r e c o n s t a n t s o f i n t e g r a t i o n . I f we r e w r i t e E q . ( 3 6 ) i s + ( X 2 - 3 2 ) ^ 3 = 0 38 38 a n d p u t In2 = x2 - s2 3 8 . 1 t h e n , t h e g e n e r a l s o l u t i o n o f E q . ( 3 8 ) i s ,i|>3 = A " s 1 n ( - n z ) + B " c o s ( f i z ) 39 w h e r e A" a n d B" a r e c o n s t a n t s o f i n t e g r a t i o n . F r o m s y m m e t r y y = 0 9M/9y = 0 9^ 2 /9y = 0 .*. A' = z = 0 9M/9z = 0 9^ 3 /9z = 0 .*. A" = 0 40 H e n c e , E q s . ( 3 7 ) a n d ( 3 9 ) b e c o m e \\>2 = B ' c o s ( B y ) \\>3 = B " c o s ( f i z ) E q . ( 2 8 ) t h e r e f o r e b e c o m e s 41 42 M = B e " D x 2 e c o s ( B y ) c o s ( Qz) 43 39 w h e r e B = c o n s t a n t o f i n t e g r a t i o n = B ' - B " D = d i f f u s i v i t y B, fi, a n d X a r e e i g e n v a l u e s . T o f i n d t h e c o n s t a n t 3, s u b s t i t u t e E q . ( 4 3 ) i n t o E q ( 2 4 ) 2 2 + B e " D X 9 e s i n ( 3 £ ) c o s ( f i z ) = C B e " D X 9 c o s ( B & ) c o s ( f i z ) 44 o r 3 t a n ( B J l ) = C 4 5 T h i s e q u a t i o n h a s a n i n f i n i t e n u m b e r o f s o l u t i o n s f o r 3. L e t us d e n o t e t h e m b y 6 , w h e r e n i s a n i n t e g e r . H e n c e E q . ( 4 5 ) c a n b e w r i t t e n a s : 3 n t a n ( 3 n £ ) = C 45.1 N o t e t h a t s u b s t i t u t i o n f r o m E q . ( 4 3 ) i n t o E q . ( 2 5 ) l e a d s a l s o t o E q . ( 4 5 ) . By a s i m i l a r m e t h o d we f i n d fi t a n ( f i L ) = C 46 w i t h fi a s s o l u t i o n s w h e r e m i s a n i n t e g e r o r m 40 ^ t a n ( f i L) = C 46.1 E q s . ( 4 5 . 1 ) a n d ( 4 6 . 1 ) c a n be s o l v e d n u m e r i c a l l y f o r 8 n a n d ft , w h i c h a r e e i g e n v a l u e s a s d e f i n e d by e q u a t i o n s ( 4 5 . 1 ) a n d ( 4 6 . 1 ) , r e s p e c t i v e l y . I t f o l l o w s f r o m E q . ( 3 8 . 1 ) t h a t We t h e r e f o r e h a v e a s a p a r t i c u l a r s o l u t i o n o f E q . ( 1 6 ) -DX 2 e M = B m e c o s ( 3 n y ) c o s ( f t m z ) 48 a n d a s t h e g e n e r a l t w o - d i m e n s i o n a l s o l u t i o n oo oo -DX 2 e M = I I B e c o s ( 3 v ) c o s ( f t z ) 49 m=l n = l m n n m w h e r e B m n = B - B n 50 mn m n E q . ( 4 9 ) may b e r e w r i t t e n a s f o l l o w s 2 2 -D3 e 0 0 -Dft 9 M ( e , y , z ) = £ B e n c o s ( 3 n y ) I B e m c o s ( y ) 51 n = l n n m = l 01 m 41 N o t e t h a t o n l y p o s i t i v e v a l u e s o f 3 n a n d Qm n e e d b e c o n -s i d e r e d s i n c e n e g a t i v e v a l u e s g i v e d e p e n d e n t p a r t i c u l a r s o l u t i o n s . T h e a v e r a g e m o i s t u r e c o n t e n t o f t h e b l o c k . o f w o o d i s : L I M A V ( 6 ) = / / M ( 6 , y , z ) d y d z / 4 £ L 52 - L - £ I n t e g r a t i o n o f E q . ( 5 1 ) a n d s u b s t i t u t i o n o f t h e r e s u l t i n E q . ( 5 2 ) y i e l d s : °° B n -3 2De °° B m - f t m 2 D 9 M A V ( 9 ) = I rk~ e s i n ( B / ) I T J - e s 1 n ( O L ) 53 A V n = l ^ n n m=l L m m T h e c o e f f i c i e n t s B a n d B o n t h e r i g h t h a n d s i d e o f m n 3 E q . ( 5 1 ) a r e f o u n d b y s u b s t i t u t i n g E q . ( 5 1 ) i n t o t h e i n i t i a l c o n d i t i o n E q u a t i o n 1 7 , 1 = I B n c o s ( 3 n y ) I B m c o s ( Q m z ) 54 n = l m=l I M u l t i p l y i n g b o t h s i d e s o f E q . ( 5 4 ) b y / c o s ( B J . y ) d y , we 0 h a v e oo / c o s t l y ) = I B m B n c o s ( Q m z ) • / c o s ( 3 j y ) c o s ( 3 n y ) d y 56 n m = 1 A 42 From s t a n d a r d o r t h o g o n a l i t y p r o c e d u r e (39) j c o s ( 3 n y ) c o s ( B j y ) d y = 0, w h e n n f j , 5 7 0 t h e r e f o r e , n = j . I n t e g r a t i o n o f E q . ( 5 6 ) g i v e s f7 = B B I B m c o s ( f t z ) 58 n mti m m m= 1 w h e r e F = s i n ( 3 n £ ) / 3 n a n d „ s i n ( 2 B A) B = { l + 4 3 n } 5 9 • L M u l t i p l y i n g b o t h s i d e s o f E q . ( 5 8 ) w i t h / c o s ^ ^ z j d z 0 we g e t L L F / c o s ( f i k z ) d z = B , B m ' B n / c o s ( f i m z ) c o s ( « k z ) d z 60 0 0 43 I f k f m, L / c o s ( f t z ) c o s ( f t , z ) = 0 61 0 T h e r e f o r e k = m, a n d E q . ( 6 0 ) a f t e r i n t e g r a t i o n b e c o m e s AA = B •B •BB•B 62 m n w h e r e AA = F s i n ( f t m L ) / f t m m ' m a n d I s i n ( 2 f t L ) B B " {2 + 4 f t " > 6 3 m C o m b i n i n g E q s . ( 6 3 ) a n d ( 6 2 ) w i t h E q . ( 5 9 ) g i v e s sin Bn£ sin ftmL Bmn = Bm'Bn = " O sTn~2FT~ ' "TTT sin 2ft L 6 4 r n , n -i r m , m i { — + ^ } { — + ^ } N u m e r i c a l s o l u t i o n o f E q . ( 5 3 ) i n c o n j u n c t i o n w i t h E q . ( 6 4 ) g i v e s t h e a v e r a g e m o i s t u r e c o n t e n t o f t h e b l o c k a s a f u n c t i o n o f t i m e . 44 2. H e a t t r a n s f e r By s e p a r a t i o n o f v a r i a b l e s T = *}(B}$2{y)$3{z) 6 5 w h e r e tj>^, <j> 2 5 a n d cf>3 a r e f u n c t i o n s o f 6 , y , a n d z , r e s p e c -t i v e l y . A s i n t h e c a s e o f m a s s t r a n s f e r , E q . ( 1 ) l e a d s t o t h e f o l l o w i n g e q u a t i o n , w h i c h i s a n a l o g o u s t o E q . ( 4 3 ) f o r m a s s t r a n s f e r : 2 T - A e " a k 9 c o s ( u y ) c o s ( v z ) 66 w h e r e A = c o n s t a n t o f i n t e g r a t i o n a = t h e r m a l d i f f u s i v i t y u , v = e i g e n v a l u e s k 2 = u 2 + v 2 67 T o f i n d t h e c o n s t a n t u ( e i g e n v a l u e ) , s u b s t i t u t e E q . ( 6 6 ) a n d E q . ( 4 9 ) i n t o E q . ( 1 2 ) , s e t t i n g z = 0 a n d y = I, 2 OO 0 0 2 2 = b e ' a k 9 c o s ( u n 5 , ) 68 45 w h e r e u n i s t h e n u m b e r o f s o l u t i o n s , n b e i n g a n i n t e g e r . By a s i m i l a r m e t h o d we f i n d 2 oo oo 2 v e - c t k 9 s i n ( v m L ) + a I I Q B s i n ( f t m L ) e " D X n 6 m v m m mn m b e " a k 2 e c o s ( v n i L ) 69 w i t h v m a s s o l u t i o n s , m b e i n g a n i n t e g e r , I t f o l l o w s f r o m E q . ( 6 7 ) t h a t k 2 = u 2 + v 2 70 n n m T h e g e n e r a l s o l u t i o n o f E q . ( 1 ) c a n now b e w r i t t e n a s f o l 1 o w s : 2 _ oo oo -ak 9 T ( 9 , y , z ) = 1 1 A e c o s ( u y ) c o s ( v z ) _ 71 m=l n = l S i n c e t h e c o e f f i c i e n t A m n = A m « A n . 72 E q . ( 7 1 ) may b e w r i t t e n a s f o l l o w s : 2 2 oo - a u 9 00 - a v m 9 T ( e , y , z ) = I A n e n c o s ( u n y ) I A m e m c o s ( v m z ) 73 n=1 m=1 E q u a t i o n s ( 7 1 ) a n d ( 7 3 ) a r e a n a l o g o u s t o m a s s t r a n s f e r 46 E q s . ( 4 9 ) a n d ( 5 1 ) . T h e c o e f f i c i e n t s A = A *A„ a r e f o u n d mn m n by t h e s a m e m e t h o d a s u s e d i n t h e c a s e o f m a s s t r a n s f e r w i t h t h e f o l l o w i n g r e s u l t : s i n ( u A ) s i n ( v m L ) A = - . ~ 74 mn u I s i n Z w l v L s i n 2 v m L f_Q_ + Q_> {JL_ + 0L_} 1 2 4 i 1 2 4 * T h e a v e r a g e w o o d t e m p e r a t u r e i s g i v e n b y : % L T A V ( 9 ) = / / T ( 0 , y > z ) d y d 2 / 4 £ L 75 -% - L I n t e g r a t i o n o f E q . ( 7 3 ) i n c o n j u n c t i o n w i t h E q . ( 7 4 ) a n d s u b s t i t u t i o n o f t h e r e s u l t i n E q . ( 7 5 ) y i e l d s 2 2 0 0 A „ -om 6 0 0 A m - a v 8 TAV< 9> - I iSre s l' n (V> t d b e 5 , ' n ( v m L ) 7 6 n=I n m-1 m E q u a t i o n ( 7 6 ) i s a n a l o g o u s t o m a s s t r a n s f e r E q . ( 5 3 ) a n d c a n b e s o l v e d n u m e r i c a l l y t o g e t t h e a v e r a g e t e m p e r a t u r e o f t h e w o o d e n b l o c k a s a f u n c t i o n o f d r y i n g t i m e . 3.6 C a l c u l a t i o n P r o c e d u r e I n a p p l y i n g t h e p r e c e d i n g m a t h e m a t i c a l m o d e l t o a n a l y -s i s o f e x p e r i m e n t a l d a t a , t h e m a s s a n d h e a t d i f f u s i v i t i e s 47 (D i n E q . ( 5 3 ) a n d a i n E q . ( 7 6 ) ) w e r e t r e a t e d a s l o o s e p a r a -m e t e r s . T h e v a l u e s o f t h e s e p a r a m e t e r s w e r e d e t e r m i n e d f o r e a c h r u n b y s e a r c h i n g f o r t h e v a l u e r e q u i r e d i n t h e t h e o r e -t i c a l e q u a t i o n s t o g i v e a g o o d m a t c h ( l e a s t - s q u a r e s f i t ) b e t w e e n c a l c u l a t e d a n d o b s e r v e d r e s u l t s o f a v e r a g e m o i s t u r e c o n t e n t a n d a v e r a g e t e m p e r a t u r e , e a c h as a f u n c t i o n o f t i m e . 1. C o m p u t e r p r o g r a m D i g i t a l c o m p u t e r p r o g r a m s f o r n u m e r i c a l s o l u t i o n o f E q s . ( 5 3 ) a n d ( 7 6 ) w e r e w r i t t e n f o r p r e d i c t i n g t h e a v e r a g e m o i s t u r e c o n t e n t a n d a v e r a g e t e m p e r a t u r e , b o t h a s a f u n c t i o n o f t i m e , f o r a b l o c k o f w o o d u n d e r g o i n g u n s t e a d y - s t a t e d r y -i n g . An a d d i t i o n a l p r o g r a m was w r i t t e n f o r c o m p u t i n g a n d p l o t t i n g m o i s t u r e d i s t r i b u t i o n ( E q . 5 1 ) a s a f u n c t i o n o f t i m e . A l i s t o f t h e F o r t r a n p r o g r a m s u s e d i s s h o w n i n A p p e n d i x A , w h i l e t h e t h e o r e t i c a l r e s u l t s o f a v e r a g e m o i s t u r e s a n d t e m p e r a -t u r e s t o g e t h e r w i t h c o r r e s p o n d i n g e x p e r i m e n t a l d a t a a p p e a r i n A p p e n d i x B. T h e o r e t i c a l r e s u l t o f m o i s t u r e d i s t r i b u t i o n w i t h i n t h e b l o c k a f t e r d i f f e r e n t p e r i o d s o f d r y i n g t i m e a r e i n c l u d e d i n A p p e n d i x D. 2. M a s s t r a n s f e r F o r c a l c u l a t i n g a v e r a g e m o i s t u r e c o n t e n t a s f u n c t i o n o f t i m e b y E q . ( 5 3 ) , t h e N e w t o n m e t h o d o f i t e r a t i o n ( 2 9 ) was e m p l o y e d t o f i n d e i g e n v a l u e s (3 n a n d ftm), i . e . , t h e r o o t s k P S"1 o f E q s . ( 4 5 . 1 ) a n d ( 4 6 . 1 ) . T h e c o n s t a n t C"= ( g p ^ p ) i n p s o E q . ( 2 3 ) i s a f u n c t i o n o f d i f f u s i v i t y D, w h i c h i s u n k n o w n . 48 F o r t u n a t e l y t h e v a l u e o f C f o r t h e e x p e r i m e n t a l c o n -d i t i o n s o f t h e p r e s e n t w o r k was a l w a y s > 100 a n d t h e e i g e n v a l u e s f o r C > 100 a r e a p p r o x i m a t e l y t h e s a m e a s i n t h e c a s e o f C = °°, ( 3 0 ) . H e n c e , e v e n l a r g e c h a n g e s i n m a s s - t r a n s f e r c o e f f i c i e n t k g , v a p o r p r e s s u r e o f w a t e r a t t h e s u r f a c e P , a n d s o l i d d e n s i t y p , h a v e v e r y l i t t l e e f f e c t o n t h e f i n a l r e s u l t o f e i g e n v a l u e s . T h e s l o p e o f t h e e q u i l i b r i u m c u r v e ( d e s o r p t i o n i s o t h e r m f o r W e s t e r n H e m l o c k ) , S t a k e n f r o m F i g . ( 6 ) t o b e a b o u t 0.2 f o r m o i s t u r e c o n t e n t o f 5- 6 % w h i c h was e x p e r i m e n t a l l y f o u n d t o b e t h e m o i s t u r e c o n -t e n t c l o s e t o t h e s u r f a c e o f t h e w o o d . T h e m a s s t r a n s f e r c o e f f i c i e n t k g , f o r u s e i n E q . ( 2 3 ) was c a l c u l a t e d f r o m t h e f o l l o w i n g e q u a t i o n g i v e n b y B e e k ( 4 , p . 4 3 3 ) - m "GW E S 2/3 . * ".f "P V } 7 7 Umf m f 0 " I ' - ^ f ' . * * w h e r e C = 0 . 7 , m = 0 , a n d S = 2.57 f o r g a s f l u i d i z e d b e d , CL* d. * u m f u n p R Q = i t * \(300-1 2 , 0 0 0 ) , a n d e m f ( 0 . 5 0 - 0 .95) , h e n c e E q . ( 7 7 ) e y ( l - E m f ) m may b e r e w r i t t e n : ^ e m f • ( 2 . 5 7 ) 2 / 3 . 0.7 78 w h e r e K f i w = m a s s - t r a n s f e r c o e f f i c i e n t , f t . / h r . 49 E q . ( 7 7 ) i s v a l i d f o r m a s s t r a n s f e r b e t w e e n a f l u i d i z e d b e d a n d a w a l l o r a n o b j e c t . T h e p r o p e r t i e s o f t h e f l u i d i z e d b e d u s e d a r e g i v e n i n T a b l e ( 4 ) . F o r t h e p r e s e n t s y s t e m w i t h v i s c o s i t y ( y ) a n d d e n s i t y (p) o f a i r a t t h e b e d t e m p e r a t u r e ( T b = 2 1 7 ° F ) t h e v a l u e o f t h e m a s s t r a n s f e r c o e f f i c i e n t b y k g 2 w o r k s o u t t o 1 2 8 I b m . / f t . h r . a t m . T h e a v e r a g e m o i s t u r e c o n -t e n t o b t a i n e d a f t e r o n e h o u r o f d r y i n g was u s e d a s t h e s t a r t -i n g m o i s t u r e c o n t e n t o f t h e f a l l i n g - r a t e p e r i o d s o a s t o e x c l u d e t h e i n i t i a l h e a t i n g - u p p e r i o d f r o m t h e c a l c u l a t i o n s . 3. H e a t t r a n s f e r I n o r d e r t o c a l c u l a t e a v e r a g e w o o d t e m p e r a t u r e a s a f u n c t i o n o f t i m e u s i n g E q . ( 7 6 ) , t h e N e w t o n m e t h o d o f i t e r a -t i o n ( 2 9 ) was e m p l o y e d t o f i n d e i g e n v a l u e s ( u n , a n d v ) , i . e . , t h e r o o t s o f E q s . ( 6 8 ) a n d ( 6 9 ) . H o w e v e r , t h e e x i s t -e n c e o f t h e t e r m s 3M/9y a n d 3M/3z i n E q s . ( 1 2 ) , ( 1 3 ) , ( 1 4 ) , a n d ( 1 5 ) m a d e t h e b o u n d a r y c o n d i t i o n s n o n - l i n e a r . I n o r d e r t o s i m p l i f y t h e p r o b l e m , t h e f o l l o w i n g a p p r o x i m a t e p r o c e d u r e was a d o p t e d : T h e a v e r a g e w o o d t e m p e r a t u r e m e a s u r e d e x p e r i -m e n t a l l y a f t e r o n e h o u r o f d r y i n g was u s e d a s t h e s t a r t i n g t e m p e r a t u r e o f t h e f i r s t i n t e r v a l . T h e d r y i n g t i m e was t h e n d i v i d e d i n t o i n t e r v a l s o f o n e h o u r . F o r e a c h i n t e r v a l , 3M/3y a n d 3M/3z w e r e a s s u m e d c o n s t a n t a n d w e r e e v a l u a t e d a t t h e m i d p o i n t o f t h a t i n t e r v a l , t a k i n g t i m e 8 = 0, a t t h e b e g i n n i n g o f t h e i n t e r v a l . T h e e i g e n v a l u e s ( u a n d v ) f o r e a c h i n t e r -n m v a l w e r e t h e n e v a l u a t e d u s i n g E q s . ( 6 8 ) a n d ( 6 9 ) . T a k i n g t h e f i n a l t e m p e r a t u r e a t t h e e n d o f a t i m e i n t e r v a l t o b e t h e 50 i n i t i a l t e m p e r a t u r e a t t h e b e g i n n i n g o f t h e n e x t i n t e r v a l , a n d a s s u m i n g t h a t t h e i n i t i a l t e m p e r a t u r e s o f e a c h i n t e r v a l i s u n i f o r m t h r o u g h o u t t h e b l o c k , i t t h e n b e c o m e s p o s s i b l e t o d e t e r m i n e t h e c o e f f i c i e n t s A _ o f t h e i n t e r v a l u n d e r c o n s i d e r a -mn t i o n u s i n g E q . ( 7 4 ) . A m o r e a c c u r a t e a p p r o x i m a t i o n c o u l d h a v e b e e n o b t a i n e d i f , i n s t e a d o f t h e u n i f o r m d i s t r i b u t i o n a s s u m e d , t h e a c t u a l t e m p e r a t u r e d i s t r i b u t i o n a t t h e e n d o f t h e p r e -v i o u s i n t e r v a l h a d b e e n u s e d i n t h e u s u a l o r t h o g o n a l i t y p r o -c e d u r e f o r f i n d i n g t h e s e c o e f f i c i e n t s . T o c h e c k t h e v a l i d i t y o f t h e a p p r o x i m a t i o n p r o c e d u r e u s e d , t h e c a l c u l a t i o n was r e p e a t e d u s i n g a s h o r t e r t i m e i n t e r v a l ( 1 / 2 h r . ) . T h e r e s u l t s f o r h a l f - h o u r a n d o n e - h o u r i n t e r v a l s , s h o w n i n F i g . ( 7 ) , a r e s e e n t o be w i t h i n 2% o f e a c h o t h e r . I n E q s . ( 6 8 ) a n d ( 6 9 ) , ADp sm Q h a " k ( T -T ) a n d b " k ~ K s u b V K s T h e h e a t o f e v a p o r a t i o n A a s a f u n c t i o n o f a v e r a g e s u r f a c e t e m p e r a t u r e o f w o o d d u r i n g t h e f a l l i n g - r a t e p e r i o d was r e a d f r o m t h e S t e a m T a b l e ( 3 2 ) a n d t h e e f f e c t i v e d i f f u s i v i t y D, was o b t a i n e d f r o m t h e m a s s t r a n s f e r c a l c u l a t i o n s d e s c r i b e d i n t h e p r e v i o u s s e c t i o n . T h e d e n s i t y a n d t h e r m a l c o n d u c t i v i t y o f w o o d w e r e o b t a i n e d f r o m t h e l i t e r a t u r e ( s e e T a b l e 5) a t a v e r -a g e m o i s t u r e a n d t e m p e r a t u r e c o n d i t i o n s o v e r t h e d r y i n g p e r i o d . T h e v a l u e o f h e a t t r a n s f e r c o e f f i c i e n t ( h ) was c a l c u -l a t e d u s i n g t h e f o l l o w i n g c o r r e l a t i o n p r o p o s e d b y W e n d e r a n d Fig. 7 A V E R A G E W O O D T E M P E R A T U R E v s . T I M E C A L C U L A T E D B Y EQ. 7 6 U S I N G D I F F E R E N T T I M E I N T E R V A L S • time interval 1 hr. O time interval V2 nr. r u n n o 4 air flow rate-1.2 Umf bed temperature 6 7 / \ t i m e 8- (hrs) 52 C o o p e r ( 3 , p . 2 7 2 ) f o r f l u i d i z e d b e d t o i m m e r s e d v e r t i c a l t u b e h e a t t r a n s f e r : = 0 . 0 1 8 4 4 c R ( l - e f ) ( - E ^ - ) d U 0 2 3 C 0 , 8 D 0 , 6 6 (_J>1_) (_I>sand) ( ! s | n d ) . y " p g f o r d pU _2 2 _ ) 2 — = 10 - 1 0 ^ y ( R e n o . i n p r e s e n t e x p e r i m e n t s ~ 1 2 ) w h e r e C R = c o r r e c t i o n f a c t o r f o r n o n - a x i a l l o c a t i o n o f i m m e r s e d t u b e s = 1, f o r a v e r t i c a l t u b e p o s i t i o n e d a t t h e b e d ' s a x i s ( o u r c a s e ) . T h e f l u i d i z a t i o n c o n d i t i o n s u s e d i n t h i s w o r k w e r e w i t h i n t h e r a n g e o f v a r i a b l e s o n w h i c h E q . ( 7 9 ) i s b a s e d . C H A P T E R 4 E X P E R I M E N T A L STUDY 4.1 E q u i p m e n t T h e e q u i p m e n t u s e d i s i l l u s t r a t e d i n F i g . ( 8 ) . A i r i s s u p p l i e d f r o m t h e m a i n s t h r o u g h g l o b e v a l v e C a n d r o t a -m e t e r D, ( c a l i b r a t i o n c h a r t i n A p p e n d i x C) t o t h e e l e c t r i c a l h e a t e r E , w h e r e i t i s h e a t e d t o t h e d e s i r e d t e m p e r a t u r e . H o t a i r t h e n e n t e r s t h e f l u i d i z e d b e d c o l u m n H, w h i c h c o n s i s t s o f a 5 . 7 5 " d i a m e t e r x 3' h i g h s t a i n l e s s s t e e l p i p e f i t t e d w i t h a s i g h t g l a s s I , t h r o u g h a m u l t i o r i f i c e g a s d i s t r i b u -t o r G. T h e d i s t r i b u t o r h a s 17 o r i f i c e s o f 0 . 6 " d i a m e t e r a n d i s b a c k e d w i t h a 60 m e s h s c r e e n t o a v o i d l e a k a g e o f s o l i d s t h r o u g h t h e h o l e s . I r o n - c o n s t a n t a n t h e r m o c o u p l e s J w e r e u s e d t o m e a s u r e t h e t e m p e r a t u r e o f t h e b e d a t d i f f e r e n t l o c a t i o n s a s w e l l a s t e m p e r a t u r e s w i t h i n t h e w o o d e n b l o c k a t p o s i t i o n s s h o w n i n F i g . ( 9 ) . A s t a n d a r d D e l m h o r s t r e s i s t a n c e m o i s t u r e m e t e r c a p a b l e o f m e a s u r i n g m o i s t u r e s up t o 6 5 % d r y - b a s i s was u s e d t o m e a s u r e t h e m o i s t u r e c o n t e n t o f t h e w o o d d u r i n g d r y i n g . T h e c a l i b r a t i o n c h a r t f o r t h e m o i s t u r e m e t e r p r o v i d e d b y t h e m a n u f a c t u r e r i s i n c l u d e d i n A p p e n d i x C. T h e c a l i b r a t i o n was c h e c k e d b y c o m p a r i n g m o i s t u r e c o n -t e n t s m e a s u r e d b y t h e m e t e r a g a i n s t r e s u l t s o b t a i n e d b y t h e o v e n - d r y i n g m e t h o d ( s e e T a b l e 1 ) , a n d t h e t w o w e r e f o u n d t o 53 54 C- globe valve D- rotameter E- electrical heater G- distributor H- cylindrical column I - sight window J- thermocouples K-temperature indicator L- electrodes M- moisture meter N-cyclone FIG. 8 DIAGRAM OF EQUIPMENT 55 ® thermocouples ^ electrodes FIG. 9 LOCATION OF THERMOCOUPLES AND ELECTRODES note- standard blockcalled a 2"x 4" actually is l,5"x3,5" 5 6 b e w i t h i n a b o u t 5% o f e a c h o t h e r . T A B L E 1. ACCURACY OF M O I S T U R E METER F i n a l M o i s t u r e C o n t e n t (%) Run No. M e t e r R e a d i n g * O v e n - D r y i n g M e t h o d 1 15 1 5 . 6 12 15 1 5 . 8 2 20 2 0 . 8 3 3 7 . 5 38.1 4 15 1 5 . 8 5 15 1 5 . 7 6 15 1 5 . 5 7 15 1 5 . 9 8 15 1 5 . 3 11 27 2 7 . 9 * E l e c t r o d e s l o c a t e d a t a d i s t a n c e o f l / 5 t h t h e b l o c k t h i c k n e s s f r o m t h e s u r f a c e . 4.2 P r o c e d u r e B l o c k s o f W e s t e r n H e m l o c k , 2 i n . x 4 i n . x 1 f t . l o n g c o n t a i n i n g 7 0 % t o 9 0 % m o i s t u r e ( d r y b a s i s ) w e r e p r o v i d e d , a n d e x a m i n e d a f t e r d r y i n g , b y M a c M i l l a n B l o e d e l R e s e a r c h L t d . T h e s a m p l e s w e r e c u t a c r o s s t h e g r a i n , a n d w e r e f r e e o f k n o t s , p i t c h , s t r e a k s , s p i t s o r o t h e r d e f e c t s . B o t h e n d s o f t h e s a m p l e w e r e s e a l e d w i t h e p o x y r e s i n a n d c o v e r e d w i t h 57 1 / 1 6 " t h i c k a s b e s t o s c l o t h ( t w o - d i m e n s i o n a l d r y i n g ) t o p r e -v e n t t r a n s f e r o f m o i s t u r e a n d h e a t a l o n g t h e g r a i n . I n s o m e e x p e r i m e n t s , e i t h e r t h e e d g e s ( y d i r e c t i o n ) o r t h e l a r g e s i d e s ( z d i r e c t i o n ) w e r e a d d i t i o n a l l y i n s u l a t e d i n t h e same m a n n e r t o a c h i e v e o n e - d i m e n s i o n a l d r y i n g . T h e a s b e s t o s c l o t h was s e c u r e d t o t h e w ood w i t h w i r e . T h e s a m p l e s , a f t e r i n s u -l a t i n g , w e r e m a r k e d f o r i d e n t i f i c a t i o n , p l a c e d i n p o l y e t h y -l e n e b a g s a n d s t o r e d i n a c o n s t a n t h u m i d i t y r o o m ( t e m p e r a -t u r e 4 0 ° F , RH - 5 0 % ) u n t i l f u r t h e r p r o c e s s i n g . T h e f l u i d i z e d b e d , o f -20 + 30 m e s h O t t a w a s a n d ( p b = 8 9 . 0 3 l b m . / f t . 3 a n d p s a n d = 1 6 4 . 2 l b m . / f t . ) was o p e r a t e d w i t h t h e s a m e b e d d e p t h ( 1 6 " s e t t l e d ) , a n d a t a c o n s t a n t a i r f l o w r a t e (U = 1.2 U m f ) f o r a l l r u n s e x c e p t r u n n o . 7 (U = 1.3 u " m f ) a n d r u n n o . 8 (U = 1.1 U f ) . T h e o b s e r v e d m i n i m u m f l u i d i z a t i o n v e l o -c i t y , U m ^ , was 1.3 f t . / s e c . T h e b e d t e m p e r a t u r e was v a r i e d f r o m o n e r u n t o t h e o t h e r ( 1 7 5 , 1 9 0 , 2 0 4 , a n d 2 1 7 ° F ) b y c o n t r o l l i n g t h e t e m p e r a t u r e o f t h e i n l e t a i r . T h e t e s t s a m p l e , p r e v i o u s l y w e i g h e d a n d f i t t e d w i t h t h e m o i s t u r e m e a s u r i n g e l e c t r o d e s a n d t h e r m o c o u p l e s , ( F i g , 9 ) , was m o u n t e d i n a s p e c i a l l y d e s i g n e d h o l d e r ( F i g . 1 0 ) , a n d was i n s e r t e d i n t o t h e p r e h e a t e d b e d o p e r a t i n g a t s t e a d y -s t a t e c o n d i t i o n s . T h e s a m p l e was p o s i t i o n e d i n t h e b e d s o t h a t i t was f u l l y s u b m e r g e d a n d was w e l l r e m o v e d f r o m t h e w a l l a n d b a s e o f t h e c o l u m n , as s h o w n i n F i g u r e ( 1 0 ) . T h e t e m p e r a t u r e o f t h e b e d , t e m p e r a t u r e s a t d i f f e r e n t p o i n t s i n t h e t e s t s a m p l e , as w e l l a s t h e a v e r a g e m o i s t u r e c o n t e n t o f t h e s a m p l e , w e r e r e c o r d e d a t r e g u l a r t i m e i n t e r v a l s 58 Ifluidized bed sample CO I surface of expanded bed metal hanger minimum distance! IV) distributor Fig.10 POSITION OF SAMPLE IN FLUIDIZED BED 59 T h e h o l e s f o r t h e ( 1 / 8 " d i a . ) e l e c t r o d e s w e r e d r i l l e d u n d e r -s i z e t o i n s u r e a t i g h t f i t , a n d t h e e l e c t r o d e s w e r e i n s e r t e d i n t o t h e w o o d t h r o u g h a r u b b e r s e a l r i n g i n o r d e r t o a v o i d c o n d e n s a t i o n o r e v a p o r a t i o n i n t h e h o l e d u r i n g d e c r e a s i n g r e l a t i v e h u m i d i t y c o n d i t i o n s . When t h e l u m b e r r e a c h e d t h e d e s i r e d f i n a l m o i s t u r e c o n t e n t o f a r o u n d 1 5 % , t h e s a m p l e was r e m o v e d f r o m t h e b e d a n d w e i g h e d i m m e d i a t e l y . T h e i n i t i a l m o i s t u r e c o n t e n t o f t h e s a m p l e was d e t e r m i n e d b y t h e o v e n -d r y i n g m e t h o d ( d r y i n g t o c o n s t a n t w e i g h t a t 2 1 2 ° F ) , s i n c e i n i t i a l m o i s t u r e s w e r e o u t s i d e t h e u p p e r l i m i t m e a s u r a b l e b y t h e m o i s t u r e m e t e r ( 6 5 % ) . T h e f i n a l m o i s t u r e c o n t e n t s w e r e a l s o d e t e r m i n e d b y t h e a b o v e m e t h o d a s a c h e c k o f t h e c o r r e c t n e s s o f t h e m o i s t u r e m e t e r r e a d i n g s ( s e e T a b l e 1 ) . T h e a v e r a g e m o i s t u r e c o n t e n t o f t h e t e s t s a m p l e was d e t e r m i n e d u s i n g t h e p r o c e d u r e s u g g e s t e d b y D u n l o p a n d B e l l ( r e f . 1 6 , p . 1 8 5 ) . T h e s e a u t h o r s f o u n d , b y i n t e g r a t i n g t h e r o u g h l y p a r a b o l i c m o i s t u r e c o n t e n t p r o f i l e s o f d r y i n g w o o d , t h a t " t h e m o i s t u r e c o n t e n t i n a p l a n e l o c a t e d a t o n e - f i f t h o f t h e t h i c k n e s s o f t h e m a t e r i a l f r o m i t s s u r f a c e i s u s u a l l y v e r y n e a r t h e a v e r a g e o f t h e p i e c e . " T h e m o i s t u r e c o n t e n t o f t h e w o o d s a m p l e s i n t h e e x p e r i m e n t s w e r e t h e r e f o r e o b t a i n e d b y p l a c i n g t h e m e t e r e l e c t r o d e s a t t h e a b o v e d i s t a n c e f r o m o n e o f t h e u n i n s u l a t e d s u r f a c e s f o r t h e c a s e o f o n e - d i m e n -s i o n a l d r y i n g a n d f r o m t h e f r o n t s u r f a c e i n t h e c a s e o f t w o -d i m e n s i o n a l d r y i n g . T h e d a t a i n T a b l e ( 1 ) p r o v i d e e x p e r i m e n t a l s u p p o r t f o r a s s u m i n g t h a t t h e m o i s t u r e m e t e r i n d e e d g a v e v a l u e s c l o s e t o 60 t h e a v e r a g e m o i s t u r e c o n t e n t o f t h e b l o c k , ' i n c o n f o r m i t y w i t h t h e r u l e s u g g e s t e d b y D u n l o p a n d B e l l . F u r t h e r c o n -f i r m a t i o n o f t h i s p r o c e d u r e o v e r a w i d e r m o i s t u r e r a n g e was o b t a i n e d b y m e a s u r i n g m o i s t u r e c o n t e n t s a t two p o s i t i o n s i n t h e b l o c k 2 / 5 " ( 1 / 5 x t h i c k n e s s ) a n d 1" ( c e n t r e o f b l o c k ) , u s i n g t w o p a i r s o f e l e c t r o d i e s . T h e c e n t r e v a l u e s w e r e c o n -v e r t e d t o a v e r a g e m o i s t u r e c o n t e n t s b y u s i n g t h e f o l l o w i n g e q u a t i o n g i v e n b y B r o w n e t a l . ( 3 5 , p . 8 6 ) : M„ = 3/2(M -MJ + fM 80 c a s s w h e r e M . H p, a n d M. a r e m o i s t u r e c o n t e n t s {%) a t t h e c e n t r e , c s a s u r f a c e , a n d a v e r a g e , r e s p e c t i v e l y . T h e a v e r a g e v a l u e s (M_) f r o m E q . ( 8 0 ) , w i t h M_ t a k e n a s a s 4%, s h o w r e m a r k a b l y g o o d a g r e e m e n t w i t h r e s u l t s o b t a i n e d a t t h e 2 / 5 " p o s i t i o n , ( s e e T a b l e 2 ) . E l e v e n r u n s w e r e p e r f o r m e d w i t h b e d t e m p e r a t u r e s r a n g -i n g f r o m 175 t o 2 1 7 ° F a n d U/U f f r o m 1.1 t o 1 . 3 . I n o r d e r t o c h e c k t h e q u a l i t y o f t h e w o o d a f t e r d r y i n g , f i v e e x t r a s a m p l e s w e r e d r i e d a t b e d t e m p e r a t u r e s o f 1 9 0 , 2 0 4 ( t w o s a m p l e s ) a n d 2 1 7 ° F ( t w o s a m p l e s ) . A f t e r d r y i n g , t h e b l o c k s o f H e m l o c k w e r e t e s t e d f o r d r y i n g d e f e c t s . D u r i n g t h e d r y i n g t h e f o l l o w i n g t y p e s o f d a m a g e c a n o c c u r i n w o o d : 1. C a s e h a r d e n i n g i s c a u s e d b y t o o r a p i d d r y i n g i n w h i c h t h e z o n e s n e a r t h e s u r f a c e o f t h e w o o d s h r i n k m o r e ( p a s s e s F. S. P. f a s t e r ) t h a n t h e i n n e r 61 T A B L E 2. AVERAGE M O I S T U R E CONTENT FROM EQ. ( 8 0 ) V E R S U S V A L U E S MEASURED AT 2 / 5 " FROM S U R F A C E e m a U ) MCU) M a f r o m E q . ( 8 0 ) ( % ) a T i m e D i s t a n c e f r o m t h e S u r f a c e ( H r . ) 2 / 5 " 1" 1 47.1 6 8 . 8 4 7 . 2 2 3 9 . 0 5 8 . 7 4 0 . 5 3 3 6 . 0 5 3 . 5 3 7 . 0 4 3 3 . 5 49 .9 3 4 . 6 5 3 1 . 5 4 6 . 6 3 2 . 4 6 2 9 . 6 4 3 . 7 3 0 . 5 7 2 7 . 8 41 .2 2 8 . 8 8 2 6 . 3 3 8 . 4 2 6 . 9 9 2 5 . 0 3 6 . 5 2 5 . 7 10 2 3 . 7 3 4 . 3 2 4 . 5 11 2 2 . 4 3 2 . 6 23.1 12 2 1 . 4 31 .0 2 2 . 0 13 2 0 . 0 2 8 . 9 2 0 . 6 14 1 9 . 2 2 7 . 8 1 9 . 9 15 1 8 . 0 26.1 1 8 . 7 16 17.1 2 3 . 8 1 7 . 7 17 1 6 . 3 2 3 . 3 1 6 . 9 18 1 5 . 0 2 1 . 2 1 5 . 5 62 p o r t i o n o f t h e w o o d . T h e s h e l l o f t h e w o o d i s i n t e n s i o n w h i l e t h e c o r e i s i n c o m p r e s s i o n ( a ) . S u r f a c e c h e c k i n g ( F i g . 1 2) r e l a t e d t o c a s e h a r d e n -i n g c a n o c c u r a t t h i s p o i n t . As t h e d r y i n g p r o c e e d s t h e c o r e d r i e s b e l o w F . S . P . , s h r i n k a g e s t a r t s w h i c h c r e a t e s t e n s i o n s t r e s s e s g r e a t e r t h a n t h o s e i n t h e s h e l l . H e n c e , t h e s h e l l i s now i n c o m p r e s s i o n a n d t h e c o r e i n t e n s i o n ( b ) ( s e e F i g . 1 1 , r e f . 1 6 , p . 9 3 ) . T h e t e n s i l e s t r e s s e s b u i l t u p i n c a s e h a r d e n -i n g may b e o f s u c h m a g n i t u d e t h a t r u p t u r e i n t e n -s i o n p e r p e n d i c u l a r t o t h e g r a i n may e n s u e . 2. S u r f a c e c h e c k s , F i g . ( 1 2 ) ( 1 6 , p . 9 1 ) a r e l o n g i -t u d i n a l o p e n i n g s , f r e q u e n t l y d e v e l o p e d a l o n g t h e w o o d r a y s , a n d c a n b e o b s e r v e d o n t h e t a n g e n t i a l s u r f a c e s . T h e c a u s e o f t h e s u r f a c e c h e c k i n g i s m o r e r a p i d d r y i n g o f t h e w o o d s u r f a c e t h a n t h e i n t e r i o r o f t h e w o o d . 3. H o n e y c o m b , F i g . ( 1 3 ) ( 1 6 , p . 9 4 ) o c c u r s w h e n t h e i n t e r n a l t e n s i l e f o r c e s d u e t o i m p r o p e r d r y i n g r e a c h t h e b r e a k i n g p o i n t . B r e a k s u s u a l l y s t a r t a t t h e i n t e r f a c e s b e t w e e n w o o d r a y s a n d a d j o i n i n g l o n g i t u d i n a l t i s s u e s , t h e s h o r t r a d i a l c r a c k s t h u s f o r m e d o p e n . T h i s i s a d e f e c t w h i c h i s n o t a l w a y s v i s a b l e e x t e r n a l l y . A f t e r d r y i n g , t h e b l o c k s o f H e m l o c k w e r e t e s t e d f o r e h a r d e n i n g a n d e x a m i n e d e x t e r n a l l y f o r e v i d e n c e o f t h e Fig.il Stress conditons in drying leading to case hardening Fig 13 Honeycomb deffect in the wood 64 s u r f a c e c h e c k i n g a n d i n t e r n a l l y u n d e r t h e m i c r o s c o p e f o r h o n e y c o m b i n g a n d t h e r u p t u r e i n t e n s i o n p e r p e n d i c u l a r t o t h e g r a i n . T h e p r o c e d u r e f o r t h e c a s e h a r d e n i n g t e s t i s a s f o l l o w s ( 6 ) : F r o m t h e t e s t p i e c e , c u t a s m a l l s e c t i o n a b o u t 3/8 i n . w i d e f r o m t h e c e n t r e o f t h e b o a r d . C u t s l o t s i n t h e s e c t i o n w i t h a h a n d s a w , a s s h o w n i n F i g . ( 1 4 ) . A f t e r a fe w m i n u t e s , a n e v a l u a t i o n o f t h e s t r e s s e s , c a n b e m a d e , ( c ) I f t h e o u t e r p r o n g s h a v e t u r n e d i n n o t i c e a b l y , t h e s t o c k i s s t r e s s e d . ( d ) I f t h e o u t e r p r o n g s a r e s t r a i g h t , t h e w o o d i s s t r e s s f r e e . stressed (c) (d) Fig.U.CASEHARDENING TEST 65 4.3 R e s u l t s T h e e x p e r i m e n t a l r e s u l t s a r e s u m m a r i z e d i n T a b l e ( 3 ) , t y p i c a l c u r v e s a r e s h o w n i n F i g u r e s ( 1 5 ) t o ( 2 4 ) a n d d e t a i l e d d a t a , t h e o r e t i c a l a s w e l l a s e x p e r i m e n t a l , f o r a l l t h e r u n s a r e t a b u l a t e d i n A p p e n d i x B, T a b l e s ( I ) t o ( X I I ) . F i g u r e s ( 1 5 ) , ( 1 7 ) , ( 1 8 ) a n d ( 1 9 ) a l s o i n c l u d e t h e o r e t i c a l c u r v e s o f a v e r a g e m o i s t u r e c o n t e n t v e r s u s t i m e f o r c o m p a r i s o n . A v e r a g e b l o c k t e m p e r a t u r e d a t a a r e s h o w n i n F i g . ( 2 4 ) , t h e e x p e r i m e n t a l r e s u l t s b e i n g a r i t h m a t i c a v e r a g e v a l u e s o f t e m p e r a t u r e s m e a s u r e d a t f o u r d i f f e r e n t p o s i t i o n s i n t h e b l o c k . T h e v a l u e s o f t i m e r e q u i r e d t o a t t a i n f i n a l M.C. o f 1 5 % , l i s t e d i n T a b l e ( 3 ) , w e r e m o s t l y d e t e r m i n e d e x p e r i -m e n t a l l y , b u t s o m e w e r e o b t a i n e d b y e x t r a p o l a t i n g t h e m o i s -t u r e c o n t e n t v e r s u s t i m e c u r v e t o 1 5 % M.C. ( F i g s . 1 5 , 1 7 , a n d 1 8 ) . T h e p r o p e r t i e s o f t h e f l u i d i z e d b e d u s e d a r e g i v e n i n T a b l e ( 4 ) , a n d t h e p r o p e r t i e s o f W e s t e r n H e m l o c k i n T a b l e ( 5 ) w i t h v i s c o s i t y a n d d e n s i t y o f a i r t a k e n a t t h e b e d t e m p e r a -t u r e ( T b = 2 1 7 ° F ) , t h e b e d - t o - s u r f a c e m a s s t r a n s f e r c o e f f i c -i e n t ( k ) f o r t h e s a n d b e d u s e d was c a l c u l a t e d b y E q . ( 7 8 ) 2 ( C h . 3) t o b e 128 l b m . / f t . h r . a t m . , a n d t h e h e a t t r a n s f e r c o e f f i c i e n t ( h ) b y E q . ( 7 9 ) ( C h . 3) t o b e 4 3 . 0 1 - 4 3 . 4 7 B T U / h r . f t . 2 o F . V a l u e s o f e f f e c t i v e m a s s d i f f u s i v i t y ( D ) a n d t h e r m a l d i f f u s i v i t y ( a ) w e r e o b t a i n e d b y s e a r c h i n g f o r t h e v a l u e r e q u i r e d i n E q . ( 5 3 ) ( m a s s t r a n s f e r ) a n d E q . ( 7 6 ) ( h e a t t r a n s f e r ) t o g i v e t h e b e s t ( l e a s t s q u a r e s ) f i t b e t w e e n t h e o r e -T A B L E 3. SUMMARY OF E X P E R I M E N T A L R E S U L T S Run No. U / U m f I .M.C. % B e d . Temp. T b T i m e R e q u i r e d t o A t t a i n = 1 5 % M.C. 9 ( h r . ) D r y i ng Di r e c t i on 1 1.2 86 217 18 y 12 1.2 88 204 25 y 2 1.2 89 190 38 y 3 1.2 81 217 60 z 10 1.2 85 2 0 4 85 z 4 1 .2 85 217 8 y + z 5 1.2 91 204 14 y + z 6 1.2 8 4 190 2 4 . 5 y + z 9 1.2 85 175 35 y + z ' 7 1.1 87 217 8.5 y + z 8 1.3 7 8 . 5 217 8.5 y + z 11 ( n o b e d ) 1.2 8 5 217 25 y + z cn cn 10« . . . . . . ^ 1 2 3 4 5 6 7 8 9 10 11 time 9 (hr) • +•» C C D •»-< C o o 0) 3 «>-• c/> "5 E 80 704-60+ 504 40| 30+ 20+ 10 FIG.16 M O I S T U R E C O N T E N T vs. T I M E IN T W O -- D I M E N S I O N A L D R Y I N G run nos. 4 f o ) and 11 (•) experimental data \ airflow rate - 1.56 ft/Sec=1.2 Umf V — theoretical data no bed, drying air temp. 217°F fluidized bed, at 217°F 8 9 10 time 0(hrs) CT) CO 90 80+ \ V > \ a 1^ C o c o o <D k. 3 +-» w o E 704-60 f 50 f 404-30 20 FIG.17 M O I S T U R E C O N T E N T v s . T I M E O N E D I M E N S I O N A L D R Y I N G ( Y D I R E C T I O N ) -+-2 3 theoretical values • experimental data bed temp. T b - 190 °F -+-4 7 8 v time (MhrsJ 10 11 90+ 80 ( V S -0) -s-> C CD 70f 560f O (1) w. =50] cv) o E 404 FIG.18 M O I S T U R E C O N T E N T v s . T I M E IN O N E D I M E N S I O N A L D R Y I N G ( Z D I R E C T I O N ) theoretical values o experimental data bed temp. Tb= 204 °F 30 201 7 8 9 time 9-(1rirs.) 10 n vs. TIMp ECTIONS exp. data v O theoretical values run no. 4 1 3 direction Y + Z Y Z bed temp. T b=2l7 e^ air flow=L2 Umf O o o Q O 6 7 . 8 9 time 0(hrs.) 10 11 EFFECT OF BED TEMPERATURE ON DRYING RATE Fig.20 IN TWO DIMENSIONAL DRYING D R Y I N G R A T E S W I T H A N D W I T H O U T F L U I D I Z E D F i g 2 1 B E D ( T W O - D I M E N S I O N A L D R Y I N G ) 120+ 100+ <b v . E I'D £ 80 03 U) 40+ 20] fluidized bed _ y Run no 4 -f- • no bed, at 217°F Jf -• n 6 0 , . , 8 0 moisture content (0/0) d.b. Fi s 2 2 D R Y I N G T I M E vs. B E D F O R M O I S T U R E R A N G E ( ~ 9 0 t o 15%) T E M P E R A T U R E ( t w o - d i m e n s i o n a l d r y i n g ) 40 \~ <b 30 time c 20-10-1 1 1 ^  170 180 190 200 210 220 b e d t e m p e r a t u r e T b v F) 75 TEMPERATURE HISTORY OF "LUMBER Tu 1" 3/; "^v; +t run no 5 ; T 0 =204 # F ; air f l o w , U = 1.2 Umf ; 2lU 2" (experimental) 2004-> .CO 1804-Fig.24 A V E R A G E W O O D T E M P E R A T U R E vs. T I M E IN T W O -- D I M E N S I O N A L D R Y I N G * " v experimental data A theoretical values run. no. 5 bed temp. \- 204°F air flow rate U=1.2 Umf <7> time88- (hrs.? 10 11 T A B L E 4. P R O P E R T I E S OF THE F L U I D I Z E D BED D i a m e t e r o f p a r t i c l e s ( d p ) M i n i m u m f l u i d i z a t i o n v e l . ( U m f ) H e i g h t o f b e d a t U m f ( L m f ) H e i g h t o f s e t t l e d b e d ( L m ) V o i d f r a c t i o n a t U ^ ( e m f ) O p e r a t i n g v e l o c i t i e s ( U ) H e i g h t o f e x p a n d e d b e d ( L f ) V o i d f r a c t i o n a t U ( e ^ ) B u l k d e n s i t y o f s a n d ( p b ) P a r t i c l e d e n s i t y o f s a n d ( P s a n c | ) S p e c i f i c h e a t o f s a n d ( c p s a n c j ) 0 . 7 1 8 mm (-20 +30 m e s h ) 1.3 f t . / s e c . 1 7 " 1 6 " 0 . 4 6 1 . 4 3 , 1 . 5 6 , a n d 1.69 f t . / s e c 2 0 " , 2 2 " , a n d 2 3 " 0 . 6 , 0 . 6 4 , a n d 0.65 8 9 . 0 l b m . / f t . 3 1 6 4 . 2 l b m . / f t . 0.191 B T U / l b m . ° F T A B L E 5. P R O P E R T I E S OF WESTERN HEMLOCK 78 S p e c i f i c g r a v i t y ( o v e n - d r y b a s i s ) - 0.4 ( 3 5 , p . 1 4 ) D e n s i t y o f w e t w o o d ( 1 6 , p . 1 6 7 ) ^ 30 l b m . / f t . 3 ('32.5% M.C.) ( p s ) S p e c i f i c h e a t o f w e t w o o d * 0 . 4 2 B T U / l b m . ° F ( 1 6 , p . 2 4 6 ) ( 3 2 . 5 % M.C.) ( C ) p s T h e r m a l c o n d u c t i v i t y ( 3 5 , p . 1 1 2 ) * 0.08 B T U / f t . h r . ° F ( 3 2 . 5 % M.C.) ( k s ) T A B L E 6. F L U I D I Z E D B E D - T O - S U R F A C E HEAT T R A N S F E R C O E F F I C I E N T S h ( B T U / f t . 2 h r . ° F ) C A L C U L A T E D BY EQ. ( 7 9 ) B e d T e m p . A i r V e l o c i t y h R u n No. °F U / U m f B T U / f t . 2 h r . ° F 4 2 1 7 1.2 4 2 . 3 5 2 0 4 1 .2 4 3 . 3 6 190 1.2 4 3 . 4 9 17 5 1.2 4 3 . 4 7 217 1.1 4 3 . 0 8 217 T. 3 4 3 . 5 11 ( b e d ) 217 1.2 4.2 79 t i c a l a n d e x p e r i m e n t a l r e s u l t s . T h e d i f f u s i v i t y v a l u e s t h u s o b t a i n e d f o r e a c h r u n a r e t a b u l a t e d i n T a b l e ( 7 ) . F i g u r e ( 2 5 ) g i v e s a c o m p a r i s o n b e t w e e n m a s s d i f f u s i v i -t i e s f o u n d i n t h i s w o r k a n d v a l u e s o b t a i n e d b y o t h e r i n v e s t i -g a t o r s ( 3 7 , p . 1 2 8 ) . B i g g e r s t a f f ( 3 7 ) m e a s u r e d t h e r a t e s o f d r y i n g o f s m a l l , s p e c i m e n s o f E a s t e r n H e m l o c k s a p w o o d f r o m t h e f i b e r s a t u r a t i o n p o i n t t o t h e o v e n - d r y c o n d i t i o n a t t e m p e r a t u r e s r a n g i n g f r o m 5 0 ° t o 1 2 0 ° C . A f o r c e d - c o n v e c -t i o n o v e n was u s e d t o d r y t h e s a m p l e s . D i f f u s i o n c o e f f i c i e n t s w e r e c a l c u l a t e d f r o m t h e s q u a r e o f t h e l o s s i n m o i s t u r e - t i m e b a s i s . T h e s e n s i t i v i t y o f t h e M.C. v e r s u s t i m e p r e d i c t i o n t o t h e v a l u e o f d i f f u s i v i t y i s i l l u s t r a t e d i n F i g . ( 2 6 ) , a n d o f w o o d t e m p e r a t u r e v e r s u s t i m e p r e d i c t i o n t o t h e v a l u e o f t h e r m a l d i f f u s i v i t y i n F i g . ( 2 7 ) . TABLE 7. VALUES OF E F F E C T I V E MASS D I F F U S I V I T Y (D) AND THERMAL D I F F U S I V I T Y ( a ) FOUND BY LEAST SQUARE F I T OF T H E O R E T I C A L AND EXPERIMENTAL DRYING CURVES Mass T h e r m a l Run 1 No. Bed Temp. T b °F Moi s t u r e Range % O p e r a t i n g A i r V e l o c i t y U / U m f Di r e c t i on o f D r y i n g -Di f f us i v i t y D • 1 0 4 f t . 2 / h r . Di f f u s i ' a-10' f t . 2 / h i 1 217 ( 4 7 . 1 - 1 5 ) 1.2 y 1.4 -12 204 ( 5 8 - 1 5 ) 1.2 y 1.2 -2 190 ( 6 7 - 2 0 ) 1 .2 y 1.0 -3 217 ( 6 2 - 3 7 . 5 ) 1 .2 z 1.4 -10 204 ( 6 9 - 4 5 ) 1.2 z 1.2 -4 217 ( 3 2 - 1 5 ) 1.2 y +' z 1.4 2.5 5 204 ( 4 5 - 1 5 ) 1.2 y + z 1.2 3.0 6 190 ( 6 8 - 1 5 ) 1.2 y + z 1.0 3.5 9 175 ( 6 4 - 1 5 ) 1 .2 y + z 0.8 4.0 7 217 ( 3 3 - 1 5 ) 1.1 y + z 1 .4 2.0 8 217 ( 3 3 - 1 5 ) 1.3 y + z 1.4 2.5 11 (no b e d ) 217 ( 6 3 - 2 3 ) 1.2 y + Z 1 .4 2.5 D I F F U S I O N C O E F F I C I E N T S F R O M - L I T E R A T U R E ( 3 7 , FIG.5 ) A N D D I F F U S I O N C O E F F I C I E N T S F O U N D IN T H I S W O R K vs. D R Y I N G T E M P E R A T U R E • . from literature M.C.RANGE (26-0%) O our values M.C. RANGE (77-15%) 28 27 S E N S I T I V I T Y O F A V E R A G E W O O D T E M P . vs. T I M E P R E D I C T I O N T O V A L U E S O F T H E R M A L D I F F U S I V I T Y . experimental data (oC = 0.0035 ft/jl(.) theoretical values . (oc = 0.004 f U r ) (oU 0.003 -n- ) (ot= 00035 -u- J 5 -+-8 9 time 6- (hrs) C H A P T E R 5 D I S C U S S I O N OF R E S U L T S 5.1 C o n t r o l l i n g M e c h a n i s m T h e d r y i n g c u r v e s i n F i g . ( 2 0 ) , w h i c h a r e d r a w n f r o m t h e d a t a i n F i g . ( 1 5 ) , s h ow t w o s t a g e s : a c o n s t a n t r a t e p e r i o d , f o l l o w e d b y a f a l l i n g r a t e p e r i o d . H o w e v e r , t h e f i r s t m o i s t u r e m e a s u r e m e n t was m a d e a f t e r o n e o r two h o u r s o f d r y i n g s o t h a t t h e s h a p e o f t h e M.C. v e r s u s t i m e c u r v e s ( F i g s . 1 5 , 1 7 , a n d 1 8 ) d u r i n g t h e i n i t i a l o n e o r t w o h o u r s , w h e n t h e c o n s t a n t - r a t e p e r i o d m i g h t h a v e e x i s t e d , i s n o t k n o w n . A c c o r d i n g t o d r y i n g t h e o r y , t h e d r y i n g r a t e d u r i n g t h e f i r s t p e r i o d i s g o v e r n e d b y e v a p o r a t i o n o f m o i s t u r e f r o m t h e s o l i d s u r f a c e , a n d d u r i n g t h e s e c o n d p e r i o d b y d i f f u s i o n o f b o u n d w a t e r t h r o u g h t h e s o l i d . T h e s u r f a c e t e m p e r a t u r e o f w o o d , e s t i m a t e d b y e x t r a p o l a t i n g t h e m e a s u r e d t e m p e r a t u r e p r o f i l e s ( F i g . 23 a n d A p p e n d i x B, T a b l e s I t o X I I ) , r o s e t o v a l u e s h i g h e r t h a n t h e a d i a b a t i c s a t u r a t i o n t e m p e r a t u r e o f t h e d r y i n g a i r i n l e s s t h a n h a l f a n h o u r . T h u s , t h e c o n s t a n t -r a t e p e r i o d , i f i t e x i s t e d , l a s t e d o n l y f o r a v e r y s h o r t t i m e . A b o v e t h e f i b e r s a t u r a t i o n p o i n t ( F . S . P . - 3 0 % M.C. ( 1 6 ) ) , t h e c e l l c a v i t i e s c o n t a i n v a r y i n g a m o u n t s o f f r e e w a t e r , b u t t h e y a r e n e v e r f i l l e d w i t h i t . H o w e v e r , t h e c e l l w a l l s a r e s a t u r a t e d w i t h w a t e r . As l o n g a s t h e c e l l w a l l s a r e s a t u r a t e d w i t h w a t e r , no u n b a l a n c e d f o r c e e x i s t s w h i c h 84 85 w o u l d t e n d t o c a u s e d i f f u s i o n f r o m r e g i o n s o f h i g h c o n c e n -t r a t i o n t o t h o s e o f l o w c o n c e n t r a t i o n ( 3 5 ) . T h e a g r e e m e n t o b t a i n e d b e t w e e n e x p e r i m e n t a l a n d t h e o r e -t i c a l v a l u e s o f M . C , s t a r t i n g a f t e r o n e o r t w o h o u r s o f d r y i n g ( F i g . 1 5 ) s u g g e s t s t h a t a p p a r e n t F . S . P . c o u l d be a s h i g h a s 6 5 % M.C. a t t h e l o w e r d r y i n g t e m p e r a t u r e u s e d . I t i s p o s s i b l e t h a t d u r i n g t h e f i r s t p e r i o d , a b o v e t h e f i b e r s a t u r a t i o n p o i n t , d r y i n g was g o v e r n e d b y t h e e x t e r n a l m a s s t r a n s f e r r a t e a s w e l l a s b y t h e i n t e r n a l m o v e m e n t o f f r e e w a t e r f r o m t h e c e l l c a v i t i e s . I n v i e w o f t h e d i f f i c u l t y i n j u d g i n g w hen t h e c o n s t a n t r a t e p e r i o d e n d e d , i t was a s s u m e d i n a l l c a l c u l a t i o n s t h a t t h e f a l l i n g r a t e p e r i o d s t a r t e d a f t e r o n e o r t w o h o u r s o f d r y i n g , e v e n t h o u g h a t h i g h t e m p e r a -t u r e s ( 2 1 7 ° F , - 2 0 4 ° F , F i g . 1 5 ) i t a c t u a l l y s t a r t e d e a r l i e r . 5.2 E f f e c t o f O p e r a t i n g V a r i a b l e s 1. B e d t e m p e r a t u r e T h e s t r o n g i n f l u e n c e o f b e d t e m p e r a t u r e on d r y i n g r a t e c a n be s e e n f r o m t h e d a t a i n F i g . ( 1 5 ) w h i c h h a v e b e e n r e -p l o t t e d i n F i g . ( 2 2 ) as d r y i n g t i m e f o r t h e m o i s t u r e r a n g e - 80 t o 1 5 % v e r s u s b e d t e m p e r a t u r e . F i g . ( 2 2 ) s h o w s t h a t i n c r e a s i n g t h e b e d t e m p e r a t u r e f r o m 1 7 5 ° F t o 2 1 7 ° F c a u s e d t h e d r y i n g t i m e t o d e c r e a s e f r o m 35 h r s . t o 8 , h r s . T h e . e f f e c t o f b e d t e m p e r a t u r e i s r e f l e c t e d i n d i f f u s i v i t y v a l u e s ( T a b l e 7 ) , w h i c h i n c r e a s e d f r o m 0 . 0 0 0 0 8 f t . 2 / h r . a t 1 7 5 ° F t o 0 . 0 0 0 1 4 f t . 2 / h r . a t 2 1 7 ° F . 86 2. A i r f 1 o w r a t e V a r i a t i o n i n a i r f l o w r a t e up t o 3 0 % a b o v e t h e m i n i m u m f 1 u i d i z a t i o n r a t e h a d l i t t l e e f f e c t o n d r y i n g t i m e a s s h o w n i n T a b l e ( 3 ) . I t was o b s e r v e d t h a t a t a n o p e r a t i n g v e l o c i t y 2 0 % a b o v e U ^ , t e m p e r a t u r e s a t d i f f e r e n t l o c a t i o n s i n t h e b e d w e r e v e r y u n i f o r m . E i t h e r i n c r e a s i n g o r d e c r e a s i n g t h e a i r f l o w r a t e (U = 1.3 U m f o r U = 1.1 U m f ) c a u s e d t e m p e r a t u r e d i f f e r e n c e s t o a r i s e w i t h i n t h e b e d , a l t h o u g h i n a p p e a r a n c e t h e b e d s e e m e d t o be a s w e l l f l u i d i z e d a s a t U = 1.2 U m f 3. F l u i d i z e d b e d - d r y i n g v e r s u s a i r - d r y i n g F i g u r e s ( 1 6 ) a n d ( 2 1 ) s h o w t h e e f f e c t o f t h e p r e s e n c e o f t h e f l u i d i z e d b e d o n d r y i n g t i m e . B o t h r u n s w e r e o p e r a t e d a t t h e s a m e b e d t e m p e r a t u r e s ( T ^ = 2 1 7 ° F ) , t h e same a i r f l o w r a t e (U = 1.2 U m f = 1.56 f t . / s e c ) , a n d t h e s a m e I . M . C . ( 8 5 % ) . W i t h o u t t h e b e d , t h e t i m e r e q u i r e d t o t a k e m o i s t u r e down t o 1 5 % was 25 h o u r s ( o b t a i n e d b y e x t r a p o l a t i o n ) w h i l e w i t h t h e b e d , t h e t i m e r e q u i r e d was o n l y 8 h o u r s . T h i s c o m p a r i s o n u n d e r l i n e s t h e m a i n a d v a n t a g e o f d r y i n g l u m b e r i n a f l u i d i z e d b e d o f i n e r t p a r t i c l e s w h i c h a r i s e s f r o m t h e much h i g h e r h e a t t r a n s f e r c o e f f i c i e n t s o b t a i n a b l e w i t h f l u i d i z e d b e d s ( 4 3 B T U / h r . f t . ° F , s e e T a b l e 6) t h a n w i t h c o n v e c t i v e h e a t t r a n s -f e r ( 4 B T U / h r . f t . 2 ° F ) . k P S" 1 As p o i n t e d o u t e a r l i e r , t h e c o n s t a n t C = n 0  P S o i n E q . ( 4 5 . 1 ) , u s e d i n f i n d i n g t h e m a s s t r a n s f e r e i g e n v a l u e s , i s a l w a y s l a r g e a n d i n f a c t a p p r o a c h e s i n f i n i t y . T h i s i m p l i e s 87 t h a t t h e i n t e r n a l r e s i s t a n c e t o m a s s t r a n s f e r i n w o o d (<*• D~ ) u n d e r c o n n e c t i v e d r y i n g c o n d i t i o n s i s a l w a y s m u c h g r e a t e r t h a n t h e e x t e r n a l r e s i s t a n c e ( = k . " * ' ) . I n o t h e r w o r d s , t h e d i f f u s i o n m o d e l p r e d i c t s t h a t t h e d r y i n g p r o c e s s i n t h e f a l l i n g - r a t e p e r i o d s h o u l d b e i n d e p e n d e n t o f t h e e x t e r n a l e n v i r o n m e n t . I t s h o u l d t h e r e f o r e b e e x p e c t e d t h a t f o r a g i v e n d r y i ng t e m p - e r a s u r e , t h e a v e r a g e m o i s t u r e c o n t e n t - t i m e c u r v e s f o r d i f f e r e n t f l u i d i z e d b e d v e l o c i t i e s , a n d e v e n i n t h e a b s e n c e o f t h e b e d , s h o u l d y i e l d t h e s a m e d i f f u s i v i t y v a l u e s . A s c a n b e s e e n f r o m T a b l e ( 7 ) ( r u n n o s . 7, 8, 4, a n d 1 1 ) t h i s i s i n d e e d t h e c a s e . T h e g o o d a g r e e m e n t o b t a i n e d b e t w e e n t h e e x p e r i m e n t a l a n d t h e o r e t i c a l r e s u l t s , a n d t h e i n s e n s i t i v i t y o f d i f f u s i v i t y v a l u e s t o c h a n g e s i n t h e e x t e r -n a l c o n d i t i o n s , w o u l d s e e m t o s u b s t a n t i a t e t h e v a l i d i t y o f t h e d i f f u s i o n m o d e l f o r t h e f a l l i n g - r a t e p e r i o d . A l t h o u g h t h e e x t e r n a l c o n d i t i o n s h a v e no o b s e r v a b l e e f f e c t o n d r y i n g d u r i n g t h e f a l l i n g - r a t e p e r i o d , t h e y a r e o b v i o u s l y o f g r e a t i m p o r t a n c e a t t h e b e g i n n i n g o f d r y i n g a s s h o w n b y t h e much m o r e r a p i d i n i t i a l d r y i n g i n t h e f l u i d i z e d b e d t h a n i n a i r a l o n e ( F i g . 1 6 ) . 5.3 Q u a l i t y T e s t s I n o r d e r t o c h e c k t h e q u a l i t y o f d r i e d w o o d , f i v e w o o d s a m p l e s a f t e r d r y i n g w e r e t e s t e d ( b y M a c M i l l a n B l o e d e l R e s e a r c h L t d . ) . T h e r e s u l t s o f t h e t e s t a r e s h o w n i n T a b l e ( 8 ) . I t c a n b e s e e n f r o m T a b l e ( 8 ) t h a t t h e b l o c k s o f W e s t e r n H e m l o c k d r i e d a t b e d t e m p e r a t u r e o f 2 0 4 ° F a n d b e l o w d i d n o t 88 s u f f e r a n y d e f e c t s d u r i n g d r y i n g , w h i l e t h e ' q u a l i t y o f w o o d d r i e d a t 2 1 7 ° F was a d v e r s e l y a f f e c t e d . A p h o t o g r a p h i l l u s t -r a t i n g t h e a p p e a r a n c e o f s a m p l e s s u b j e c t e d t o t h e s t r e s s t e s t i s s h o w n i n F i g . ( 2 8 ) . T A B L E 8. R E S U L T S OF Q U A L I T Y T E S T S ON F L U I D I Z E D BED D R I E D WOOD Run No. B e d Temp. (°F) D r y i n g T i m e ( h r . ) M o i s t u r e R a n g e (%) Q u a l i t y 13 1 9 0 ° F = 25 =80-=15 No d r y i n g d e f e c t s 14 2 0 4 ° F = 14 =80-=15 No d r y i n g d e f e c t s 15 2 0 4 ° F = 15 - 8 0 - « 1 5 No d r y i ng d e f e c t s 16 2 1 7 ° F = 8 = 80-=15 D r y i n g d e f e c t s 1. C a s e h a r d e n i ng 2. V e r y s m a l l a n d n a r r o w h o n e y c o m b i n g 3. Same s u r f a c e c h e c k s 17 2 1 7 ° F =9 - 9 0 - ^ 1 5 D r y i n g d e f e c t s 1. C a s e h a r d e n i ng 2. V e r y s m a l l a n d n a r r o w h o n e y c o m b i n g 5.4 T h e o r y V e r s u s E x p e r i m e n t 1. M a s s t r a n s f e r F i g u r e s ( 1 5 ) , ( 1 7 ) , a n d ( 1 8 ) s how g o o d a g r e e m e n t b e t w e e n m e a s u r e d m o i s t u r e c o n t e n t s o f w o o d d u r i n g d r y i n g a n d v a l u e s c a l c u l a t e d b y t h e t h e o r e t i c a l m o d e l d e s c r i b e d i n C h a p t e r 3. S i m i l a r a g r e e m e n t was o b t a i n e d f o r a l l o t h e r r u n s 90 a l s o , d e t a i l e d d a t a f o r w h i c h a r e p r e s e n t e d i n A p p e n d i x B. T h e e f f e c t i v e d i f f u s i v i t y D f o r e a c h r u n , w h i c h i s t h e v a l u e r e q u i r e d i n E q . ( 5 3 ) t o g i v e t h e b e s t f i t b e t w e e n t h e t h e o r e -t i c a l c u r v e s a n d t h e e x p e r i m e n t a l d a t a , a r e t a b u l a t e d i n T a b l e ( 7 ) . T h e m a g n i t u d e o f t h e s e v a l u e s , a s w e l l a s t h e i r t e m p e r a t u r e d e p e n d e n c e , i s c o n s i s t e n t w i t h p u b l i s h e d v a l u e s o f d i f f u s i v i t y o f wa t e r i n wood, as can be seen i n F i g , ( 2 5 ) . I t h a s b e e n f o u n d t h a t a f t e r a g i v e n d r y i n g t i m e , t h e a v e r a g e m o i s t u r e c o n t e n t d u r i n g t w o - d i m e n s i o n a l d r y i n g ( M . C . y Z ) a p p r o x i m a t e l y e q u a l s t h e p r o d u c t o f a v e r a g e m o i s t u r e c o n t e n t s d u r i n g d r y i n g i n t h e y d i r e c t i o n ( M .C. ) a n d i n t h e z d i r e c t i o n ( M . C . ) . T h e t h e o r e t i c a l b a s i s f o r t h e a b o v e f i n d i n g i s t h e f o l l o w i n g e q u a t i o n , ( 3 8 , p . 8 0 ) : X = f(fi|)f(5|) 81 I L f o r d i f f u s i o n c o n t r o l l e d d r y i n g o f a r e c t a n g u l a r b a r o f t h i c k -n e s s 21 a n d w i d t h 2 L , w i t h s e a l e d e n d s , w h e r e X = f r a c t i o n o f w a t e r u n r e m o v e d , d i m e n s i o n i e s s . ~ C o n s i d e r f o r e x a m p l e t h e d a t a f o r r u n n o s . 4, 1, a n d 3 ( A p p e n d i x B) i n t h e f i r s t 8 h o u r s o f d r y i n g , p r e s e n t e d i n T a b l e ( 9 ) . D a t a f o r t h e o t h e r r u n s ( A p p e n d i x B) s h o w a s i m i l a r b e h a v i o r . I t was a l s o f o u n d t h a t d i f f u s i o n c o e f f i c i e n t s i n y , z , a n d y + z d i r e c t i o n s ( T a b l e 7) w e r e t h e same f o r t h e same b e d t e m p e r a t u r e . 91 T A B L E 9. COMPARISON BETWEEN E X P E R I M E N T A L ( M . C . y z ) AND C A L C U L A T E D M O I S T U R E CONTENTS FOR BED T E M P . = 2 1 7 ° F AND U = 1.2 U -T i m e ( h r . ) M . C . y (%)• M.C. •(*) M - C y z (*) M.C.y x M . C . Z (X) 1 47.1 6 8 ( e x t r a p . ) 32 31 .9 2 39 6.2 24 2 4 . 2 3 36 60 21 2 1 . 6 4 3 3 . 5 6 8 . 1 19 1 9 . 5 5 31 .5 5 6 . 6 18 1 7 . 8 6 29 .6 55 . 1 17 1 6 , 3 7 2 7 . 8 5 4 . 2 16 15.1 8 2 6 . 3 53 15 14 2. H e a t t r a n s f e r G o o d a g r e e m e n t was o b t a i n e d b e t w e e n e x p e r i m e n t a l a n d t h e o r e t i c a l a v e r a g e w o o d t e m p e r a t u r e s as i l l u s t r a t e d i n F i g . ( 2 4 ) a n d s h o w n b y t h e d a t a i n A p p e n d i x B. T h e a v e r a g e t h e r m a l d i f f u s i v i t y a f o r e a c h r u n was d e t e r m i n e d , a s f o r m a s s t r a n s -f e r , b y m a t c h i n g t h e t h e o r e t i c a l c u r v e w i t h e x p e r i m e n t a l d a t a . T h e r e s u l t s f o r t w o - d i m e n s i o n a l d r y i n g a r e t a b u l a t e d i n T a b l e ( 7 ) . T h e s e n s i t i v i t y o f t h e a v e r a g e w o o d t e m p e r a -t u r e v e r s u s t i m e p r e d i c t i o n t o t h e v a l u e o f t h e r m a l d i f f u s i -v i t y i s s h o w n i n F i g . ( 2 7 ) . T h e v a l u e s o f a f o u n d i n t h i s w o r k ( 0 . 0 0 2 - 0 . 0 0 4 f t . / h r . ) a r e o f t h e s a m e o r d e r a s t h e v a l u e 9 2 c a l c u l a t e d f r o m w o o d p r o p e r t i e s i n l i t e r a t u r e (a = ^ s / p s C p S = 0 . 0 0 6 ) . T h e i n v e r s e d e p e n d e n c e o f t h e r m a l d i f f u s i v i t y a w i t h w o o d t e m p e r a t u r e f o u n d i n t h i s w o r k w o u l d b e e x p l a i n e d i f k s i n c r e a s e s w i t h t e m p e r a t u r e a t a s l o w e r r a t e t h a n C p S -3. D i s t r i b u t i o n o f m o i s t u r e d u r i n g d r y i n g F i g u r e s ( 2 9 ) a n d ( 3 0 ) s h ow t y p i c a l d i s t r i b u t i o n s o f m o i s t u r e c o n t e n t w i t h i n t h e w o o d e n b l o c k i n t h e y a n d z d i r e c t i o n s a f t e r o n e h o u r a n d two h o u r s o f d r y i n g r e s p e c t i v e l y , c a l c u l a t e d b y E q . ( 5 1 ) , a t 2 1 7 ° F w i t h s t a r t i n g M.C. o f 3 2 % -d r y b a s i s , ( c o r r e s p o n d i n g t o e x p e r i m e n t a l r u n n o . 4 ) . S i m i -l a r c u r v e s f o r h o u r l y i n t e r v a l s up t o 8 h r s . a r e i n c l u d e d i n A p p e n d i x D. B e c a u s e o f s y m m e t r y , t h e m o i s t u r e p r o f i l e s a r e g i v e n o n l y f o r o n e q u a d r a n t ( y = 0, &/2; z = 0, L / 2 ) o f t h e b l o c k o f w o o d . No m e a s u r e m e n t s o f m o i s t u r e d i s t r i b u t i o n w i t h i n t h e b l o c k w e r e made b u t a v e r a g e m o i s t u r e c o n t e n t s b a s e d o n t h e p r e d i c t e d p r o f i l e s , c a l c u l a t e d b y E q . ( 5 3 ) , g a v e g o o d a g r e e m e n t w i t h e x p e r i m e n t a l l y o b t a i n e d v a l u e s ( A p p e n d i x . B ) , p r o v i d i n g s u p p o r t f o r t h e v a l i d i t y o f E q . ( 5 1 ) . 93 0, T H E T A = 1 . O H R S , .0 F.g.29. DISTRIBUTION OF MOISTURE IN WOOD THETfl = 2 . O H R S . .0 Fig.30. DISTRIBUTION OF MOISTURF IN WOOD C H A P T E R 6 COMPARISON WITH K I L N DRYING 6.1 D r y i n g T i m e T a b l e ( 1 0 ) s h o w s c o m p a r a t i v e r e s u l t s o f d r y i n g H e m l o c k i n a f l u i d i z e d b e d a n d i n a k i l n a t a p p r o x i m a t e l y t h e same a i r d r y b u l b t e m p e r a t u r e . T h e k i l n d r y i n g d a t a f o r 2 " x l 0 " x 3 ' ( e n d - c o a t e d ) W e s t e r n H e m l o c k a r e t h o s e r e p o r t e d b y S o l o m o n ( 3 4 ) who w o r k e d w i t h an e x p e r i m e n t a l k i l n o f i n t e r n a l s i z e 3 f t . w i d e x 3 f t . l o n g x 6 f t . d e e p . T h e d r y i n g t i m e i n t h e f l u i d i z e d b e d i s s e e n t o b e much s m a l l e r t h a n i n t h e . k i l n . T h e a i r v e l o c i t y i n t h e k i l n ( 3 4 ) i s m u c h g r e a t e r t h a n i n t h e f l u i d i z e d b e d , b u t t h e c a l -c u l a t e d h e a t t r a n s f e r c o e f f i c i e n t f o r t h e k i l n ( h = 15.1 2 B T U / h r . f t . ° F ) i s m u c h s m a l l e r t h a n f o r t h e f l u i d i z e d b e d ( h = 43 B T U / h r . f t . 2 o F ) , d u e t o t h e c o n t r i b u t i o n o f p a r t i c l e c o n v e c t i o n t o f l u i d i z e d b e d h e a t t r a n s f e r . N o t e t h a t t h e a i r w e t b u l b t e m p e r a t u r e d u r i n g t h e k i l n d r y i n g was -1-ower t h a n d u r i n g f l u i d i z e d bed d r y i n g . I n a d d i t i o n , t h e u n i f o r m a n d e a s i l y c o n t r o l l e d t e m p e r a -t u r e o f a f l u i d i z e d b e d s h o u l d g i v e m o r e u n i f o r m d r y i n g a n d h e n c e , s h o u l d r e s u l t i n b e t t e r q u a l i t y o f d r i e d l u m b e r . 6.2 E c o n o m i c s A c o n c e p t u a l . s c h e m e f o r f l u i d i z e d b e d d r y i n g o f l u m b e r 9 4 T A B L E 1 0 . F L U I D I Z E D BED V S . K I L N DRYING OF HEMLOCK T e m p e r a t u r e A i r F1 ow T i m e R e q u i r e d t o D r y B u l b Wet B u l b 0 I.M.C. D r y t o 1 5 % M.C. f t . 3 f t . ( ° F ) ( ° F ) mi n . s e c . (%) ( h r . ) F l u i d i z e d b e d * 2 0 4 = 88 1 8 . 7 2 1.56 85 14 K i l n ( 3 4 ) 1 6 0 - 2 1 8 1 5 0 - 2 0 0 5 4 0 0 10 60 80 * D a t a f o r r u n n o . 5. 96 o n t h e i n d u s t r i a l s c a l e i s c o s t e d i n T a b l e ( 1 1 ) . T h e f o l l o w -i n g d e s i g n b a s i s was u s e d f o r s i z i n g a n d c o s t i n g t h e d r y i n g p l a n t : 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 0 . C a p a c i t y : 36 m i l l i o n F B M / y r . w h e r e F e e t B o a r d M e a s u r e ( F B M ) i s a u n i t = T ' x T ' x T M o i s t u r e r a n g e : 9 1 % ( d r y - b a s i s ) t o 1 5 % ( d r y - b a s i s ) D r y i n g a i r t e m p e r a t u r e D r y i n g t i m e B a t c h s i z e L o a d i n g a n d u n l o a d i n g t i m e W o r k i n g d a y s / y r . B e d m a t e r i a l . A i r v e l o c i t y ( = 1 . 2 u " m f ) S i z e o f f l u i d i z e d b e d , b a s e d o n 1" s p a c i n g b e t w e e n b o a r d s . 2 0 4 ° F 14 h r s . 5 1 4 0 p i e c e s o f l u m b e r , 2 " x 4 " x 2 0 ' 2 h r s . 350 -20 +30 m e s h s a n d 1.56 f t . / s e c . 30 f t . d i a . x 30 f t . T h e c a p i t a l c o s t o f a n e q u i v a l e n t k i l n d r y i n g f a c i l i t y ( 3 d o u b l e k i l n s , 36 m i l l i o n F B M / y r . ) i s e s t i m a t e d a t $ 6 0 0 , 0 0 0 a n d i t s o p e r a t i n g c o s t a t $10/MFBM ( 4 2 ) . T h u s t h e f l u i d i z e d b e d i s s e e n t o o f f e r a c o n s i d e r a b l e e c o n o m i c a d v a n t a g e i n c a p i t a l c o s t . N o t e t h a t MFBM i s a u n i t = 1 0 0 0 ( T ' x T ' x l ' ) l u m b e r . T A B L E 1 1 . ECONOMICS OF F L U I D I Z E D BED D R Y I N G OF LUMBER - C A P I T A L COST D e s c r i p t i on C o s t ( $ ) 1. E q u i p m e n t c o s t * 3 0 ' d i a . x 3 0 ' h i g h . m.s. p l u s b l o w e r , d i r e c t f i r e d h e a t e r , c y c l o n e s , p i p i n g d u c t i n g . v e s s e l a i r a n d 158,000 2. I n s t a l l a t i o n c o s t * i n c l . s u p p o r t s s t r u c t u r e , e l e c t r i c a l s , i n s u l a -t i o n , c o n t r a c t o r s f e e ( 1 0 0 % o f e q u i p -m e n t c o s t ) 158,000 3. L o a d i n g - u n l o a d i n g e q u i p m e n t c o s t ( r e f . 41.) 1 0 0 , 0 0 0 C a p i t a l C o s t i 416,000 * C o s t d a t a t a k e n f r o m r e f e r e n c e ( 40, 1967) and up-dated u s i n g t h e M a r s h a l a n d S t e v e n ' s i n f l a t i o n i n d e x f r o m C h e m i c a l E n g i n e e r i n g . T A B L E 1 1 . ( C O N T I N U E D ) t O P E R A T I N G COST I t e m U s a g e U n i t P r i c e C o s t ( $ / y r . ) 1. E l e c t r i c i t y f o r a i r blower 52200 c f m a t 17 p s i 15,000,000 k w h / y r . 1.2 c/kwh 180,000 2. F u e l c o s t * 52200 c f m f r o m 7 0 ° F t o 2 5 0 ° F 58,000 x io 6 B T U / y r . $ 4 . 1 0 / 6 . 3 x l O 6 BTU 38,000 3. M a i n t e n a n c e c o s t ( 5 % o f c a p i t a l c o s t ) 20,800 4. L a b o r c o s t 1 m a n / s h i f t $ 8 / h r . 67,000 5. S u p e r v i s i o n ( 3 0 % o f . l a b o r c o s t ) 20,000 6. D e p r e c i a t i o n c o s t ( 1 0 % o f c a p i t a l c o s t ) 41,600 O p e r a t i n g C o s t 370,000 * $10/MFBM * F u e l c o n s u m p t i o n h a s b e e n e s t i m a t e d w i t h o u t a l l o w i n g f o r r e c y c l i n g o f t h e a i r , a n d t h e r e f o r e r e p r e s e n t s t h e u p p e r l i m i t o f h e a t r e q u i r e m e n t . N o t e t h a t $4.10/6.3 x 1 0 6 BTU i s f o r n e t h e a t i n g v a l u e , based on e q u i v a l e n t p r i c e o f o i l and n a t u r a l g a s . C H A P T E R 7 C O N C L U S I O N S T h e f o l l o w i n g c o n c l u s i o n s c a n b e d r a w n f r o m t h e r e s u l t s o f t h i s i n v e s t i g a t i o n . 1. T h e t i m e t a k e n t o d r y W e s t e r n H e m l o c k o f 2 " x 4 " s i z e i m m e r s e d i n a f l u i d i z e d b e d o f s a n d a t 2 0 4 ° F , f r o m a m o i s t u r e c o n t e n t o f 9 1 % ( d r y - b a s i s ) t o 1 5 % , was f o u n d t o b e 14 h o u r s a s a g a i n s t 25 h o u r s f o r a i r d r y i n g w i t h a i r t e m p e r a t u r e o f 2 1 7 ° F a n d a t a i r v e l o c i t y o f 1.56 f t . / s e c . 2. t h e r a t e o f d r y i n g s h o w e d a m a r k e d i n c r e a s e w i t h i n c r e a s i n g f l u i d i z e d b e d t e m p e r a t u r e ( r a n g e s t u d i e d : 1 7 5 - 2 1 7 ° F ) , b u t w o o d d r i e d a t b e d t e m p e r a t u r e s a b o v e 2 0 4 ° F s u f f e r e d a l o s s i n q u a l i t y , e v i d e n c e d b y c a s e -h a r d e n i n g , s u r f a c e c h e c k i n g a n d s m a l l a n d n a r r o w h o n e y c o m b i n g i n t h e i n t e r i o r o f t h e w o o d . 3. V a r i a t i o n i n a i r f l o w r a t e up t o 3 0 % a b o v e t h e m i n i m u m f l o w r e q u i r e d f o r f l u i d i z a t i o n d i d n o t s h o w a n y n o t i c e a b l e e f f e c t o n t h e r a t e o f d r y i n g . 4. T h e t e m p e r a t u r e a n d m o i s t u r e h i s t o r y o f w o o d d u r i n g d r y i n g s u g g e s t e d t h a t i n d r y i n g f r o m = 8 5 % t o 1 5 % m o i s t u r e , t h e c o n s t a n t r a t e p e r i o d , i f i t e x i s t e d , l a s t e d f o r a v e r y s h o r t p e r i o d (< 1/2 h r . ) . 5. A t h e o r e t i c a l m o d e l t o d e s c r i b e t h e d r y i n g p r o c e s s 99 100 i n t h e f a l l i n g r a t e p e r i o d , b a s e d o n l i q u i d d i f f u s i o n f o r i n t e r n a l m a s s t r a n s f e r , was f o r m u -l a t e d . T h e m o d e l t a k e s i n t o a c c o u n t s i m u l t a n e o u s t r a n s f e r o f h e a t , e x t e r n a l l y b y c o n v e c t i o n a n d - i n t e r n a l l y b y c o n d u c t i o n . P r e d i c t i o n s f r o m t h e m o d e l , w i t h a s s i g n e d v a l u e s o f m a s s d i f f u s i v i t y a n d t h e r m a l d i f f u s i v i t y , s h o w e d g o o d a g r e e m e n t w i t h e x p e r i m e n t a l d a t a o n v a r i a t i o n o f m o i s t u r e c o n t e n t a n d t e m p e r a t u r e ( a v e r a g e v a l u e s f o r t h e b l o c k ) w i t h d r y i n g t i m e . M o i s t u r e p r o f i l e s w i t h i n t h e d r y i n g b l o c k w e r e a l s o c a l c u l a t e d . J T h e d i f f u s i v i t y v a l u e s r e q u i r e d f o r o b t a i n -i n g t h e b e s t f i t b e t w e e n t h e o r e t i c a l p r e d i c t i o n s a n d e x p e r i m e n t a l r e s u l t s w e r e f o u n d t o be c o n s i s t e n t w,i t h l i t e r a t u r e v a l u e s f o r w o o d , f o r b o t h m a s s a n d h e a t d i f f u s i o n . A r o u g h e s t i m a t e o f t h e c o s t o f f l u i d i z e d b e d d r y -i n g o n t h e i n d u s t r i a l s c a l e s h o w s t h a t t h e m e t h o d o f f e r s s u b s t a n t i a l e c o n o m i e s i n t h e c a p i t a l c o s t when compared w i t h t h e c o n v e n t i o n a l k i l n d r y i n g p r o c e s s . The opera-t i n g c o s t works o u t t o a v a l u e s i m i l a r t o t h a t f o r k i l n d r y i n g , b u t i s l i k e l y t o be r e d u c e d by improvements i n t h e d e s i g n o f the f l u i d i z e d bed d r i e r , e.g. use o f a r e c t a n g u l a r u n i t , p o s i t i o n i n g t h e lumber h o r i z o n t a l l y i n t h e d r i e r , r e c i r c u l a t i o n o f t h e a i r , e t c . NOMENCLATURE S y m b o l U n i t s mn S u r f a c e a r e a f t . C o e f f i c i e n t o f a s e r i e s i n E q . ( 7 1 ) C o n s t a n t d e f i n e d b y ( E q . 1 0 , C h . 3) C o e f f i c i e n t i n ( E q . 9, C h . 2) b e d t e m p e r a t u r e d e p e n d e n t ' C o n s t a n t d e f i n e d b y ( E q . 1 1 , f t C h . 3) -1 B mn C C* C R C P 9 ^ p s a n d C o e f f i c i e n t o f a s e r i e s i n E q . ( 5 3 ) C o n s t a n t d e f i n e d b y E q . ( 2 3 ) C o n s t a n t i n E q . ( 7 7 ) C o r r e c t i o n f a c t o r o f n o n a x i a l l o c a t i o n o f i m m e r s e d t u b e s , E q . ( 7 9 ) S p e c i f i c h e a t o f w e t w o o d S p e c i f i c h e a t o f g a s S p e c i f i c h e a t o f s a n d P a r t i c l e d i a m e t e r f t . -1 B T U / l b m . ° F B T U / l b m . ° F B T U / l b m . ° F f t . E f f e c t i v e d i f f u s i v i t y o f w a t e r f t . / h r . i n w o o d E f f e c t i v e d i f f u s i v i t y o f w a t e r f t . / h r . v a p o r t h r o u g h d r y w o o d l a y e r 101 102 S y m b o l U n i t s F . S . P . h I.M.C. k k 'Gw a L L, AL, L m f Lm L f Mw M.C. F i b e r s a t u r a t i o n p o i n t H e a t t r a n s f e r c o e f f i c i e n t a c r o s s g a s f i l m I n i t i a l m o i s t u r e c o n t e n t T h e r m a l c o n d u c t i v i t y o f a i r T h e r m a l c o n d u c t i v i t y o f w e t w o o d M a s s t r a n s f e r c o e f f i c i e n t a c r o s s g a s f i l m M a s s t r a n s f e r c o e f f i c i e n t C o n s t a n t i n ( E q . 5, C h . 2) C o e f f i c i e n t s i n ( E q . 8, C h . 2) b e d t e m p e r a t u r e d e p e n d e n t e i g e n v a l u e s = /u 2 + v 2, r n m * H a l f t h i c k n e s s o f w o o d H a l f w i d t h o f w o o d T h i c k n e s s o f w o o d - Wen a n d L o o s m o d e l T h i c k n e s s o f d r y l a y e r H e i g h t o f b e d a t U mf H e i g h t o f s e t t l e d b e d H e i g h t o f e x p a n d e d b e d M o l e c u l a r w t . o f w a t e r M o i s t u r e c o n t e n t B T U / f t . 2 h r . ° F % B T U / f t . h r . ° F B T U / f t . h r . ° F I b m . / h r . f t . a t m . f t . / h r . h r . " 1 f t . ' f t . f t . f t . f t . i rich. i n c h . i n c h . 1 b . m o l e s 103 S y m b o l M . C . y M . C . z M . C . y z m a U n i t s M. M = M ( 9 , y , z ) m m 0 ' m o o m s m c %m M AV A v e r a g e M.C. i n y d i r e c t i o n A v e r a g e M.C. i n z d i r e c t i o n A v e r a g e M.C. i n y + z d i r e c t i o n s A v e r a g e m o i s t u r e c o n t e n t M o i s t u r e c o n t e n t a t t h e c e n t r e o f w o o d M o i s t u r e c o n t e n t ~ a t t h e s u r -f a c e o f w o o d A v e r a g e M.C. c a l c u l a t e d b y E q . ( 8 0 ) D i m e n s i o n l e s s m o i s t u r e c o n t e n t m-m f u n c t i o n o f 0 a n d rru-m ' 0 °° d i r e c t i o n s M o i s t u r e c o n t e n t a t a n y t i m e M o i s t u r e c o n t e n t o f w o o d a t 6 = 0 , a n d 8 -> °°, r e s p e c t i v e l y M o i s t u r e c o n t e n t a t s u r f a c e C r i t i c a l m o i s t u r e c o n t e n t P e r c e n t a g e m o i s t u r e c o n t e n t A v e r a g e m o i s t u r e c o n t e n t , d i m e n s i o n l e s s % % % % % l b m . w a t e r 1 bm. d r y - w o o d l b m . w a t e r l b m . d r y - w o o d l b m . w a t e r l b m . d r y - w o o d 1 bm. w a t e r l b m . d r y - w o o d dm/d9 = D r y i n g r a t e i n f a l l i n g - r a t e ( d m / d e ) ^ a i i p e r i od % / h r , 104 S y m b o l U n i t s m' ( d m / d e ) N. w v p d s s c C o n s t a n t i n E q . ( 7 7 ) D r y i n g r a t e i n c o n s t a n t - r a t e p e r i o d F l u x o f w a t e r v a p o r V a p o r p r e s s u r e a t s u r f a c e P a r t i a l p r e s s u r e o f w a t e r a t s u r f a c e P a r t i a l p r e s s u r e o f w a t e r i n b e d V a p o r p r e s s u r e o f w a t e r a t V a p o r p r e s s u r e o f w a t e r a t P a r t i a l p r e s s u r e o f w a t e r i n g a s V a p o r p r e s s u r e o f w a t e r a t T F l u x o f h e a t t r a n s f e r s c l b m . w a t e r , l b m . d r y - w o o d , h r . 2 1 b m o l e s / h r . f t . a t m . a t m . a t m . a t m . a t m . a t m . a t m . B T U / f t . 2 h r . * Re U d „ p R S c S l S c R e y n o l d s n o . , " y ( l - e f ) d i m e n s i o n l e s s G a s c o n s t a n t S l o p e o f d e s o r p t i o n i s o t h e r m ( E q . 2 0 ) , ( F i g . 6) T h i c k n e s s o f v e n e e r ( E q . 7, C h . 2) S c h m i d t n o . , d i m e n s i o n l e s s G a s d r y - b u l b t e m p e r a t u r e a t m . f t . 3 / l b m o l e s ° F mm 105 S y m b o l U r n t s T S u r f a c e t e m p , d u r i n g e v a p o r a - °F t i o n i n c o n s t a n t - r a t e p e r i o d T^ S u r f a c e t e m p , o f d r y l a y e r °F To Temp, o f i n t e r f a c e b e t w e e n °F w e t a n d d r y l a y e r s T^ B e d t e m p e r a t u r e °F T S u r f a c e t e m p , d u r i n g f a l l i n g - °F r a t e p e r i o d t B e d t e m p . ( E q . 7, C h . 2) °C T . - T T = j — j — , d i m e n s i o n i e s s 1 b ~ ' 0 t e m p e r a t u r e T A v e r a g e t e m p , i n t h e w o o d , °F a ( E q s . 11 , 1 2 , C h . 2) T.wfe) A v e r a g e w o o d t e m p . , d i m e n s i o n -M V l e s s T Temp, a t a n y p o i n t i n s i d e w o o d °F T g I n i t i a l t e m p , o f b l o c k °F U O p e r a t i n g a i r v e l o c i t y f t . / s e c . U m ^ M i n i m u m f l u i d i z a t i o n v e l o c i t y f t . / s e c . un E i g e n v a l u e s - h e a t t r a n s f e r f t . 1 ( y d i r e c t i o n ) v m E i g e n v a l u e s - h e a t t r a n s f e r f t . 1 m 3 ( z d i r e c t i o n ) F r a c t i o n o f m o i s t u r e u n r e m o v e d , d i m e n s i o n i e s s 1 0 6 S y m b o l x D i r e c t i o n o f f l o w a l o n g t h e g r a i n U n i t s f t , D i r e c t i o n o f f l o w a c r o s s t h e g r a i n f t . D i r e c t i o n o f f l o w a c r o s s t h e g r a i n f t . E i g e n v a l u e s - m a s s t r a n s f e r ( y d i r e c t i o n ) f t , 8 m E i g e n v a l u e s - m a s s t r a n s f e r ( z d i r e c t i o n ) -A 2 2 6 n + Qm , e i g e n v a l u e s m a s s t r a n s f e r f t . f t -1 p s a n d P a r t i c l e d e n s i t y o f s a n d B u l k d e n s i t y o f s a n d l b m . / f t , l b m . / f t , w I n i t i a l w t . o f w a t e r p e r u n i t l b m . / f t , v o l u m e M s 0 p V e m f e f a D e n s i t y o f w e t w o o d D e n s i t y o f o v e n - d r y w o o d D e n s i t y o f a i r V i s c o s i t y o f a i r V o i d f r a c t i o n a t U mf V o i d f r a c t i o n a t U = k / p C . t h e r m a l d i f f u s i s s ps v i t y l b m . / f t . l b m . / f t . 3 l b m . / f t . 3 l b m . / f t . h r . f t . V h r . 107 S y m b o l U n i t s 9 T i m e h r . x T i m e , ( E q . 7, C h . 2) s e c . A L a t e n t h e a t o f v a p o r i z a t i o n B T U / l b m . ip, (6) ,^2^5 > F u n c t i o n s o f 9, y , z r e s p e c -t i v e l y - m a s s t r a n s f e r * 3 ( z ) <J>-| (9) . ^ ( y ) » F u n c t i o n s o f 9, y , z r e s p e c -t i v e l y - h e a t t r a n s f e r R E F E R E N C E S 1. L o o s , W.E., F o r e s t P r o d u c t J o u r n a l 21_, 44 ( 1 9 7 1 ) . 2. B a b a i l o v , V . E . a n d P e t r i , V . N . , L e s n o i J o u r n a l 1_, No. 1, 8 5 ( 1 9 7 4 ) . 3. L e v e n s p i e l , 0. a n d K u n i i , D., " F l u i d i z a t i o n E n g i n e e r i n g " , W i l e y & S o n s , I n c . , New Y o r k ( 1 9 7 ) . 4. D a v i d s o n , J . E . a n d H a r r i s o n , D., " F l u i d i z a t i o n " , A c a d e m i c P r e s s , L o n d o n a n d New Y o r k ( 1 9 7 1 ) . 5. Z i e g l e r , E . N . , K o p p e l , L . B . , a n d B r a z e t t o n . W.T., I n d . E n g . C h e m . 3, No. 2, M a y , 9 5 , ( 1 9 6 4 ) ; 3, No. 4, N o v . , 3 2 5 , "("1964) . 6. B r o w n , W.H., "An I n t r o d u c t i o n t o t h e S e a s o n i n g o f T i m b e r " , V o l . 1, P e r g a m o n P r e s s , T h e M a c M i l l a n C o m p a n y , New Y o r k ( 1 9 6 5 ) . 7. P e r r y , R.H., a n d C h i l t o n , C.H., " C h e m i c a l E n g i n e e r s H a n d -b o o k " , F i f t h E d i t i o n , M a c G r a w H i l l , New Y o r k ( 1 9 7 4 ) . 8. P e c k , R . E . , a n d W a s a n , D. T . , A d v a n c e s i n Chem. E n g . 9_, 2 4 7 , 3 0 6 , A c a d e m i c P r e s s ( 1 9 7 4 ) . 9. S h e r w o o d , T . K . , I n d . E n g . Chem., 2J_, 1 2 ( 1 9 2 9 ) . 1 0 . Newman, A . B . , T r a n s . A . I . C h . E . , 27_, 2 1 0 - 3 3 3 ( 1931 )., 1 1 . B r a m h a l l , G., " F i c k ' s Laws a n d B o u n d W a t e r D i f f u s i o n " , ( P a p e r i n P r e s s ) , F o r e s t P r o d u c t R e s e a r c h B r a n c h , D e p a r t m e n t o f F o r e s t r y o f C a n a d a , V a n c o u v e r . 1 2 . C e a g l s k e , N.H., a n d H o u g e n , O.A., T r a n s . A . I . C h . E . , 33_, 2 8 3 ( 1 9 3 7 ) . 1 3 . F u l f o r d , G.D., C a n . J . Chem. E n g . 4 7 , 3 7 8 ( 1 9 6 9 ) . 1 4 . K i s a k u r e k , B . , P e c k , R . E . , a n d C a k a l o z , T . , C a n . J . Chem. E n g . , 53^, F e b r u a r y , 53 ( 1 9 7 5 ) . \ 1 5 . Stamm, A . J . , "Wood a n d C e l l u l o s e S c i e n c e " , R o n a l d P r e s s C o m p a n y , New Y o r k ( 1 9 6 4 ) . „ ' . 1 0 8 109 1 6 . K o l l m a n n , F . F . P . , a n d C d t e , W.A., " P r i n c i p l e s o f Wood S c i e n c e a n d T e c h n o l o g y " , ( I S o l i d W o o d ) , S p r i n g e r -V e r l a g , New Y o r k ( 1 9 6 8 ) . 1 7 . L e b e d e v , P.D., I n t . J . H e a t M a s s T r a n s f e r , 1_, 2 9 4 ( 1 9 6 1 ) . 1 8 . K u m a r , I . J . , a n d N a r a n g , H.N., I n t . J . H e a t M a s s T r a n s -f e r , 9, 9 5 ( 1 9 6 6 ) ; I b i d . , ^ 0 , 1 0 9 5 ( 1 9 6 7 ) . 1 9 . V a l c h a r , J . , p p . 4 0 9 - 4 1 8 i n P r o c . 3 r d I n t e r n a t . H e a t T r a n s f e r C o n f e r e n c e , C h i c a g o , A u g . 1 9 6 6 , ]_, A . S . M . E . -A . I . C h . E . , New Y o r k ( 1 9 6 6 ) , ( c i t e d i n r e f . 1 3 ) . 2 0 . K r i s c h e r , 0., " D i e W i s s e n s c h a f t 1 i c h e n G r u n d l a g e n d e r T r o c k h u n g s t e c h n i k " , 2 n d E d i t i o n , S p r i n g e r , B e r l i n ( 1 9 6 3 ) , ( c i t e d i n r e f . 1 3 ) . 2 1 . L y k o v , A . V . , " H e a t a n d M a s s T r a n s f e r i n C a p i l l a r y -P o r o u s B o d i e s " , P e r g a m o n P r e s s , O x f o r d ( 1 9 6 6 ) , ( c i t e d i n r e f . 1 3 ) . 2 2 . Wen, C.Y., a n d L o o s , W.E., Wood S c i e n c e , ^, No. 2, 87 ( 1 9 6 9 ) . 2 3 . L e v a , M., a n d G r u m m e r , M., I n d . E n g . Chem. 4 0 , 4 1 5 ( 1 9 4 8 ) , ( c i t e d i n r e f . 5 ) . 2 4 . L e v a , M., W e i n t r a u b , M., a n d G r u m m e r , M., Chem. E n g . P r o g r . , 4 5 , 5 6 3 ( 1 9 4 9 ) , ( c i t e d i n r e f , 5 ) . 2 5 . L e v a , M., G e n e r a l D i s c u s s i o n o f H e a t T r a n s f e r , L o n d o n , S e p t e m b e r , ( 1 9 5 1 ) , ( c i t e d i n r e f . 5 ) . 2 6 . Dow, W.M., a n d J a k o b , M., Chem. E n g . P r o g r . 4_7, 6 3 7 ( 1 9 5 1 ) , ( c i t e d i n r e f , 5 ) . 2 7 . V a n H e e r d e n , C , N o b e l , A . P . P . , a n d V a n K r e v e l e n , D.W., Chem. E n g . S c i . J_, No. 2, 51 ( 1 9 5 1 ) , ( c i t e d i n r e f . 5 ) . 2 8 . V a n H e e r d e n , C , N o b e l , A . P . P . , a n d V a n K r e v e l e n , D.W., I n d . E n g . Chem. £ 5 , 1 2 3 7 ( 1 9 5 3 ) , ( c i t e d i n r e f . 5 ) . 2 9 . C a r a h a n , B., L u t h e r , H.A., a n d W i l k e s , J . O . , " A p p l i e d N u m e r i c a l M e t h o d s " , J o h n W i l e y & S o n s , New Y o r k ( 1 9 7 0 ) . 3 0 . C a r s l a w , H.S., a n d J a e g e r , J . C , " C o n d u c t i o n o f H e a t i n S o l i d s " , C l a r e n d o n P r e s s , ( 1 9 4 7 ) . 3 1 . S o l o m a n , M., F o r e s t P r o d u c t L a b , V a n c o u v e r , P e r s o n a l C o m m u n i c a t i o n . no 3 2 . K e e n a n , J . H . , a n d K e y e s , F . G . , " T h e r m o d y n a m i c P r o p e r t i e s o f S t e a m " , J o h n W i l e y & S o n s , New Y o r k ( 1 9 4 8 ) . 3 3 . T o o m e y , R.D., a n d J o h n s t o n e , H . F . , Chem. E n g . P r o g . S y m p o s i u m S e r i e s , 49_, No. 5, 51 ( 1 9 5 3 ) . 3 4 . S o l o m a n , M., F o r e s t P r o d u c t s J o u r n a l , 1 5 , No. 3, 122 ( 1 9 6 5 ) . 3 5 . B r o w n , H.P., P a n s h i n , A . J . , a n d F o r s a i t h , C C , " T e x t -b o o k o f Wood T e c h n o l o g y " , V o l . I I , M c G r a w - H i l l B o o k C o m p a n y , I n c . , New Y o r k ( 1 9 5 2 ) . 3 6 . P a n s h i n , A . J . , a n d Z e e u w , C , " T e x t b o o k o f Wood T e c h n o -l o g y " , V o l . I , M c G r a w - H i l l B o o k C o m p a n y , New Y o r k ( 1 9 6 4 ) . 3 7 . B i g g e r s t a f f , T . , F o r e s t P r o d u c t J o u r n a l , 1 5 , No. 3, 127 ( 1 9 6 5 ) . 3 8 . T r e y b a l , R . E . , " M a s s - T r a n s f e r O p e r a t i o n s " , M c G r a w - H i l l , New Y o r k , ( S e c o n d E d i t i o n ) . 3 9 . W y l i e , C.R., " A d v a n c e d E n g i n e e r i n g M a t h e m a t i c s " , M c G r a w -H i l l B o o k C o m p a n y , New Y o r k ( 1 9 6 0 ) . 4 0 . C l a r k , W.E., C h e m i c a l E n g i n e e r i n g , 7 4 - 1 , No. 6, 1 7 8 ( 1 9 6 7 ) . ~ 4 1 . P e r s o n a l C o m m u n i c a t i o n f r o m D r . V. M a t h u r , M a c M i l l a n B l o e d e l R e s e a r c h , V a n c o u v e r . 42. Tarn, S., " D r y i n g o f Lumber i n a F l u i d i z e d Bed", B.A.Sc. T h e s i s , U.B.C ( 1 9 7 4 ) . A P P E N D I X A COMPUTER PROGRAMS No. 1 A v e r a g e M o i s t u r e C o n t e n t C a l c u l a t e d b y E q . ( 5 3 ) No. 2 A v e r a g e Wood T e m p e r a t u r e C a l c u l a t e d b y E q . ( 7 6 ) No. 3 D i s t r i b u t i o n o f M o i s t u r e C a l c u l a t e d b y E q . ( 5 1 ) Note : Sample computer o u t p u t s a r e p r e s e n t e d i n Ap p e n d i x D. I l l 112 S y m b o l s u s e d i n t h e f o l l o w i n g p r o g r a m m e s : C a l c u l a t i o n o f a v e r a g e m o i s t u r e c o n t e n t - P r o g r a m m e No. 1 LZ s L = 2" LY = I = 1" MA -»- d i m e n s i o n i e s s a v e r a g e m o i s t u r e c o n t e n t i n y + z d i r e c t i o n MCO = M n a v e r a g e e x p t l . m o i s t u r e c o n t e n t a t t h e b e g i n n i n g o f f a l l i n g - r a t e p e r i o d ( l b m . / l b m . d r y w o o d ) MT a v e r a g e t h e o r . M.C. i n t h e w o o d a t a n y t i m e ( l b m . / l b m . d r y - w o o d ) ME •> a v e r a g e e x p t l . M.C. i n t h e w o o d a t a n y t i m e ( l b m . / l b m . d r y - w o o d ) T E T = 6 -> d r y i n g t i m e ( h r s . ) D = D -> d i f f u s i o n c o e f f i c i e n t ( f t . / h r . ) B E T = 3 -> e i g e n v a l u e i n y d i r e c t i o n ( f t . - 1 ) OM = Q -*- e i g e n v a l u e i n z d i r e c t i o n ( f t . - 1 ) MY d i m e n s i o n l e s s a v e r a g e M.C. i n y d i r e c t i o n MZ -* d i m e n s i o n l e s s a v e r a g e M.C. i n z d i r e c t i o n C a l c u l a t i o n o f a v e r a g e w o o d t e m p . - P r o g r a m m e No. 2 TA -*• d i m e n s i o n l e s s a v e r a g e w o o d t e m p , i n y + z d i r e c t i o n TY -> d i m e n s i o n l e s s a v e r a g e w o o d t e m p , i n y d i r e c t i o n T Z d i m e n s i o n l e s s a v e r a g e w o o d t e m p , i n z d i r e c t i o n T T -> a v e r a g e t h e o r . w o o d t e m p , a t a n y t i m e ( y + z d i r e c t i o n s ) , ( ° F ) TE a v e r a g e e x p t l . w o o d t e m p , a t a n y t i m e ( y + z d i r e c t i o n s ) , ( 0 F) PMY = 9 M / 8 y 113 PMZ = 9M/3z T E T T -> t i m e i n t h e m i d p o i n t o f e a c h i n t e r v a l , u s e d t o c a l c u l a t e 9M/8y a n d 8M/3z, ( h r s . ) A L F A = a -»• t h e r m a l d i f f u s i v i t y ( f t . 2 / h r . ) U E u -> h e a t e i g e n v a l u e i n y d i r e c t i o n ( f t . ~ ^ ) V E v •> h e a t e i g e n v a l u e i n z d i r e c t i o n ( f t . " ' ' ) 3. M o i s t u r e d i s t r i b u t i o n i n t h e w o o d - P r o g r a m m e No. 3 TB E -*• b e d t e m p e r a t u r e , ( ° F ) C E k g P v p S " 1 / p s D ( f t ' _ 1 ) MY -> d i mens i o n l e s s m o i s t u r e c o n t e n t a s f u n c t i o n o f y d i r e c t i o n a n d 9 MZ -> d i mens i o n l e s s m o i s t u r e c o n t e n t a s f u n c t i o n o f z d i r e c t i o n a n d 9 M -> d i mens i o n l e s s m o i s t u r e c o n t e n t a s f u n c t i o n o f y z d i r e c t i o n s a n d 6 MC d i s t r i b u t i o n o f m o i s t u r e d u r i n g d r y i n g ( l b m . / l b m . d r y - w o o d ) 114 PROGRRMZ 1*0. I FORTRAN IV G COMPILER MAIN 10-21-75 11:40:31 PAGE 0001 C MAIN PROGRAM 0001 IMPLICIT REAL*8<A-H.O-Z) 0002 DIMENSION OM(2000),BET(2000),TET(50),MEl50),MT(50) 0003 REAL*8 LZ , LY,MY,MZ,MA,MCOtME,MT 0004 READ(5,4) IRUN.TB.C 0005 READ(5,1) II,K 0006 DO 300 J=1,K 0007 READ(5,17) TET(J),ME(J) 0008 17 F0RMATI2F10.5) 0009 300 CONTINUE 0010 TET0=TET(1I 0011 00 400 J = l ,K 0012 TET(J)=TET(J)-TETO 0013 400 CONTINUE 0014 URITE(6,5) IRUN.TB.C 0015 4 FORMAT(14»2F 12.5) 0016 5 FORMAT(1H1,5X,'RUN N0='.I5/3X,•BED TEMP.=•,F10.5/5X,•C='» F12.5/) 0017 WRITEI6.2) 0018 2 FORMAT(7X,'TET ME MT 0 1 SIG'//) 0019 1 FORMAT(214) 0020 MC0=ME(1) 0021 LY=1./12. 0022 LZ=l./6. 0023 DO 3000 1=1,1000 0024 CALL AV(C,X,LY,I) 0025 BET(I)=X 0026 CALL AV(C,X,LZ, I ) 0027 OM(I)=X 0028 3000 CONTINUE 0029 0=0.0 0030 7 D=D+0.00001 0031 SIG=0.0 0032 DO 500 J=1,K 0033 N=l 0034 MY=0.0 0035 13 BETT=BET(N)*LY 0036 • BM=2.*DSIN(BETT)/(SETT+DSIN(2.*BETT)/2.) 0037 FY=D* ( EET t N ) *BET(N) ) 0038 BY=BK*DSIN(BETT)/BETT 0039 XY=BY*DEXP(-FY*TcT(J)) 0040 MY=MY+XY 0041 IF(N.EO.l) GO TO 8 C CHECK THE CONVERGENCE 0042 CON=XY/MY 0043 IF(DABS(CON).LT.0.00001) GO TO 100 0044 IFIN.LT.1000) GO TO 8 0045 WRITE<6,11) 0046 11 FORMAT(IX,'MY NCT CONVERGED") 0047 GO TO 100 0048 8 N=N*1 0049 GO TO 13 0050 100 MZ=0.0 0051 N=l 0052 6 OMT=OM(N)*LZ 0053 BN=2.*DS IN(OMT)/(OMT + OSIN{2.*OMT )/2.) 0054 FZ=D*(CM(N)*OM(N)) 0055 BZ=BN*DSINIOMT)/OMT FORTRAN IV G COMPILER MAIN 10-21-75 0056 XZ=BZ*DEXP(-FZ*TETl J)) 0057 MZ=MZ*XZ 0058 IF(N.EC.l) GO TO 9 : C CHECK THE CONVERGENCE 0059 CON=XZ/MZ 0060 IF(DABS(CCN).LT.0.00001) GC TO 20J 0061 IF(N.LT.IOOO) GO TO 9 0062 WRITE16.12) 0063 12 FORMAT(IX,* HZ NOT CONVERGED') 0064 GO TO 200 0065 9 N=N+1 0066 GO TO 6 C AVERAGE MOISTURE CONTENT 0067 200 MA=MY*PZ 0068 MT(J)=MA*MCO 0069 WRITE16.3) TET(J),ME(J),MT(J) 0070 3 FORMAT(3 F 15.6) 0071 SIGS=( MEUl-MTIJ) ) * (ME (J )-MT (J) J 0072 SIG=SIGS+SIG 0073 500 CONTINUE 0074 WRITE(6,19)D,SIG 0075 19 F0RMATJ45X.2F10.5) 0076 IFID.GT.0.001) GO TO 21 0077 GO TO 7 0078 21 STOP 0079 END TOTAL MEMORY REQUIREMENTS 008A62 BYTES CCMPILE TIME = 0.4 SECONDS 116 FORTRAN IV G COMPILER MAIN C SUBPROGRAM OOOl SUBROUTINE AV(CiX,LiI) 0002 IMPLICIT R2AL*8<A-H.O-Z) 0003 REAL*8 L 0004 F12(A)=A*DTAN(A*L)-C 0005 P 1 = 3.141593 0006 H=0.001 0007 X1=((I-1)*PI/L)+PI/(2.*L>-0.0001 0008 2 X2=X1-H 0009 A1=F12(X1) 0010 A2=F12(X2) 0011 AM=A1*A2 0012 IF(AM.LT.O.O) GO TO 10 0013 X1=X2 0014 C GO TO 2 NEWTON METHOD ITERATION 0015 10 X=lX1*A2-X2*A1)/(A2-A1) 0016 IF<DABS(X-X2J.LT.0.00001) GO TO 7 0017 X1=X2 0018 X2=X 0019 A1=F12(X1) 0020 A2=F12(X2) 0021 GO TO 10 0022 7 RETURN 0023 END TOTAL MEMORY REQUIREMENTS 000396 BYTES COMPILE TIME = 0.1 SECONDS 117 PRQGZaritlE. M>. 2 FORTRAN IV G COMPILER MAIN 1 2 - 0 1 - 7 5 2 2 : 4 8 : 4 7 C MAIN PROGRAM C CALCULATION OF AVERAGE T " M P . IN Y AND Z DIRECTION 0001 IMP ICIT R ~ A L * 8 < A - H . O - Z ) 0002 DIMENSION B E T ( 1 0 0 ) , O M ( 1 0 0 ) , T E T ( 5 0 ) , 1 T E T T ( 5 0 ) , T E ( 5 0 ) , T T ( 5 0 ) , P M Y ( 5 0 ) , P M Z ( 5 0 ) 0003 R c A L * 8 L Y . L Z 0004 READ(0 14) I R U N , T 8 , D , A , 3 0005 W R I T E ( 6 , 5 ) I R U N , T 3 , D 0006 R E A D ( 8 , 1 ) K 0007 4 F 0 R M A T ( I 4 , 4 F 1 0 . 5 ) 0008 1 FORMAT 114) 0009 5 FORM AT{1 H I , 5 X , ' R U N NO . = • , I 5 / 3 X , • BED TEMP, 2 « D = ' , F 1 0 . 5 / > 0010 DO 600 J = 1,K 0011 REA0<3 ,17 ) T ? T ( J ) , T E ( J ) , T E T T ( J ) 0012 17 F O R M A T ( 3 F 1 0 . 5 ) 0013 600 CONTINUE 0014 C = 1 0 0 0 . 0 0015 W R I T E ( 6 , 2 ) 0016 2 FORMAT(7X, ' T E T TE 3ALFA S I G « / / > 0017 L Y = 1 . / 1 2 . 0018 L Z = l . / 6 . 0019 DO 3000 1=1 ,100 0020 CALL E V M ( C , X , L Y , I ) 0021 B E T ( I ) = X 0022 CALL E V M ( C , Y , L Z , I J 0023 OM(I)=Y 0024 W R I T E ( 7 , 7 J X , Y 0025 7 FORMAT12F10 .3 ) 0026 3000 CONTINUE 0027 DO 300 J = 1 , K 0028 SY=0.0 0029 SZ=0 .0 0030 S Y 1 = 0 . 0 0031 S Z 1 = 0 . 0 0032 DO 700 I=1 ,100 0033 B E T T = B E T ( I J * L Y 0034 OMT = OM(I)!<LZ 0035 8 M = 2 . * D S I N ( 8 5 T T ) / ( r 3 E T T + D S I N ( 2 . * B c T T ) / 2 . ) 0036 BN=2 . *0S IN(0MT ) / (OM.T+DS IN ( 2 . * 0 M T J / 2 . J 0037 FY = D<:( EcT( I J"*8c1T ( I J J 0038 FZ = D*t 0 M ( I J * O M ( I ) ) 0039 BY=BM*8ET( IJ * Q S I N ( B E T T ) 0040 B Z = B N * O M ( I ) * D S I N ( O M T » 0041. XY=BY*DEXP ( - F Y f T ^ T T t J 1 J 0042 X Z = B N * O t X P ( - r Z; f : T f : T T (J J J 0043 X Y 1 = B M * D E X P ( - F Y * T 2 T T ( J ) ) 0044 XZ1 = B Z * D E X P { - F Z * T E T T ( J J J 0045 SY=SY+XY 0046 • SZ=SZ+XZ 0047 SY1=SY1+XY1 0048 SZ1=SZ1+XZ1 0049 700 CONTINUE 0050 P M Y ( J ) = S Y * S Z 0051 P M Z ( J ) = S Y 1 * S Z 1 0052 WRITE<9,8) P M Y U J , P M Z ( J ) 0053 8 F O R M A T ( 2 F 1 0 . 5 J 118 FORTRAN IV G COMPILER MAIN 12-01-75 0054 300 CONTINUE 0055 ALFA=0.0 0056 27 ALFA=ALFA*0.0005 0057 T0=TE(1) 0058 TT(1)=TE(11 0059 SIG=0.0 0060 DO 500 J=ltK 0061 N = i 0062 TY=0„0 0063 11=0.0 0064 13 CALL EVH(A,B,PMY(Ji-l) ,LY,U,N) 0065 WRITGU0.22) U 0066 22 FORMAT{F 10.3) 0067 UT=U*LY 0068 3M = 2 . * DS IN (UT ) / (UT +DS INI 2 . *UT ) / 2 . ) 0069 FY=ALFA*(U*U) 0070 BY=8M*DSIMtUT)/UT 0071 XY=BY"*D5XP(-FY) 0072 TY= TY + XY 0073 IF(NoEC.l)' GO TO 88 C CHECK THE CONVERGENCE 0074 CON=XY/TY 0075 IF(DABS(CON).LT.0.00001) GO TO 100 0076 IF(N.LT.IOO) GO TO 88 0077 WRITE(6,11) 0078 11 FORMAT(IX,'TY NCT CONVERGED') 0079 GO TO 100 0080 88 N=N + 1 0081 GO TO 13 0082 100 TZ=0.0 0083 N=l 0084 V=0.0 0085 6 CALL EVH(A,B,PMZ(J+l),LZ,V,N) 0086 WRITE(10,22) V 0087 VT=V*LZ 0088 BN=2o*DSIN(VT)/(VT+DSIN(2.*VTJ/2.) 0089 FZ=ALFA*(V*V) 0090 BZ=BN*DSIN(VTJ/VT 0091 XZ=BZ*DEXP(-FZ) 0092 TZ=TZ+XZ 0093 IF(N.EO.l) GO TO 9 C CHECK THE CONVERGENCE 0094 CON=XZ/TZ 0095 IFlDABS(CON).LT.0.00001) GO TO 200 0096 IF(N.LT.IOO) GO TO 9 0097 WRITE(6,12) 0098 12 FORMAT(IX,'TZ NOT CONVERGED*) 0099 GO TO 200 0100 9 N=N«-1-0101 GO TO 6 C AVERAGE TEMPERATURE 0102 200 TA=TY*TZ 0103 TT(J*-1 )=TB-TA*(T3-T0) 0104 TO=TT(J+l) 0105 WRITEI6.33) TE T(J)» TE(J)» TT(J) 0106 33 FORMAT(3F15.6) 0107 IFJJ.EQ.1) GO TO 500 0108 SIGS=IT5(J)-TT(J))*(T^«J)-TT(J)) 119 FORTRAN IV G COMPILER MAIN 12-01-75 22:48:47 0109 SIG=SIGS+SIG 0110 500 CONTINUE 0111 WRITc(6,19) ALFA.SJG 0112 19 FORMAT(45X,2F10.5) 0113 IF(ALFA.GT.0.01) GO TO 21 0114 GO TO 27 0115 21 STOP 0116 ENO TOTAL MEMORY REQUIREMENTS 001BF6 BYTES COMPILE.TIME = 0.6 SECONDS 1 2 0 FORTRAN IV G COMPILER MAIN 12-01-75 22:48:48 C SUBPROGRAM 0001 SUBROUTINE EVM(C,X,L,I) 0002 IMPLICIT REAL*8(A-H,0-Z) 0003 REAL*8 L 0004 F12(A)=A*DTAN(A*L)-C 0005 PI=3.141593 0006 H=0.001 0007 Xl=(I I-1)*PI/L)+PI/(2.*L)-0.0001 0008 Xl=( I I-1MPI/L )+PI/< 2 . *L)-0.0001 0009 2 X2=X1-H 0010 A1=F12(XU 0011 A2=F12(X2) 0012 AM=A1*A2 0013 IF(AMoLT.O.O) GO TO 10 0014 X1=X2 0015 GO TO 2 C NEWTON METHOD ITERATION 0016 10 X=(X1*A2-X2*«1 ) / (A2-A1) 0017 IF(DABS(X-X2).L'T. 0.00001) GO TO 7 0018 Xi=X2 0019 X2=X 0020 A1=F12(X1) 0021 A2=F12(X2) 0022 GO TO 10 0023 7 RETURN 0024 ENO TOTAL MEMORY REQUIREMENTS 0003D6 BYTES COMPILE TIME = 0.1 SECONDS FORTRAN IV G COMPILER MAIN 1.2-01-75 C SUBPROGRAM 0001 SUBROUTINE EVH U , B, S , L , X , I) 0002 IMPLICIT R5AL*8l4-H.O-Z) 0003 REAL*8 L 0004 F12(G)=G*OSIN(G*L)+A*S-B*DCOS(G*L) 0005 H=l. 0006 IFII.GT.1) GO TO 3 0007 X1=X 0003 GO TO 2. 0009 3 X1=X+1. 0010 2 X2=X1+H 0011 G1=F121X1) 0012 G2=F12(X2) 0013 GM=G1*G2 0014 IF(GM.LT.O.O) GO TO 10 0015 X1 = X2 0016 GO TO 2 C NEWTON METHOD ITERATION 0017 10 X=(X1*G2-X2*S1)/(G2-G1) 0018 IF(DABS(X-X2).LTo0.00001) GO TO 7 0019 X1 = X2 0020 X2 = X 0021 Gl=F12(Xl) 0022 G2=F12(X2) 0023 GO TO 10 0024 7 RETURN 0025 END TOTAL MEMORY REQUIREMENTS 0003E4 BYTES COMPILE TIME = 0.1 SECONDS 122 PRQGRRM VO. 3 **LAST SIGNON WAS: 22:48:45 MGN DEC 01/75 USER "MAYA" SIGNED ON AT 09:42:26 ON MQN OEC 22/75 $LIST M 1 C CALCULATION OF MOISTURE PROFILE IN THE WOOD 2 C MAIN PROGRAM 3 IMPLICIT REAL*8(A-H .O-Z) 4 DIMENSION OM(2000) ,GET12000) ,Y (30 ) , Z(60),MY(30 ), 4.2 5 3 MZ (60 ) , M ( 60 ,60 ) , Y P l 6 0 ) , ZP (60 ) 5 REAL*8 LZ,LY,MY,MZ,MCO 5.25 REAL*4 YP,ZP.M.CN 6 READ(5,4) IRUN,T3,C 7 WRITE(6,5)I RUN,T8 8 4 FORMAT!14,2F 12„5) 9 5 F0RMAT(1H1,5X,'RUN N 0 = ' , I5/3X, ' B E D TEMP=', F10.5/) 13 MCO=0.32 14 D=0«00015 15 LY=1./12. 16 LZ=l./6. 17 DO 3000 1=1,2000 18 CALL AV(C,X,LY,I) 19 BET(I)=X 20 CALL AV(C,X,LZ,I) 21 OM(I)=X 123 22 3000 CONTINUE 22.25 y p ( i ) = 2 . 5 22.5 DO 800 1=2,26 22.6 YPl I ) = YP ( I-D+0.2 22.7 800 CONTINUE 22.8 ZP( 1) = 0.0 22.81 DO 900 J=2,51 22. 82 Z P ( J ) = Z P ( J - l ) + 0 . 2 22,83 900 CONTINUE 23 TET=1.0 24 DO 300 K=l,8 25 Y(1)=0.0 26 DO 400 1=1 ,26 27 N=l 28 MY(IJ =0 o 0 29 13 BETT=BET(N)*LY 30 BM = 2. *DSIN(BETT)/IBETTvDSIN(2.*BETT)/2. ) 31 FY= D*(BET(N)* BET(N ) ) 32 XY=BM*DEXP(-FY*TET)*DCOS(BET(N)*Y( I) ) 33 MY(I)=MYt I )+XY 34 IF{N.E0,1 ) GO TO 8 35 C CHECK THE CONVERGENCE 36 CON=XY/MY(I) 37 IF(DABS(CON).LT.0.0000000001) GO TO 100 38 IF{No LT. 2000) GO TO 8 39 WRITE(6,11) 40 11 FORMAT(IX,'MY NCT CONVERGED') 41 GO TO 100 . 42 8 N=N + 1 43 GO TO 13 44 100 Y( I +1) = Y (I J+LY/25. 45 400 CONTINUE 46 Z(1)=0.0 47 DO 500 J=l , 5 1 48 N=l 49 MZ(J)=0.0 50 6 OMT=OM(N)*LZ 51 BN = 2.*DS!N(OMT)/(OMT + DSIN(2.*OMT)/2. ) 52 FZ=D*(OM(N)*OM(N)) 53 XZ=BN#OEXP(-FZ*TcT)*DCOS(OM(N)*Z(J ) ) 54 MZ(J)=MZ(J)+XZ 55 I F ( N . E Q . l ) GO TO 9 56 C CHECK THE CONVERGENCE 57 CON=XZ/MZ(J) 58 IF(DABS(CON).LT.0.0000000001) GO TO 200 59 IF<N.LT.20001 GO TO 9 60 WR1TE(6,12) 61 12 FORMAT(IX,'MZ NOT CONVERGED' I 62 GO TO 200 63 9 N=N + 1 64 GO TO 6 65 200 Z(J+1)=Z(JJ+LZ/50. 66 500 CONTINUE 67 DO 600 1=1,26 68 DO 700 J=l,51 69 M(J, I ) = MY( I )*MZ(J)*MC0*100, 73. 25 700 CONTINUE 73.5 600 CONTINUE 73.6 . CALL AXISIO.0,2. 5,«Z «,-1, 10.0,0.0,0.0,0.2) 73. 7 CALL PLOT(10.0,2.5,3) 124 73.71 CALL PLOT<10.0,7.5,2) 73.72 CALL PLOT{0.0,7.5,2) 73.82 CALL AXI Sl0.0,2.5,•Y• , 1 , 5 . 0 , 9 0 . 0 , 0 . 0 ,0.2) 73.83 CN=5.0 73. 84 DC 910 I=1 ,6 73.85 CALL CNTQUR( ZP,51, YP, 26,M,60,CN,3.0,CN) 73.86 CN=CN+5.0 73. 87 910 CONTINUE 74.12 CALL SYMBOL(0 o 5 , 8 . 0 , 0 . 2 8, ' T H E TA =',0.0,7) 74.37 CALL NUMBER(2.42,8.0,0.28,TET,0.0,1) 74.62 CALL PLOTl14.0 , 0 .0 , -3 ) 74.87 TET=TET+1.0 74.97 300 CONTINUE 75.25 CALL PLOTND 76 STOP 77 END 78 C SUBPROGRAM 79 SUBROUTINE AV(C,X,L,I) 80 IMPLICIT REAL*6(A-H,0-Z) 81 REAL*8 L 82 F12(A)=A*DTAN(A#L )-C 83 PI=3.141593 84 H=0.001 85 X1=(( I-1)*PI/L)+PI/(2.*L)-0.0001 86 2 X2=X1-H 87 A1=F12(X1) 83 A2=F12(X2) 89 AM=A1#A2 90 IF(AM.LT.O.O) GO TO 10 91 X1=X2 92 GO TO 2 93 C NEWTON METHOD ITERATION 94 10 X=(X1*A2-X2*A1)/(A2-A1) 95 IF(DABS(X-X2).LT.0.00001) GO TO 7 96 X1=X2 97 X2=X 98 A1=F12(M) 99 A2=F12(X2) 100 GO TO 10 101 7 RETURN 104 END END OF FILE $SIG A P P E N D I X B SUMMARY OF E X P E R I M E N T A L DATA AND T H E O R E T I C A L R E S U L T S OF M O I S T U R E CONTENT V S . T I M E AND T E M P E R A -T U R E V S . T I M E FOR B E S T - F I T V A L U E S OF D AND a 1 2 5 T A B L E B - I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 1 Wood T e m p e r a t u r e , ° F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i m e ( h r . ) 1/4" 2 / 5 " 3 / 4 " 1" A v e r a g e V a l u e E x p t l . T h e o r . ( E q 0 61 61 61 61 61 86 0.5 165 1 6 3 1 56 150 1 5 8 . 7 5 1 195 1 9 2 185 180 1 7 6 . 0 4 7 . 1 47.1 2 199 1 9 6 190 185 1 9 2 . 5 3 9 . 0 3 9 . 6 3 203 2 0 0 194 190 1 9 6 . 7 5 3 6 . 0 3 6 . 4 3 4 210 2 0 8 2 0 0 196 2 0 3 . 5 0 3 3 . 5 3 4 . 0 4 5 2 1 4 2 1 2 2 0 4 197 2 0 6 . 7 5 31 .5 3 2 . 0 1 6 215 2 1 3 2 0 5 198 2 0 7 . 7 5 2 9 . 6 3 0 . 0 3 7 216 2 1 5 2 0 9 199 2 0 9 . 7 5 2 7 . 8 2 8 . 6 2 8 2 1 7 2 1 6 200 200 2 1 0 . 5 2 6 . 3 2 7 . 1 4 9 " " " II 2 5 . 0 25 .76 10 n 2 3 . 7 2 4 . 4 8 11 II 2 2 . 4 2 3 . 2 7 12 " " " II 21 .4 22.1 3 13 " " " " II 2 0 . 0 21 .04 14 II 1 9 . 2 2 0 . 0 1 5 1 8 . 0 1 9 . 0 4 16 " 17.1 18.11 17 " " n 1 6 . 3 1 7 . 2 3 18 II 1 5 . 0 1 6 . 3 9 A i r f l o w : U = 1.2 U m f = 1.56 f t . / s e c ; B e d T e m p . , T b = 2 1 7 ° F ; D = 1.4 x 1 0 " 4 f t . 2 / h r . D r y i n g D i r e c t i o n •+ y . T A B L E B - I I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 2 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i me ( h r . ) 1/4" 2 / 5 " 3/4" 1" A v e r a g e V a l u e E x p t l . T h e o r . ( E q . 53) 0 6 0 . 5 6 0 . 5 6 0 . 5 6 0 . 5 6 0 . 5 89 1/2 138 1 3 5 1 2 5 1 1 5 1 2 8 . 2 5 ( e x t r a p . ) 1 1 56 1 53 1 4 5 139 1 4 8 . 2 5 78 2 174 1 7 2 164 1 58 1 6 5 . 2 5 67 ( e x t r a p . ) 6 7 . 0 3 178 176 169 1 6 5 1 7 2 . 2 5 62 6 3 . 0 7 4 181 178 172 169 1 7 5 . 0 60 5 9 . 7 2 5 183 181 177 1 7 2 1 7 8 . 2 5 5 5 . 7 5 6 . 8 8 6 1 8 5 184 180 1 7 6 181 .25 53.1 5 4 . 3 9 7 188 1 8 6 1 8 2 179 1 8 3 . 7 5 51 .0 5 2 . 1 3 8 189 187 183 181 1 8 5 4 8 . 5 50.01 9 189 187 1 8 3 181 185 4 6 . 2 4 8 . 1 3 10 189 1 8 7 183 181 185 4 5 . 0 4 6 . 3 2 11 190 187 183 181 1 8 5 . 2 5 43.1 4 4 . 6 1 1 2 II II II II II 41 .4 4 2 . 9 8 13 II II n II n 4 0 . 0 41 .43 14 n n n n n 38.1 3 9 . 9 5 T A B L E B - I I . ( C O N T I N U E D ) Wood T e m p e r a t u r e , ° F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i m e A v e r a g e ( h r . ) 1 / 4 " 2 / 5 " 3 / 4 " 1" V a l u e E x p t l . T h e o r . ( E q . 5 3 ) 1 5 1 9 0 1 8 7 1 8 3 181 1 8 5 . 2 5 3 6 . 8 3 8 . 5 3 16 • I M M 3 5 . 1 37 . 1 7 17 •t I I n 3 3 . 7 3 5 . 8 6 18 " • I n I I " 3 2 . 4 3 4 . 5 9 19 • I I I H 3 1 . 1 3 3 . 3 8 20 " • I n n " 3 0 . 0 3 2 . 2 2 21 • I I I n 2 8 . 7 31 . 0 8 22 " n I I n 11 2 8 . 0 2 9 . 9 9 23 H n n 2 6 . 7 2 8 . 9 4 24 " H I I I I 2 6 . 0 2 7 . 9 3 25 I I H n 2 4 . 6 2 6 . 9 6 26 " I I I I n " 2 4 . 0 2 6 . 0 1 27 " " 2 2 . 9 2 5 . 1 1 28 " n I I n n 2 2 . 0 2 4 . 23 29 n H I I " 2 1 . 0 2 3 . 3 8 30 1 9 0 1 8 7 1 8 3 181 1 8 5 . 2 5 2 0 . 0 2 2 . 5 7 A i r f l o w : U = 1 . 2 U m f = 1 . 5 6 f t . / s e c ; B e d Temp., T b = 1 9 0 ° F ; D r y i n g D i r e c t i o n -> y D = 1 . 0 x 1 0 ~ 4 f t . 2 / h r . T A B L E B - I I I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 3 Wood T e m p e r a t u r e , ° F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i m e A v e r a g e E x p t l . T h e o r . ( E q . 53) ( h r . ) 1/4" 2 / 5 " 3 / 4 " 1" V a l u e 0 61 61 61 61 61 81 1/2 150 148 137 132 141 .75 6 7 . 9 ( e x t r a p . ) 1 168 165 1 56 1 50 1 5 9 . 7 5 2 172 170 160 155 1 6 4 . 2 4 6 2 . 0 6 2 . 0 3 183 181 173 168 1 7 4 . 0 0 6 0 . 0 6 0 . 2 1 4 192 190 183 175 1 8 2 . 6 6 58.1 5 8 . 4 8 5 197 195 1 8 8 181 188 5 6 . 6 57 .03 6 2 0 2 2 0 2 1 9 4 1 8 8 195 55.1 5 5 . 7 4 7 206 2 0 4 1 9 6 190 1 9 6 . 6 6 5 4 . 2 5 4 . 58 8 212 211 204 197 2 0 4 5 3 . 0 53.51 9 2 1 6 2 1 4 207 199 2 0 6 . 6 6 5 2 . 6 5 2 . 5 2 10 217 2 1 6 209 200 2 0 8 . 0 5 1 . 0 51 .58 11 I I n I I I I I I 50 5 0 . 7 0 12 I I n H I I I I 49 4 9 . 8 6 13 I I I I I I n I I 48 4 9 . 0 6 14 I I I I ii I I I I 4 7 . 5 4 8 . 2 9 T A B L E B - I I I . ( C O N T I N U E D ) Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i me A v e r a g e T h e o r . ( E q . 53) ( h r . ) 1/4" 2/5" 3/4" 1" V a l u e E x p t l . 15 217 216 209 200 208 46. 5 47.55 16 n II n I I 46.2 46.83 17 n II n I I n 45.2 ' 46.15 18 II n I I n 44.5 45.48 19 •I n I I •I II 44.0 44.83 20 •I II II •I 43.0 44.19 21 I I II n n 42.6 43.57 22 •I II I I H n 42.0 42.97 23 II II •I n II 41 .2 42.39 24 n II n H 40.0 41 .81 25 n n n •I 39.9 41 .25 26 n II n n 39.6 40.70 27 n M n n •1 39 40.17 28 n II n H 38. 5 39 .64 29 n II n n 38.2 39.13 30 217 216 209 200 208 37.5 38. 62 A i r F l o w : U = 1.2 U f = 1.56 f t . / s e c ; B e d T e m p . , T b = 2 1 7 ° F ; D i r e c t i o n o f F l o w -»• z D = 1 . 4 x 1 0 " 4 f t . 2 / h r . T A B L E B - I V . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 4 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e A v e r a g e Wood T e m p e r a t u r e T i m e h r . ) 1/4" 2 / 5 " 3 / 4 " 1" E x p t l . T h e o r . ( E q . 53) E x p t l . T h e o r . ( E q 0 61 61 61 61 61 85 1/2 169 167 153 143 158 1 202 200 190 180 193 193 32 32 2 209 207 2 0 0 190 201 .5 1 9 7 . 6 24 2 4 . 5 3 2 1 3 212 2 0 6 1 9 4 2 0 6 . 2 5 2 0 1 . 8 9 21 21 .64 4 2 1 4 2 1 5 208 198 207 2 0 5 . 3 7 19 1 9 . 5 6 5 217 2 1 6 210 200 2 0 8 . 7 5 2 0 8 . 1 1 18 1 7.86 6 217 216 211 200 211 2 1 0 . 2 3 17 1 6 . 4 2 7 n H H II n 2 1 1 . 8 7 16 1 5 . 1 6 8 II II n H 2 1 3 . 1 2 15 1 4 . 0 4 A i r F l o w R a t e : U = 1.2 U m f ; B e d T e m p . , T f a = 2 1 7 ° F ; D r y i n g D i r e c t i o n •*• y + z ; D = 1.4 x 1 0 " 4 f t . 2 / h r . ; a = 2.5 x 1 0 " 3 f t . 2 / h r . T A B L E B-V. E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 5 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e A v e r a g e Wood T e m p e r a t u r e T i m e T h e o r . ( E q . 53) ( h r . ) 1/4" 2 / 5 " 3 / 4 " 1" E x p t l . T h e o r . ( E q . 53) E x p t l . 0 64 64 64 6 4 6 4 91 1/2 1 53 151 140 133 1 4 4 . 2 5 1 175 1 7 3 162 1 56 1 6 6 . 5 1 6 6 . 5 45 4 5 2 187 185 178 170 1 8 0 . 0 1 7 4 . 3 7 36 3 5 . 4 9 3 192 190 185 180 1 8 6 . 7 5 1 8 1 . 5 5 29 31 .84 4 194 1 9 2 187 182 1 8 8 . 7 5 1 8 7 . 2 2 2 7 . 2 2 9 . 1 5 5 196 195 190 185 191 .75 191 .56 25.1 2 6 . 9 6 6 1 9 8 197 193 189 194.2.5 1 9 4 . 8 2 2 3 . 5 2 5 . 0 9 7 199 198 195 1 9 2 1 9 6 . 0 1 9 7 . 2 6 22 2 3 . 4 5 8 200 199 196 194 1 9 7 . 2 5 199 .06 2 0 . 5 21 .98 9 2 0 4 202 198 1 9 5 1 9 7 . 7 5 2 0 0 . 3 9 1 9 . 3 2 0 . 6 5 10 I I H n n H 201 .68 1 8 . 3 1 9 . 4 3 11 I I n I I n H 1 7 . 6 1 8 . 3 0 12 n H n n H 16.8 17 .26 13 I I I I n 15.8 1 6 . 2 8 14 204 202 198 195 1 9 7 . 7 5 15.0 1 5 . 3 8 A i r F l o w R a t e : U = 1.2 U f = 1.56 f t . / s e c ; B e d Temp., T b = 2 0 4 ° F ; D = 1.2 x 10 f t . 2 / h r . a = 3.0 x 1 0 " 3 f t . 2 / h r . ; D r y i n g D i r e c t i o n -> y + z. T A B L E B - V I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 6 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e A v e r a g e Wood T e m p e r a t u r e T i m e ( h r . ) 1/4" 2 / 5 " 3 / 4 " 1" E x p t l . T h e o r . ( E q . 76) E x p t l . T h e o r . ( E q . 53) 0 60 60 60 60 60 84 1/2 142 140 130 120 1 3 3 1 1 6 5 163 153 148 1 5 7 . 2 5 1 5 7 . 2 5 68 ( e x t r a p . ) 6 8 2 172 170 160 1 56 1 6 4 . 5 1 6 4 . 5 1 55 5 4 . 8 2 3 178 176 166 164 171 .1 1 7 1 . 1 1 48 4 9 . 7 3 4 1 8 5 . 1 8 3 172 1 6 5 1 7 6 . 2 5 1 7 6 . 2 3 44 4 5 . 9 6 5 188 186 176 170 1 8 0 . 1 0 1 8 0 . 0 5 41 .8 4 2 . 8 8 6 190 1 8 8 180 174 1 8 2 . 9 1 8 2 . 8 5 3 8 . 0 4 0 . 2 4 7 190 188 183 179 1 8 4 . 9 1 8 4 . 8 9 3 6 . 8 3 7 . 9 2 8 190 1 8 8 1 8 5 1 8 2 1 8 6 . 4 1 8 6 . 3 6 3 4 . 5 3 5 . 8 3 9.5 - " " " " " 1 8 9 . 9 2 32 3 3 . 0 4 11 " " " " 29 3 0 . 5 7 1 2 . 5 " " " 27 2 8 . 3 5 1 5 . 5 " " 24 2 4 . 4 9 1 6 . 5 " " . " 23 2 3 . 3 5 1 7 . 5 " " " 21 .5 2 2 . 2 6 19 " " 20 2 0 . 7 5 20 " " " 19 1 9 . 7 9 2 1 . 5 " " " " " 18 1 8 . 4 6 2 2 . 5 " " " 17 1 7 . 6 3 2 3 . 5 " " " " 16 1 6 . 8 3 2 4 . 5 190 1 8 8 185 182 1 8 6 . 4 15 1 6 . 0 7 A i r F l o w R a t e : U = 1.2 U m f = 1.56 f t . / s e c ; B e d T e m p . , T b = 1 9 0 ° F ; D r y i n g D i r e c t i o n -*• y + z D = 1.0 x 1 0 ' 4 f t . 2 / h r . ; a = 3.5 x 1 0 " 3 f t . 2 / h r . T A B L E B - V I I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 7 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % T i m e ( h r . ) D i s t a n c e f r o m 1/4" 2 / 5 " Su r f a c e 3 / 4 " 1" A v e r a g e E x p t l . Wood T e m p e r a t u r e T h e o r . ( E q . 76) E x p t l . T h e o r . ( E q . 53) 0 71 71 71 71 71 87 1/2 1 7 8 175 160 152 1 6 6 . 2 5 44 1 209 2 0 5 1 9 5 185 1 9 8 . 5 5 1 9 8 . 5 5 33 33 2 212 2 0 9 2 0 0 192 2 0 0 . 3 1 201 .76 25 2 5 . 4 9 3 2 1 4 211 2 0 3 195 2 0 5 . 7 2 0 4 . 8 1 22 2 2 . 6 4 4 2 1 6 2 1 4 206 198 2 0 8 . 4 2 0 7 . 3 6 1 9 . 5 2 0 . 5 4 5 2 1 7 2 1 5 206 202 2 1 0 . 0 2 0 9 . 4 2 18.6 1 8 . 8 4 6 217 2 1 6 2 1 0 2 0 5 2 1 2 . 0 211 .06 1 7 . 5 1 7 . 3 9 7 217 216 2 1 0 2 0 5 2 1 2 . 0 2 1 2 . 3 6 1 6 . 8 1 6 . 1 2 8.5 2 1 7 216 210 2 0 5 2 1 2 . 0 1 1 3 . 9 8 1 5 . 0 1 4 . 5 A i r F l o w R a t e : U = 1.3 U f = 1.69 f t . / s e c ; B e d Temp., T f a = 2 1 7 ° F ; D r y i n g D i r e c t i o n y + z ; D = 1.4 x 1 0 " 4 f t . 2 / h r . ; a = 2.0 x 1 0 " 3 f t . 2 / h ' r . C O T A B L E B - V I I I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 8 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e A v e r a g e Wood T e m p e r a t u r e T i me ( h r . ) 1 /4" 2 / 5 " 3 / 4 " 1" E x p t l . T h e o r . ( E q . 76) E x p t l . T h e o r . ( E q . 0 62 62 62 62 62 7 8 . 5 0.5 179 1 7 7 162 154 1 6 8 * 1 204 201 191 180 194 194 3 3 . 0 33 2 211 2 0 8 200 192 200 1 9 7 . 5 9 2 4 . 0 2 5 . 5 3 2 1 4 . 5 2 1 1 . 5 2 0 3 1 9 5 2 0 3 . 1 6 2 0 1 . 3 6 2 1 . 5 2 2 . 6 4 4 2 1 5 2 1 3 207 199 206 .3 2 0 4 . 6 1 9 . 5 2 0 . 5 4 5 2 1 6 2 1 4 209 200 2 0 7 . 6 2 0 7 . 2 5 18.6 1 8 . 8 4 6 2 1 7 2 1 6 211 201 2 0 9 . 3 2 0 9 . 3 9 17.0 1 7 . 3 9 7 2 1 7 2 1 6 211 201 2 0 9 . 3 211 .08 1 6 . 5 1 6 . 1 2 8.5 217 2 1 6 211 201 2 0 9 . 3 2 1 2 . 8 2 15 1 4 . 5 0 A i r F l o w R a t e : U = 1.1 U m f = 1.43 f t . / s e c ; B e d Temp., T b = 2 1 7 ° F ; D r y i n g D i r e c t i o n -> y + z ; D = 1.4 x 1 0 ~ 4 f t . 2 / h r . ; a = 2.5 x 1 0 " 3 f t . 2 / h r . T A B L E B - I X . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 9 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e A v e r a g e Wood T e m p e r a t u r e i me h r . ) 1/4" 2 / 5 " 3/4" 1" E x p t l . T h e o r . ( E q . 76) E x p t l . T h e o r . ( E 0 61 61 61 61 61 85 1/2 126 124 113 105 117 77 ( e x t r a p . ) 1 148 1 4 5 134 127 1 3 8 . 5 1 3 8 . 5 2 155 152 143 137 1 4 6 . 8 1 4 4 . 7 64 6 4 3 162 159 150 147 1 5 4 . 5 1 5 5 . 5 57 5 8 . 5 4 168 166 156 152 1 6 0 . 5 1 5 8 . 8 5 4 . 2 5 5 . 2 5 172 170 162 155 1 6 4 . 7 1 6 2 . 9 50 5 1 . 5 6 174 172 165 160 1 6 7 . 8 1 6 6 . 7 47 4 8 . 5 7 175 174 168 163 170 1 6 8 . 9 45.1 4 6 . 2 8 175 174 170 1 6 7 1 7 1 . 4 1 7 7 . 5 4 3 . 2 4 4 . 2 11 175 174 171 170 1 7 2 . 5 1 7 4 . 2 8 38 3 8 . 5 15 175 174 171 170 1 7 2 . 5 1 7 5 . 9 1 3 2 . 7 3 3 . 4 19 " " " " " 29 3 0 . 2 22 " 2 5 . 3 2 5 . 8 26 " " " 22 21 .5 28 11 20 1 9 . 2 31 " " 18 17.1 33 " " 1 6 . 5 15.2 35 175 1 7 4 171 170 1 7 2 . 5 15 14 A i r F l o w R a t e : U = 1.2 U m f = 1.56 f t . / s e c ; B e d T e m p . , T b = 1 7 5 ° F ; D r y i n g D i r e c t i o n •*• y + z D = 0.8 x 1 0 " 4 f t . 2 / h r . ; a = 2 x 1 0 " 3 f t . 2 / h r . T A B L E B-X. E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 10 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i me ( h r . ) 1/4" 2 / 5 " 3 / 4 " 1" A v e r a g e V a l u e E x p t l . T h e o r . ( E q . 5 3 ) 0 71 71 71 71 71 85 1/2 1 152 1 50 139 1 3 2 1 4 3 . 2 5 2 166 163 151 1 4 4 1 5 6 . 0 3 177 175 165 1 58 1 6 8 . 7 5 69 .0 ( e x t r a p . ) 6 9 . 0 4 186 183 175 1 6 7 1 7 7 . 7 5 67 .0 ( e x t r a p . ) 6 7 . 6 4 5 195 193 182 174 1 8 6 . 0 0 6 6 . 0 6 6 . 0 9 6 199 197 186 179 1 9 0 . 2 5 64.1 6 4 . 7 4 7 200 198 187 180 1 9 1 . 5 0 63.1 6 3 . 5 1 8 202 200 190 1 8 4 1 9 4 . 0 0 6 1 . 4 6 2 . 3 8 .9 203 201 191 184 1 9 4 . 7 5 6 1 . 0 61 .33 10 2 0 4 202 1 9 2 1 8 5 1 9 5 . 7 5 59.7 6 0 . 3 4 11 I I I I n n • I 5 8 . 4 59.41 12 n n n n I I 5 7 . 4 5 8 . 5 2 13 n I I n n I I 5 6 . 6 5 7 . 6 6 14 I I n I I n I I 5 6 . 0 5 6 . 8 5 T A B L E B-X. ( C O N T I N U E D ) Wood T e m p e r a t u r e , °F A v e r a g e M.C. % D i s t a n c e f r o m S u r f a c e T i me A v e r a g e ( h r . ) 1 / 4 " 2 / 5 " 3 / 4 " 1 " V a l u e E x p t l . T h e o r . ( E q . 5 3 ) 1 5 2 0 4 2 0 2 1 9 2 1 8 5 1 9 5 . 7 5 5 5 . 0 5 6 . 0 7 1 6 " " " n I I 5 4 . 2 5 5 . 3 1 1 7 " " • I H 5 3 . 4 5 4 . 5 8 1 8 " " " I I I I 5 3 . 0 5 3 . 8 7 1 9 " " " n n 5 2 . 0 5 3 . 1 9 2 0 " " I I n 51 . 5 5 2 . 5 1 21 " " I I I I 51 51 . 8 6 2 2 " " " n • I 5 0 . 2 51 . 2 3 2 3 " " " H n 4 9 . 4 5 0 . 6 1 2 4 " n H 4 8 . 7 5 0 . 0 2 5 " I I n 4 8 . 2 4 9 . 4 1 2 6 " " " n it 4 7 . 3 4 8 . 8 2 2 7 " " " I I H 4 7 4 8 . 2 5 2 8 " " n n 4 6 . 6 4 7 . 7 0 2 9 " 11 n n 4 5 . 7 4 7 . 1 5 3 0 2 0 4 2 0 2 1 9 2 1 8 5 1 9 5 . 7 5 4 5 . 0 4 6 . 6 1 A i r F1 ow: D = 1 . 2 x U = 1 l O " 4 • 2 U m f = f t . 2 / h r . 1 . 5 6 f t . / s e c . ; B e d T e m p . , T ^ = = 2 0 4 ° F ; D r y i n g D i r e c t i o n z ; T A B L E B - X I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 11 (NO BED) Wood T e m p e r a t u r e , ° F A v e r a g e M.C. % T i m e ( h r . ) D i s t a n c e f r o m S u r f a c e 1 / 4 " 2 / 5 " 3 / 4 " 1 " A v e r a g e E x p t l . Wood T e m p e r a t u r e T h e o r . ( E q . 7 6 ) E x p t l . T h e o r . ( E q . 5 3 ) 0 6 1 6 1 6 1 6 1 6 1 8 5 1 1 9 3 1 9 3 2 2 0 1 1 9 7 . 5 5 6 3 6 2 . 6 3 2 0 6 . 5 2 0 1 . 8 2 5 6 5 5 . 6 4 2 0 7 . 0 2 0 5 . 2 9 5 0 5 0 . 4 5 2 0 9 . 0 2 0 8 . 0 4 4 5 4 6 . 2 6 2 1 0 . 0 2 1 0 . 1 7 4 3 4 2 . 7 7 2 1 1 . 0 2 1 1 . 8 2 3 9 3 9 . 6 8 2 1 1 . 0 2 1 3 . 0 8 3 7 3 6 . 8 9 I I 2 1 3 . 8 4 3 4 3 4 . 3 1 0 - n 3 1 . 5 3 2 . 0 1 1 n - 3 0 2 9 . 8 8 1 2 n 2 7 . 5 2 7 . 9 4 1 3 I I 2 6 . 0 2 6 . 1 5 1 4 I I 2 5 . 2 4 . 4 8 1 5 2 1 1 . 0 2 3 2 2 . 9 3 A i r F l o w : U = 1.56 f t . / s e c ; A i r T e m p . , = 2 1 7 ° F ; D r y i n g D i r e c t i o n -> y + z ; D = 1.4 x 1 0 " 4 f t . 2 / h r . ; a = 2.5 x 1 0 " 3 f t . 2 / h r . T A B L E B - X I I . E X P E R I M E N T A L AND T H E O R E T I C A L DATA FOR RUN NO. 12 Wood T e m p e r a t u r e , °F A v e r a g e M.C. % T i m e D i s t a n c e f r o m S u r f a c e A v e r a g e ( h r . ) 1/4" 2 / 5 " 3 / 4 " 1" V a l u e ' E x t p l . T h e o r . ( E q . 53) 0 60 60 60 60 60 88 1/2 152 149 137 130 142 72 ( e x t r a p . ) 1 173 1 70 160 152 1 6 3 . 7 5 58 58 2 185 1 8 3 176 168 178 49 4 9 . 4 3 187 185 178 170 180 45.1 4 5 . 8 4 4 192 189 1 8 4 179 186 4 2 . 3 43.1 1 5 195 192 1 8 7 1 8 3 1 8 9 . 2 5 40 4 0 . 8 6 197 195 190 185 191 .75 37 3 8 . 7 7 7 199 197 193 189 1 9 4 . 5 3 5 . 9 3 6 . 9 3 8 200 198 1 9 5 192 1 9 6 . 2 5 3 4 . 2 3 5 . 24 9 202 199 1 9 6 1 9 3 1 9 7 . 5 3 2 . 4 3 3 . 6 7 10 2 0 4 202 198 195 1 9 9 . 7 5 31 .0 3 2 . 2 2 11 " I I n H 2 9 . 5 3 0 . 8 1 12 " n n n 28.1 2 9 . 4 9 13 I I n I I I I 2 7 . 0 2 8 . 2 4 14 " n H I I n 2 5 . 5 2 7 . 0 5 15 " " I I n H 2 4 . 3 2 5 . 9 1 16 I I I I H 2 3 . 5 2 4 . 8 2 17 11 I I I I I I 2 2 . 3 2 3 . 7 8 18 11 n n I I 2 1 . 3 2 2 . 7 8 19 n n I I 2 0 . 6 21 .83 20 " I I I I M 1 9 . 7 2 0 . 9 2 21 " n I I I I 18.8 20 .04 22 I I I I n 17.8 19.21 23 H n n 17.0 1 8 . 4 0 24 " n H H I I 16.0 1 7 . 6 4 25 2 0 4 2 0 2 198 1 9 5 1 9 9 . 7 5 15 1 6 . 9 A i r F l o w : U = 1.2 U m f = 1.56 f t . / s e c ; D = 1.2 x 1 0 ~ 4 f t . 2 / h r . ; B e d Temp., T = 20.4°F; D r y i n g D i r e c t i o n y . A P P E N D I X C C A L I B R A T I O N CHARTS - I . R o t o m e t e r - I I . M o i s t u r e M e t e r 141 142 150+ 100+ 50t Fig.C-I C A L I B R A T I O N C H A R T F O R T H E R O T A M E T E R tube-- R-12M-25-4 float= 12- RS-221 10 20 30 SC.F.M. air at 7 0 F & 14.7 P . S . I . A p. r CALIBRATION CHART FOR THE l g ' " ELECTRIC MOISTURE METER o 10 20 30 40 50 moisture content,dry basis MC.(%) APPENDIX D No. 1 M o i s t u r e D i s t r i b u t i o n Data by Eq. (51) No. 2 Computer O u t p u t - A v e r a g e M.C. by Eq. (53) No. 3 Computer O u t p u t - A v e r a g e Wood Temp, by Eq. (76) 144 No. .1 M o i s t u r e D i s t r i b u t i o n Data by Eq. (51) 0 J H E T R = 3.0HRS.. P > : »• FIG. I 0,THETfl = 4.0HRS. LEAF 146 OMITTED IN PAGE NUMBERING. I c-l-io d. o e. s 147 148 e.THETfl = 7 . OHRS, 0 . 0 0 . 2 0 . 4 0 . 6 O.B 1.0 1.2 1.4 1.6 l . B 2 .0 2(inch) FIG. VI 149 No. 2 Computer O u t p u t - Ave r a g e M.C. by Eq. (53) RUN NQ= 8 BED TEMP.= 217. C=100000.OOOOO TET ME MT D SIG 0 . 0 0.330000 0.329123 1.000000 0.240000 0.309154 2.000000 0.215000 0.300682 3.OOCOOO 0.195000 0.294248 4.000000 0.186000 0. 283872 5.000000 0.175000 0.284172 6.C00000 0. 170000 0.279951 7.000000 0.165000 0.276094 7.500000 0.150000 0.274276 0 . 0 0.330000 0.329123 1.000000 0.240000 0.300682 2.000000 0.215000 0.288872 3.000000 0.195000 0.279951 4.000000 0.186000 0.272524 5.000000 0.175000 0.266053 6.000000 0.170000 0.260260 7.000000 0. 165000 0.254982 7.500000 0.150000 0.252501 0 . 0 0.330000 0.329123 1.000000 0.240000 0.294248 •2.-OC OOOO 0.215000 0.279951 3.000000 0.195000 0.269189 4.000000 0.186000 0.260260 5.OOCOOO 0.175000 0.252501 6.000000 0.170000 0.245573 7.000000 0.165000 0.239275 7.500000 0. 150000 0.236319 0 . 0 0.330000 ' 0.329123 1.000000 0.240000 0.288872 2.000000 0.215000 0.272524 3.OOOOOC 0.195000 0.260260 4.000000 0.136000 0.250111 5.00 0000 0.175000 0.241313 6.COOOCO 0.170000 0.233475 7.000000 0.165000 0.226365 7.500000 0.150000 0.223034 0 .0 0.330000 0.329123 1.000000 0.240000 0.284172 2.000000 0.215000 0.266053 3.000000 0.195000 0.252501 4.000000 0.1860C0 0.241313 5.000000 0. 175000 0.231637 6.000000 0.170000 0.223034 7.COOOOO 0.165000 0.215244 7.500000 0.150000 0.211599 0 . 0 0.330000 0.329123 1.000000 0.240000 0.279951 2.000000 0.215000 0.260260 0.00001 0.08435 0.00002 0.05888 0.00003 0.04287 0.00004 0.03159 0.00005 0.02326 3.000000 0.195000 0.245573 4.000000 0.186000 0.233475 5.000000 0.175000 0.223034 6.000000 0.170000 0.213768 7.000000 0.165000 0.205392 7.500000 0.150000 0.201478 0.0 0.3300C0 0.329123 1.000000 0.240000 0.276094 2.000000 0.215000 0.254982 3.000000 0.195000 0.239275 4.000000 0.186000 0.226365 5.000000 0.175000 0.215244 6.000000 0.170000 0.205392 7.000000 0.165000 0.196503 7.500000 0.150000 0.192354 0.0 0.330000 0.329123 1.000000 0.240000 0.272524 2.000000 0.215000 0.250111 3.000000 0.195000 0.233475 4.OCOOOO 0.186000 0.219831 5.000000 0.175000 0.208098 6.000000 0.170000 0.197723 7.000000 0. 165000 0.188376 7.500000 0.150000 0.184019 0.0 0.330000 0.329123 1.000000 0.240000 0.269189 2.000000 0.215000 0.245573 3.000000 0.195000 0.228084 4.000000 0.186000 0.213768 5.000000 0.175000 0.201478 6.000000 0.170000 0.190629 '7.000000 0.165000 0.180872 7.500000 0.150000 0.176328 0.0 0.330000 0.329123 1.000000 0.240000 0.266053 2.000000 0.215000 0.241313 3.000000 0. 195000 0.223034 4.000000 0.186000 0.208098 5.000000 .0.175000 0.195299 6.000000 0.170000 0.184019 7.000000 0.165000 0.173889 7.500000 0.150000 0.169177 0.0 0.330000 0.329123 1.OCOGOC 0.240000 0.263083 2.000000 0.215000 0.237292 3.000000 0.195000 0.2182 74 4.000000 0.186000 0.202765 5.000000 0.175000 0.18S496 6.000000 0.170000 0.177820 7.000000 0.165000 0.167351 7.500000 0.150000 0.162488 0.0 0.330000 0.329123 1.000000 0.240000 0.260260 2.000000 0.215000 0.233475 0.00006 0.01696 0.00007 0. 01215 0.00008 0.00848 0.00009 0.00572 0.00010 0.00370 0.00011 0.00229 3 o 0 0 0 0 0 0 0 . 1 9 5 0 0 0 0 . 2 1 3 7 6 8 4 . 0 0 0 0 0 0 0 . 1 3 6 0 0 0 0 . 1 9 7 7 2 3 5 . 0 0 0 0 0 0 0 . 1 7 5 0 0 0 0 . 1 8 4 0 1 9 6 . 0 0 0 0 0 0 0 . 1 7 0 0 0 0 0 . 1 7 1 9 7 8 7 . 0 C C 0 0 0 0 . 1 6 5 0 0 0 0 . 1 6 1 1 9 9 7 . 5 0 0 0 0 0 0 . 1 5 0 0 0 0 0 . 1 5 6 1 9 8 0.0 0 . 3 3 0 0 0 0 0 . 3 2 9 1 2 3 1 . 0 0 0 0 0 0 0 . 2 4 0 0 0 0 0 . 2 5 7 5 6 5 2 . 0 0 0 0 0 0 0 . 2 1 5 0 0 0 0 . 2 2 9 8 4 0 3 . 0 0 0 0 0 0 0 . 1 9 5 0 0 0 0 . 2 0 9 4 8 2 4 . 0 0 0 0 0 0 0 . 1 8 6 0 0 0 0 . 1 9 2 9 3 6 5 . 0 0 0 0 0 0 0 . 1 7 5 0 0 0 0 . 1 7 8 8 2 7 6 . 0 0 0 0 0 0 0 . 1 7 0 0 0 0 0 . 1 6 6 4 5 0 7 . 0 0 0 0 0 0 0 . 1 6 5 0 0 0 0 . 1 5 5 3 8 7 7 . 5 0 0 0 0 0 0 . 1 5 0 0 0 0 0 . 1 5 0 2 6 1 0.0 0 . 3 3 0 0 0 0 0 . 3 2 9 1 2 3 1 . 0 0 0 0 0 0 0 . 2 4 0 0 0 0 0 . 2 5 4 9 8 2 2 . 0 0 0 0 0 0 0 . 2 1 5 0 0 0 0 . 2 2 6 3 6 5 3 . 0 0 0 0 0 0 0 . 1 9 5 0 0 0 0 . 2 0 5 3 9 2 4 . 0 0 0 0 0 0 0 . 1 8 6 0 0 0 0 . 1 8 8 3 7 6 5 . 0 0 0 0 0 0 0 . 1 7 5 0 0 0 0 . 1 7 3 8 8 9 6.O C O O O O 0 . 1 7 0 0 0 0 0 . 1 6 1 1 9 9 7 . 0 0 0 0 0 0 0 . 1 6 5 0 0 0 0 . 1 4 9 8 7 7 7 . 5 0 0 0 0 0 0 . 1 5 0 0 0 0 0 . 1 4 4 6 3 8 0.0 0 . 3 3 0 0 0 0 0 . 3 2 9 1 2 3 1 . 0 0 0 0 0 0 0 . 2 4 0 0 0 0 0 . 2 5 2 5 0 1 2 . 0 0 0 0 0 0 0 . 2 1 5 0 0 0 0 . 2 2 3 0 3 4 3 . 0 0 0 0 0 0 0 . 1 9 5 0 0 0 0 . 2 0 1 4 7 8 4 . 0 0 0 0 0 0 0 . 1 8 6 0 0 0 0 . 1 8 4 0 1 9 5 . 0 0 0 0 0 0 0 . 1 7 5 0 0 0 0 . 1 6 9 1 7 7 6 . 0 0 0 0 0 0 0 . 1 7 0 0 0 0 0 . 1 5 6 1 9 8 7 . 0 0 0 0 0 0 0 . 1 6 5 0 0 0 0 . 1 4 4 6 3 8 7 . 5 0 0 0 0 0 0 . 1 5 0 0 0 0 0 . 1 3 9 2 9 6 0.0 0 . 3 3 0 0 0 0 0 . 3 2 9 1 2 3 1 . 0 0 0 0 0 0 0 . 2 4 0 0 0 0 0 . 2 5 0 1 1 1 2 . C O O O O O 0 . 2 1 5 0 0 0 0 . 2 1 9 8 3 1 3 . 0 0 0 0 0 0 0 . 1 9 5 0 0 0 0 . 1 9 7 7 2 3 4 . 0 0 0 0 0 0 0 . 1 8 6 0 0 0 0 . 1 7 9 8 4 4 5 . 0 0 0 0 0 0 0 . 1 7 5 0 0 0 0 . 1 6 4 6 7 0 6 . 0 0 0 0 0 0 0 . 1 7 0 0 0 0 0 . 1 5 1 4 2 2 7 . 0 0 0 0 0 0 0 . 1 6 5 0 0 0 0 . 1 3 9 6 4 4 7 . 5 0 0 0 0 0 0 . 1 5 0 0 0 0 0 . 1 3 4 2 1 0 0.0 0 . 3 3 0 0 0 0 0 . 3 2 9 1 2 3 1 . 0 0 0 0 0 0 0 . 2 4 0 0 0 0 0 . 2 4 7 8 0 4 2 . 0 0 0 0 0 0 0 . 2 1 5 0 0 0 0 . 2 1 6 7 4 6 3 . 0 0 0 0 0 0 0 . 1 9 5 0 0 0 0 . 1 9 4 1 1 0 4 . 0 0 0 0 0 0 0 . 1 8 6 0 0 0 0 . 1 7 5 8 3 5 5 . 0 0 0 0 0 0 0 . 1 7 5 0 0 0 0 . 1 6 0 3 4 9 6 . 0 0 0 0 0 0 0 . 1 7 0 0 0 0 0 . 1 4 6 8 5 2 7 . 0 0 0 0 0 0 0 . 1 6 5 0 0 0 0 . 1 3 4 8 7 5 7 . 5 0 0 0 0 0 0 . 1 5 0 0 0 0 0 . 1 2 9 3 5 9 0.0 0 . 3 3 0 0 0 0 0 . 3 2 9 1 2 3 1 . 0 0 0 0 0 0 0 . 2 4 0 0 0 0 0 . 2 4 5 5 7 3 2 . 0 0 0 0 0 0 0 . 2 1 5 0 0 0 0 . 2 1 3 7 6 8 0 . 0 0 0 1 2 0 . 0 0 1 3 8 0 . 0 0 0 1 3 0 . 0 0 0 9 1 . 0 . 0 0 0 1 4 0 . 0 0 0 8 0 0 . 0 0 0 1 5 0 . 0 0 1 0 2 0 . 0 0 0 1 6 0 . 0 0 1 5 2 0 . 0 0 0 1 7 0 . 0 0 2 2 5 No. 3 Computer Output - Average Wood Temp, by Eq. RUN NO." 6 BEO TEMP." 190.00000 0» 0.0001 TET TE TT ALFA S I G 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 7.000000 8. 000000 1.000000 2.000000 3.000000 4 .000000 5.000000 6.000000 7 .000000 8.000000 1.OCOOOO 2.000000 3.000000 4.0000CO 5.000000 6.000000 7.OOCOOO 8.000000 1.000000 2.000000 3.000000 4.000000 5.000000 6.OOOOOG 7.000000 8.000000 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 7.000000 8.000000 1.000000 2.COOOOO 3.000000 4 .000003 5.000000 6.000000 , 7.000000 8.000000 157.250000 164.510000 171.10C000 176.227000 ISO.100000 182.900000 184.900000 186.400000 157.250000 164.510000 171.100000 176.227000 180.100000 182.900000 184.900000 186.400000 157. 164. 171. 176. 180. 182. 184. 186. 250000 5100C0 100000 227000 100000 900000 900000 400000 157.250000 164.5100C0 171.100000 176.227000 180.100000 182.900000 184.900000 186.400000 157, 164, 171, 176, 180 182 184 186 ,250000 510000 , 100000 ,227000 , 1OOOCO ,900000 ,900000 ,400000 157.250000 164.510000 171.100000 176.227000 180.100000 182.900000 184.900000 186.400000 157, 157 159 160 162 164 166 168 250000 ,580256 ,112452 ,958741 ,895740 , 829396 ,712073 .517621 157.250000 159.381426 162.507368 165.654374 168.607436 171.300127 173.717433 175.866001 157.250000 160.744181 164.946883 168.853768 172.294569 175.255649 177.771053 179.889779 157. 161. 166. 171. 174. 173. 180. 182. 250000 873411 833845 284543 973385 002662 461220 441033 157.250000 162.851539 168.499655 173.234836 177.039492 180.038584 182.376637 184.185811 157.250000 163.721760 169.888532 174.352855 178.692836 181.609600 183.801568 185.436957 0.00051697. 95586 0.0010 714. 56704 0.0015 318.97251 0.0020 134.79773 0.0025 47.28927 0.0030 9.75650 1.000000 2.000000 3.0000CO 4.000000 5.000000 6.COOOOO 7.000000 8.000000 1. COOOOO 2.000000 3.000000 4.000000 5.000000 6.000000 7.000000 e. oooooo 1.000000 2. COOOOO 3.000000 4.000000 157.250000 164.510000 171.1OOOCO 176.227000 180.100000 182.900000 184.900000 186.400000 157.250000 164.510000 171.100000 176.227000 180.1OOOCO 182.900000 184.900000 186.400000 157.250000 164. 510000 171.100000 176.227000 157. 164. 171. 1 76. 180. 182. 184. 186. 157. 165. 172. 177. 181. 183. 185. 187. 250000 505919 106979 226183 049920 856210 694413 364256 250000 233129 191858 411479 134743 865915 751606 068512 157.250000 165.903419 173.168914 178.447781 0.0035 0.00578 0.0040 6.39986 

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