UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A study of heat transfer from steam-air mixtures to a retort pouch substrate Kisaalita, William Ssempa 1981

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1982_A7 K58.pdf [ 5.92MB ]
Metadata
JSON: 831-1.0095268.json
JSON-LD: 831-1.0095268-ld.json
RDF/XML (Pretty): 831-1.0095268-rdf.xml
RDF/JSON: 831-1.0095268-rdf.json
Turtle: 831-1.0095268-turtle.txt
N-Triples: 831-1.0095268-rdf-ntriples.txt
Original Record: 831-1.0095268-source.json
Full Text
831-1.0095268-fulltext.txt
Citation
831-1.0095268.ris

Full Text

A STUDY OF HEAT TRANSFER FROM STEAM-AIR MIXTURES TO A RETORT POUCH SUBSTRATE by WILLIAM SSEMPA (KI.SAALITA Sc. (Eng.)(Hons), Makerere U n i v e r s i t y , 1978 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Bio-Resource E n g i n e e r i n g ) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December 1981 © W i l l i a m Ssempa K i s a a l i t a , 1981 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Bio-Resource Engineering The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date December 11th 1981 T-\T-I r i o / \ i i ABSTRACT Thermal p r o c e s s i n g of foods i n r e t o r t pouches using steam-air mixtures may o f f e r advantages over a l t e r n a t e techniques; however, thermal p r o p e r t i e s of steam-air mixtures are not w e l l understood. Since r e t o r t pouches are becoming i n c r e a s i n g l y common, i t i s important to know the heat t r a n s f e r c h a r a c t e r i s t i c s of steam-air mixtures i n order to permit t h e i r e f f i c i e n t u t i l i s a t i o n . In t h i s study, a sensor was designed f o r measuring the heat t r a n s f e r c o e f f i c i e n t of steam-air mixtures using a r e t o r t pouch laminate as the condensation s u r f a c e . T h i s was i n c o r p o r a t e d i n t o a condensation chamber that was designed to accommodate steam-air mixtures, up to 50% steam at a maximum temperature of 125°C. With steam-air media f l o w i n g h o r i z o n t a l l y and on the underside of a r e t o r t pouch s u b s t r a t e , the nature of condensation was i n v e s t i g a t e d , as w e l l as the e f f e c t s of temperature, Reynolds number and the d i f f u s i o n c o e f f i c i e n t on the heat t r a n s f e r c o e f f i c i e n t . I t was concluded that the r e l e a s e of enthalpy from steam-air mixtures on the underside of a r e t o r t pouch s u b s t r a t e was by f i l m w i s e condensation. I t was a l s o concluded that the heat t r a n s f e r c o e f f i c i e n t c o u l d be p r e d i c t e d by e x p o n e n t i a l f u n c t i o n s of the s u r f a c e temperature, and the temperature d i f f e r e n c e between the steam-air medium and the s u b s t r a t e s u r f a c e . The dependence i i i of the heat t r a n s f e r c o e f f i c i e n t on the d i f f u s i o n c o e f f i c i e n t was found to be stronger at high temperature d i f f e r e n c e s . i v TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i LIST OF FIGURES v i i TERMINOLOGY ix NOMENCLATURE . x i ACKNOWLEDGEMENTS * i v INTRODUCTION • 1 A. The Retort Pouch 1 B. Thermal P r o c e s s i n g of Retort Pouched Products 4 LITERATURE REVIEW . 7 A. The B i o t Number, Bi 7 B. Heat T r a n s f e r C o e f f i c i e n t f o r Steam-air Mixtures 10 1. P r e d i c t i o n of filmwise condensation heat t r a n s f e r c o e f f i c i e n t f o r pure vapours 10 2. P r e d i c t i o n of dropwise condensation heat t r a n s f e r c o e f f i c i e n t f o r pure vapours 13 C. I n f l u e n c e of Noncondensable Gases 14 D. O b j e c t i v e s of t h i s Research 22 MECHANICAL DESIGN OF THE EXPERIMENTAL EQUIPMENT . 23 A. F u n c t i o n a l S p e c i f i c a t i o n s 23 B. Conceptual Design 24 C. Optimal Design 27 1 . Condensation chamber 27 2. End caps 34 3. Sensor block 36 4. Sensor i n s u l a t i o n 37 D. System D e s c r i p t i o n 39 EXPERIMENTAL PROCEDURE 40 RESULTS AND DISCUSSION 43 A. R e s u l t s 43 B. C o r r e l a t i o n of the Data 44 C. In f l u e n c e of Reynolds Number on the Parameters 59 D. Mode of Condensation 61 E. Average Heat T r a n s f e r C o e f f i c i e n t f o r Steam-air Thermal Processes &3 CONCLUSIONS 64 SUGGESTION FOR FURTHER STUDY 66 LITERATURE CITED 67 APPENDIX A 70 APPENDIX B 72 APPENDIX C 79 APPENDIX D 86 APPENDIX E 89 v i LIST OF TABLES Table Page I Experimental design showing temperature, a i r f r a c t i o n and mixing a i r f l o w r a t e 41 II C o r r e c t e d data f o r experiment no.5,run 10553. 43 III Estimated parameters o t i and . 51 IV Estimated parameters 3 and 3 . 51 1 2 V Estimates of B i o t numbers f o r some food products i n t h i n p r o f i l e c o n f i g u r a t i o n s 71 VI C a l c u l a t e d Reynolds number for i n v e s t i g a t i n g the v e l o c i t y e f f e c t s of the heat t r a n s f e r c o e f f i c i e n t 85 VII Atomic volumes, f o r some gases, employed in c a l c u l a t i n g f o r Dc 88 VIII Experimental and c a l c u l a t e d data 90 v i i LIST OF FIGURES F i g u r e Page 1 Pressure and temperature r e l a t i o n s h i p s f o r vapours condensing i n presence of noncondensable gases 17 2 Normalised heat t r a n s f e r c o e f f i c i e n t a g a i n s t a i r content i n PPM 21 3 Conceptual c o n f i g u r a t i o n of the sensor and the condensation chamber 25 4 Closed c y l i n d e r with i n t e r n a l and e x t e r n a l p r e s s u r e s 28 5 S e c t i o n e-e of F i g u r e 4 28 6 Sketch of s t r e s s d i s t r i b u t i o n i n the condensation chamber 33 7 End cap l o a d i n g 35 8 Sensor block l o a d i n g 35 9 Sensor c o n f i g u r a t i o n approximated to a case of two c o n c e n t r i c c y l i n d e r s 38 10 Schematic diagram of the sensor showing thermocouple p o s i t i o n s and a t y p i c a l temperature g r a d i e n t 45 11 P l o t of h a g a i n s t Ts f o r steam-air temperatures of 105,110,115,121, and 125 °C 47 12 P l o t of h a g a i n s t AT f o r steam-air temperatures of 105,110,115,121, and 1 25 ° C 48 13 P l o t of ln(h) a g a i n s t Ts f o r steam-air temperatures of 105,110,115,121, and 1 25 ° C 49 14 P l o t of ln(h) a g a i n s t AT f o r steam-air temperatures of 105,110,115,121, and 125 ° C 50 v i i i 15 P l o t of p r e d i c t e d h a g a i n s t Ts f o r steam-air temperatures of 105,110,115,121, and 125 °C 52 16 P l o t of p r e d i c t e d h a g a i n s t AT f o r steam-air temperatures of 105,110,115, 121, and 125 °C 53 17 P l o t of . i r - a g a i n s t AT 57 18 P l o t of Dc a g a i n s t AT f o r steam-air temperature range of 105 - 125 °C 58 19 P l o t of p r e d i c t e d h a g a i n s t Dc f o r steam-air temperature range of 105 - 125 °C. 60 20 Schematic l a y o u t of the steam-air mixing system, condensation chamber and the data a c q u i s i t i o n system 73 21a Condensation chamber 74 21b Condensation chamber end cap 74 22 Coolant end cap f o r the c o l d end of the sensor 75 23 Sensor block used f o r measuring the heat t r a n s f e r c o e f f i c i e n t 76 24 Sensor i n s u l a t i o n 77 25 Assembly drawing-section through sensor block 78 ix TERMINOLOGY Accommodation C o e f f i c i e n t f o r Condensation, a - the f r a c t i o n of the molecules s t r i k i n g the sur f a c e that condense. CMSa - the a i r vo l u m e t r i c f l o w r a t e in cubic metres per second. CMSsa - the steam-air v o l u m e t r i c f l o w r a t e i n cubi c metres per second. Come-up Time - the time r e q u i r e d to reach the t a r g e t r e t o r t temperature a f t e r steam or a steam-air mixture i s turned on. Heating Lag F a c t o r , j - a f a c t o r which, when m u l t i p l i e d by the d i f f e r e n c e between the r e t o r t temperature and the i n i t i a l temperature of the food product, l o c a t e s the i n t e r s e c t i o n of the exte n s i o n of the s t r a i g h t l i n e p o r t i o n of the heat p e n e t r a t i o n curve and a v e r t i c a l l i n e r e p r e s e n t i n g the beginning of the process or zero time. Heating Rate Index, f - time, i n minutes, r e q u i r e d f o r the s t r a i g h t - l i n e p o r t i o n of the heat p e n e t r a t i o n curve to t r a v e r s e one l o g c y c l e . N u m e r i c a l l y i t i s equal to the r e c i p r o c a l of the s l o p e . Normalised Heat T r a n s f e r C o e f f i c i e n t - the r a t i o of the heat t r a n s f e r c o e f f i c i e n t f o r a pure vapour over the heat t r a n s f e r c o e f f i c i e n t with noncondensables. Octahedral Shearing S t r e s s Y i e l d C r i t e r i o n - s t a t e d as f o l l o w s : I n e l a s t i c a c t i o n s at any p o i n t i n a member under any combination of s t r e s s e s w i l l begin when the maximum o c t a h e d r a l shearing s t r e s s (Tmax) becomes equal to 0.47x a v_p, where a y p i s the t e n s i l e y i e l d s t r e s s of the m a t e r i a l as determined from the standard t e n s i o n t e s t . , For a' member with , and a as the p r i n c i p a l s t r e s s e s , z Tmax = 1/3 { ( a r - a 0 ) 2 + ( a Q - a z) 2 + ( a z - o x ) * } ™ -Promoters - are substances that are s t r o n g l y a t t r a c t e d to a condensing s u r f a c e and r e p e l water. SCMSa - the standard v o l u m e t r i c f l o w r a t e i n cubic metres per second. X Slope Index, z - t h i s term accounts f o r the r e l a t i v e r e s i s t a n c e of a microorganism to the d i f f e r e n t temperatures and i t i s n u m e r i c a l l y equal to the number of degrees r e q u i r e d f o r the thermal d e s t r u c t i o n curve to t r a v e r s e one l o g c y c l e . x i NOMENCLATURE a A i r r a t i o , c a Accommodation c o e f f i c i e n t f o r condensation. A Area, m2. Bi B i o t number =hl/k. Cc S p e c i f i c heat c a p a c i t y , J/kg K. D Diameter, m. Dc D i f f u s i o n c o e f f i c i e n t , m 2/s. E Young's modulus, kN/m2. F.S. F actor of S a f e t y . g 0 Constant. g G r a v i t a t i o n a l a c c e l e r a t i o n , m 2/s. h Heat t r a n s f e r c o e f f i c i e n t , W/m2 K. hfg Latent heat of condensation, J/kg. k c,k Thermal c o n d u c t i v i t y , W/m K. L , l S i g n i f i c a n t l e n g t h or t h i c k n e s s , m. m ,m , m_ . Mass, kg. a sa M,Ma,Mb Molecular weight, kg. Nu Nusselt number =hL/k. P»PifP2'P g'P v Pressure, kN/m2 . Q Heat f l u x , W. Re Reynolds number = v D/ v . R,Rv U n i v e r s a l gas constant, J/mol.K. r, e C i r c u l a r c o o r d i n a t e s , m, degrees. r C o e f f i c i e n t of c o r r e l a t i o n , c x i i S.E. Standard E r r o r . T,Tv Temperature, Temperature of s a t u r a t e d vapours and/or steam-air mixtures, °C . AT,AT, Temperature difference,C°. t 1 Effective., gas l a y e r t h i c k n e s s * m. t Time, s, min. Va,Vs,Vsa Volume, m3 . v ,v , v V e l o c i t y , m/s . a s sa J w^  Rate of vapour flow, kg/s. x,y,z Rectangular c o o r d i n a t e s , m. a 1 L i n e a r c o e f f i c i e n t of thermal expansion,1/C°. a , a Parameters. 1 2 3 , 3 Parameters. 1 2 6 , 6 , 6 Parameters. .1 2 3 P / P _ r P r , r P < s / P < M D e n s i t y , kg/m2. d C 5 ocl z 2 a r R a d i a l stress,kN/m o"g Hoop s t r e s s , kN/m2 . o_ A x i a l stress,kN/m 2 . T e n s i l e y i e l d stress,kN/m 2 H/H ,n ,ri Absolute v i s c o s i t y , N.s/m2 oL o S a v Poisson's r a t i o . P/y../1-i /Vi Kinematic v i s c o s i t y , m2/s . a s sa Shear s t r e s s , kN/m 2 S u b s c r i p t s . a A i r . s Steam. sa Steam-air. xiv ACKNOWLEDGEMENTS The author wishes to thank the f o l l o w i n g people f o r advice and a s s i s t a n c e , without which t h i s work would have been i m p o s s i b l e . Dr. K. V. Lo, P r o f . L. M. S t a l e y and Mr. N. Jackson, Bio-Resource E n g i n e e r i n g Department, Dr. M. A. Tung, Department of Food Science, P r o f . J . Lielmezs, Department of Chemical E n g i n e e r i n g , Ms. J . Mennell, Department of H i s p a n i c and I t a l i a n S t u d i e s , a l l at the U n i v e r s i t y of B r i t i s h Columbia. 1 INTRODUCTION A. The Retort Pouch The term " r e t o r t pouch" g e n e r a l l y r e f e r s to a f l e x i b l e package made from two, three, or four p l y m a t e r i a l s . These, when f u l l y s e a l e d , w i l l act as hermetic c o n t a i n e r s that, are p r o d u c t - r e s i s t a n t and can be s t e r i l i z e d at temperatures s i m i l a r to those used f o r canned products. The r e t o r t pouch c o u l d be a d e s i r a b l e a l t e r n a t i v e to the metal can, the g l a s s j a r and the aluminum f o i l f rozen t r a y (Mermelstein, 1978). A t y p i c a l t h r e e - p l y laminate has been given by Copley (1978) as 12 ym p o l y e s t e r / 9-12 ym aluminum f o i l / 70 ym p o l y o l e f i n . Adhesives are used to hold together the c o n s t r u c t i o n and, appropiate s e l e c t i o n of these enables pouches to meet the above d e f i n i t i o n , producing products that are m i c r o b i o l o g i c a l l y s t a b l e . The three p l y pouches are most predominantly used. The f u n c t i o n of. the outer l a y e r i s to o f f e r the r e q u i r e d s t r e n g t h . The middle l a y e r of aluminum f o i l f u n c t i o n s as the b a r r i e r to gases, l i g h t and moisture. The inner l a y e r f u n c t i o n s as the heat s e a l i n g and food c o n t a c t m a t e r i a l . A d e t a i l e d m a t e r i a l s p e c i f i c a t i o n can be found in T u r t l e and Alderson (1971). 2 The r e t o r t pouch has a number of advantages over c o n v e n t i o n a l packaging methods and the su b j e c t has been d e a l t with by many authors l i k e Nieboer (1974), Davis et_ a l • (1972), Rees (1974) and Yamano et a l . (1969). B a s i c a l l y the advantages can be summarised as l e s s energy requirement, improved product q u a l i t y , longer s h e l f l i f e , weight/space c o n s e r v a t i o n and convenience. Both pouches and the paperboard d i s t r i b u t i o n c a r t o n s r e q u i r e l e s s energy to manufacture as compared to cans, j a r s and t r a y s . S t u d i e s have i n d i c a t e d that the t o t a l energy r e q u i r e d , from h a r v e s t i n g to consumption i s about 60% lower for v egetables packaged i n a r e t o r t pouch than f o r frozen vegetables and about 15% lower than f o r canned v e g e t a b l e s . Due to the f a c t that pouches have thin n e r p r o f i l e s than cans and j a r s i t takes about 30-50% l e s s time to reach s t e r i l i s i n g temperatures at the slowest h e a t i n g p o i n t s . In a d d i t i o n , pouched products are s h e l f s t a b l e at room temperature f o r at l e a s t as long as canned products. Pouched foods can e i t h e r be eaten without h e a t i n g or can be heated q u i c k l y by p l a c i n g the pouch i n b o i l i n g water f o r three to f i v e minutes. In c o n t r a s t , f r o z e n foods r e q u i r e h e a t i n g f o r about h a l f an hour. O v e r a l l , the pouched product energy requirement seems to be lower than f o r products packaged i n cans or j a r s . 3 The heat p e n e t r a t i o n r a t e i n t o the f l e x i b l e package has been found by Yamano et a l . (1969) to be three times that of canned products. As a consquence, those p a r t s of the product near the s u r f a c e are not overcooked as they may be in the case of cans or j a r s . Product q u a l i t y i s t h e r e f o r e maintained, r e s u l t i n g i n food that i s t r u e r i n c o l o u r , f i r m e r i n t e x t u r e and f r e s h e r i n f l a v o u r , with l e s s n u t r i e n t l o s s . Very a c i d i c products ( l i k e f r u i t s ) can be preserved without c o r r o s i o n problems, f o r long p e r i o d s , because of the i n e r t n e s s of the pouch m a t e r i a l . In f a c t , some pouched products have been s t o r e d f o r up to ten years under t y p i c a l warehousing c o n d i t i o n s and have been shown to be accept a b l e and m i c r o b i o l o g i c a l l y sound (Mermelstein, 1978). The pouches, both empty and f u l l , weigh l e s s than comparable cans, j a r s or t r a y s . T h i s i s due p a r t l y to vacuum packaging without the n e c e s s i t y of syrup or sauce, thereby p e r m i t t i n g up to a 40% saving i n weight and volume. In a d d i t i o n , t h i s enables some products which are normally d i f f i c u l t to pack to be packaged, e s p e c i a l l y vegetables and mature potatoes, which break down i f packaged i n b r i n e . D i s t r i b u t i o n c o s t s before and a f t e r f i l l i n g are tremendously reduced. For example, 1,000 empty, 230 g pouches weigh about 6 kg compared to 50 kg f o r e q u i v a l e n t metal cans. Empty pouches take up 85% l e s s storage space than cans. Th e r e f o r e a great deal of saving can be made on empty pouch 4 r o l l s t o c k storage. However, i t i s more d i f f i c u l t and time consuming to make and f i l l a pouch, c a r e f u l l y reduce the head space, s e a l i t and go through the r e t o r t i n g procedure, than i t i s to pack the same product i n a j a r or can and process i t r o u t i n e l y . T h i s i m p l i e s slow l i n e speeds. In a d d i t i o n to t h i s , pouch m a t e r i a l c o s t s seem to be higher than the t r a d i t i o n a l m a t e r i a l s f o r cans and j a r s . Consequently, o v e r a l l packaging c o s t s are h i g h e r . A l s o , pouched products are more s u s c e p t i b l e to mechanical damage than a r i g i d canned product or the e q u i v a l e n t f r o z e n product. B. Thermal P r o c e s s i n g of Retort Pouched Products There are two techniques that are being employed f o r thermal p r o c e s s i n g of r e t o r t pouched products, namely, hot water with o v e r r i d i n g a i r pressure and steam-air mixtures. Although pouch laminate stock and s e a l s are q u i t e rugged at ambient temperatures, t h e i r s t r e n g t h i s reduced c o n s i d e r a b l y at process temperatures. During h e a t i n g and c o o l i n g , the o v e r a l l pressure of the contents may exceed the steam pressure at the p a r t i c u l a r temperature. T h i s pressure d i f f e r e n t i a l may cause b u l g i n g of the pouch which may r e s u l t in an a i r l a y e r between the food product and the package, a c t i n g l i k e a thermal i n s u l a t o r . On the other hand, s e a l f a i l u r e may occur. The extent to which s e a l f a i l u r e may 5 take p l a c e depends on the volume packaged, the dimensional r a t i o , the a i r content of the pack or the i n t e r n a l vacuum. The compressed a i r , when added i n t o the r e t o r t , produces a t o t a l p r essure i n excess of the steam vapour pressure corresponding to the p r o c e s s i n g temperature, thus c o u n t e r a c t i n g the pressure d i f f e r e n t i a l developed w i t h i n the pouch. The hot water technique may be expensive i n that water heats slowly, due to i t s high heat c a p a c i t y . P f l u g (1975) has i n d i c a t e d that the use of water r e s u l t s i n a 50% inc r e a s e i n he a t i n g and c o o l i n g c o s t s as compared to steam. A l s o there i s the danger of v i b r a t i o n a l damage d u r i n g r e t o r t come-up, and sometimes pouches may f l o a t . For most food products i t i s important to b r i n g the r e t o r t up to process temperature as r a p i d l y as p o s s i b l e because, the slope index va l u e , z, of q u a l i t y f a c t o r s i s l a r g e r than the z value f o r m i c r o b i a l d e s t r u c t i o n . So a long come-up p e r i o d produces a r e l a t i v e l y g r e a t e r e f f e c t on q u a l i t y than on microorganisms. However, water systems have the advantage i n that they r e q u i r e l e s s mixing and are r e l a t i v e l y easy to work with. Steam-air h e a t i n g seems to so l v e the above i n d i c a t e d problems a s s o c i a t e d with hot water h e a t i n g . In a d d i t i o n , the d e s i r a b l e overpressure f o r pouch i n t e g r i t y and e f f i c i e n t heat t r a n s f e r i s provided throughout the p r o c e s s i n g p e r i o d . Perhaps i t should a l s o be p o i n t e d out that s i n c e l e s s steam i s r e q u i r e d f o r a steam-air p r o c e s s i n g medium as compared to 6 a pure steam medium there c o u l d be an i n c e n t i v e f o r energy c o n s e r v a t i o n . Despite the above advantages that steam-air systems o f f e r , there i s a lack of knowledge of the thermo-p h y s i c a l p r o p e r t i e s , and these are d e s i r a b l e f o r e f f i c i e n t u t i l i s a t i o n of the p r o c e s s i n g medium. 7 LITERATURE REVIEW A. The B i o t Number, B i . P f l u g et a l . (1965) have i n d i c a t e d that the rate of conduction h e a t i n g of a product i n c o n t a i n e r s i s a f u n c t i o n of the geometry of the c o n t a i n e r , the p h y s i c a l p r o p e r t i e s of the food, the heat t r a n s f e r c h a r a c t e r i s t i c s of the h e a t i n g medium and the heat t r a n s f e r c h a r a c t e r i s t i c s of the c o n t a i n e r . They have f u r t h e r i n d i c a t e d that i n a system f o r p r o c e s s i n g foods i n c o n t a i n e r s where the heat t r a n s f e r c o e f f i c i e n t i s l a r g e enough that the B i o t Number, B i , i s gr e a t e r than ten, the h e a t i n g r a t e of the product becomes independent of the heat t r a n s f e r c o e f f i c i e n t and i s a f u n c t i o n only of the thermal p r o p e r t i e s of the product and the c o n t a i n e r dimensions. The B i o t number may be c a l c u l a t e d as f o l l o w s : Bi = h l A ( 1 ) Where h i s the heat t r a n s f e r c o e f f i c i e n t ( W/m2.K ), 1 i s the c o n t a i n e r s m a l l e s t dimension ( m ) and k i s the product thermal c o n d u c t i v i t y ( W/m.K ). 8 Unsteady s t a t e heat t r a n s f e r , which i s predominant i n almost a l l problems of conduction heating and c o o l i n g i n the food i n d u s t r y , has been p r e v i o u s l y c o n s i d e r e d by Heldman (1975). He has w r i t t e n t h a t , "... One of the key f a c t o r s i n v o l v e d i n the e v a l u a t i o n of t r a n s i e n t or unsteady s t a t e heat t r a n s f e r i s the r e l a t i v e importance of the i n t e r n a l and e x t e r n a l r e s i s t a n c e to heat t r a n s f e r . The dimensionless number used i n e v a l u a t i n g the importance of these f a c t o r s i s the B i o t number ...; When the Bi i s low, i . e . , Bi < 0.1, the i n t e r n a l r e s i s t a n c e to heat t r a n s f e r i s c o n s i d e r a b l y l e s s than the su r f a c e r e s i s t a n c e and the so c a l l e d lumped parameter approach can be used to d e s c r i b e the heating or c o o l i n g c h a r a c t e r i s t i c s .of the body ... When Bi > 40, the i n t e r n a l r e s i s t a n c e to heat t r a n s f e r i s much gr e a t e r than the e x t e r n a l r e s i s t a n c e and the su r f a c e temperature of the obj e c t can be assumed to be equal to the he a t i n g or c o o l i n g medium temperature without s i g n i f i c a n t e r r o r . " I t appears that the statement of P f l u g and h i s a s s o c i a t e s i s a r e f i n e d form of Heldman's. C o n s i d e r i n g a number of r e p o r t a b l e products, as shown in Appendix A, packaged i n a r e t o r t pouch (140 mm x 180 mm x 10 mm.), i t can be shown that the Bi are above ten, f o r both steam and water systems. T h i s i m p l i e s that the heating r a t e s of these products i n steam and water media are independent of the heat t r a n s f e r c o e f f i c i e n t s and depend on the thermo-physical p r o p e r t i e s of the foods. 9 Thus, the heat t r a n s f e r c o e f f i c i e n t s are higher than i s necessary f o r adequate heat t r a n s f e r f o r these products i n t h i n p r o f i l e pouches. In a d d i t i o n , P f l u g and Borrero (1967) found that the he a t i n g rate index value ( f - v a l u e ) and the heat i n g l a g f a c t o r ( j - v a l u e ) f o r conduction h e a t i n g products heated i n water were between the f and j values f o r steam-a i r mixtures c o n t a i n i n g 30 and 20% a i r . By t h i s the authors concluded that steam-air mixtures down to 70% steam are s u f f i c i e n t f o r s t e r i l i s i n g food products. In other words, the heat t r a n s f e r c o e f f i c i e n t f o r the steam-air range i n que s t i o n i s s u f f i c i e n t l y high that the Bi i s l a r g e enough fo r h e a t i n g to be independent of the heat t r a n s f e r at the s u r f a c e . So f o r a given product whose thermo-physical p r o p e r t i e s are known, a c r i t i c a l heat t r a n s f e r c o e f f i c i e n t , he, can be e s t a b l i s h e d , the h e a t i n g media of which would j u s t be s u f f i c i e n t f o r p r o c e s s i n g the product i n q u e s t i o n . Assuming that the average heat t r a n s f e r c o e f f i c i e n t f o r steam-air mixtures decreases with the a i r r a t i o , a, then there e x i s t s , f o r a given product, a steam-air mixture that i s j u s t s u f f i c i e n t f o r thermal p r o c e s s i n g purposes. Knowledge of the r e l a t i o n s h i p between the heat t r a n s f e r c o e f f i c i e n t and the a i r - r a t i o i s t h e r e f o r e d e s i r a b l e . 10 B. Heat T r a n s f e r C o e f f i c i e n t f o r Steam-air Mixtures I t i s a w e l l e s t a b l i s h e d f a c t that when a s u r f a c e i s maintained at a temperature below the s a t u r a t i o n temperature of an adjacent vapour, condensation o c c u r s . Under c e r t a i n circumstances, the l i q u i d condensate wets the e n t i r e s u r f a c e . T h i s type of condensation i s r e f e r r e d to as filmwise condensation. When the su r f a c e i s not wetted by the l i q u i d , condensate forms i n d r o p l e t s which run down an i n c l i n e d s u r f a c e , c o a l e s c i n g with other d r o p l e t s . T h i s i s r e f e r r e d to as dropwise condensation. Dropwise condensation so f a r has been r e l i a b l y obtained only with steam under the i n f l u e n c e of promoters. The c o n d i t i o n s under which i t p r e v a i l s are d i f f i c u l t to maintain in p r a c t i c e , however, i t i s c h a r a c t e r i s e d by high heat t r a n s f e r c o e f f i c i e n t s which are four to e i g h t times that of filmwise condensation. 1. P r e d i c t i o n of fi l m w i s e condensation heat t r a n s f e r c o e f f i c i e n t f o r pure vapours The t h e o r e t i c a l r e l a t i o n s f o r c a l c u l a t i n g the heat t r a n s f e r c o e f f i c i e n t f o r filmwise condensation of pure vapours on v e r t i c a l tubes and p l a t e s were f i r s t o btained by Nusselt (1916). He combined the laws of a laminar flow and the energy flow through f l u i d f i l m s . An approximate a n a l y s i s n e g l e c t i n g the i n t e r f a c e r e s i s t a n c e leads to 11 r e s u l t s that agree w e l l with experimental data f o r a vapour condensing on e i t h e r a v e r t i c a l f l a t p l a t e or a v e r t i c a l c y l i n d r i c a l tube of diameter l a r g e r than 3.25 mm, le n g t h L and u n i t width as f o l l o w s : P C ( P C - P S ) g h- g k£ h = 0.943 { } °-25 (2) ncL ( TV - Ts ) Where' P i s the d e n s i t y of condensate (kg/m 3), p i s the d e n s i t y of the vapour (kg/m 3), g i s the g r a v i t a t i o n a l a c c e l e r a t i o n (m/s 2) and hfg = h'fg + 3/8 Cc (Tv-Ts) . Where hfg i s the l a t e n t heat of condensation ( J / k g ) . Cc i s the s p e c i f i c heat of the condensate (J/kg.K), Tv i s the temperature of s a t u r a t e d vapour (°K), Ts i s the w a l l s u r f a c e temperature (°K), k^ i s the thermal c o n d u c t i v i t y of the condensate (W/m.K) and n c i s the v i s c o s i t y of the condensate (N.s/m 2). D e v i a t i o n s from the above r e l a t i o n s h i p have been observed when the condensate flow becomes t u r b u l e n t , the vapour v e l o c i t y i s very high, dropwise condensation occurs p a r t i a l l y or completely and when noncondensable gases are pre s e n t . 12 For condensation on h o r i z o n t a l p l a t e s , Gerstmann and G r i f f i t h (1967) c a r r i e d out experiments on the underside of a p l a t e with water, at one atmosphere. T h e i r r e s u l t s c o r r e l a t e d w e l l as f o l l o w s : For (j> < 10 8 , Nu' = 0.81 <j> 0 , 1 9 3 (3) For 10 6 > (j) > 10 8, Nu' = 0.96 <|> 0 - 2 0 (4) Where Nu' = h A c { g o a c / (p c - p v) g }°' 5 (5) k n ( Tv - Ts ) c c cj, = _ _ (6) P c { P C " p v } ^ h f g { g o a c / ^ ( P c - P ^ ^ ' 5 a i s the accommodation c o e f f i c i e n t f o r condensation and g 0 c i s a c o n s t a n t . 13 2. P r e d i c t i o n of dropwise condensation heat t r a n s f e r c o e f f i c i e n t f o r pure vapours. The f a c t that the heat t r a n s f e r c o e f f i c i e n t f o r dropwise condensation i s much higher than that f o r filmwise condensation, has a t t r a c t e d the a t t e n t i o n of many authors, with the hope of producing a theory of heat t r a n s f e r . Since the e n t i r e process c o n s i s t s of a few random and di s c o n t i n u o u s subprocesses ( i . e . formation, growth, coalescence and departure) which are experienced by each i n d i v i d u a l d r o p l e t on a condensing s u b s t r a t e , i t i s very d i f f i c u l t f o r one to examine the process by means of the co n v e n t i o n a l exact a n a l y s i s as with filmwise condensation. However, F a t i c a and Katz (1949), Sugawara and M i c h i y o s h i (1956), Umur and G r i f f i t h (1965) and M i k i c (1969) have proposed models to approximate the proc e s s . An e x c e l l e n t f i t f o r r e l i a b l e experimental r e s u l t s has been obtained by Le Fevre and Rose (1967), f o r water at atmospheric pressure, condensing on a v e r t i c a l s u b s t r a t e with temperature d i f f e r e n c e s (AT) under 10C°. The good agreement between theory and r e s u l t s s t r o n g l y supports the f a c t that the dominant f a c t o r s a r e : s u r f a c e t e n s i o n e f f e c t s , i nter-phase matter t r a n s f e r pressure drop, conduction i n the l i q u i d , d r o p s i z e d i s t r i b u t i o n s and absence of noncondensable gases. The model i n d i c a t e s as do experimental r e s u l t s that the heat t r a n s f e r c o e f f i c i e n t i n c r e a s e s with heat f l u x . However, the 14 model, u n l i k e o t h e r s , does not c o n s i d e r the sweeping p a r t of the drop c y c l e . But elsewhere, Rose (1967) has c o n s i d e r e d the e f f e c t and has w r i t t e n t h a t , "The e f f e c t of the c o r r e c t i o n f o r " b l a n k e t i n g " by f a l l i n g d r o p l e t s becomes marked f o r the case of steam condensing on a v e r t i c a l s u r f a c e , only at and beyond the hi g h e s t heat f l u x e s o b t a i n a b l e to date. For non v e r t i c a l s u r f a c e s the c o r r e c t i o n s w i l l be important at lower heat f l u x e s . . . " U n f o r t u n a t e l y , no experimental evidence has been found in the l i t e r a t u r e f o r dropwise condensation on h o r i z o n t a l s u b s t r a t e s , which i s s i g n i f i c a n t to r e t o r t pouch p r o c e s s i n g . C. I n f l u e n c e of Noncondensable .Gases Othmer (1929) was one of the f i r s t i n v e s t i g a t o r s to give q u a n t i t a t i v e r e s u l t s f o r filmwise condensation, with steam c o n t a i n i n g small percentages of a i r . He used s t a t i c steam and v a r i e d the a i r c o n c e n t r a t i o n up to 5% by volume. He found that the presence of 0.5% a i r by volume would decrease the heat t r a n s f e r c o e f f i c i e n t by 50%. Meisenburg et a l . (1935), using an experimental f o r c e d c i r c u l a t i o n evaporator, obtained some r e s u l t s with a i r content up to 4% by weight. They c o r r e l a t e d t h e i r r e s u l t s by means of an e m p i r i c a l equation and found that the values of the steam heat t r a n s f e r c o e f f i c i e n t when a i r was present depended on the a i r content of the mixture, the temperature of the 15 condensing steam, and the temperature drop (AT). The influence of noncondensable gas has been studied by Kusak (1958). He condensed methanol out of a methanol-air mixture in a set of v e r t i c a l l y mounted condensers. The Reynolds number of the gas vapour stream at the i n l e t varied from 768 to 7670, the percent a i r at the i n l e t varied from 13.9% to 75.3%. The condensers used were of three lengths and three diameters; these were respectively 4, 12 and 24 inches, and 0.5, 1.0 and 1.5 inches. He obtained empirical correlations for downflow and for upflow by the method of least squares as follows: h (ID / Re) 1/ 3 = 7.12e~ 2- 7 9 6 a (Downflow) (7) h (LD / Re) 1/ 3 = 7.55e~ 3° 0 7 2 a (Upflow) (8) Where L i s the length of the condenser, D i s the diameter of the condenser and Re i s the Reynolds number. 16 C o n s i d e r a b l e progress has been made in recent years towards the t h e o r e t i c a l understanding of the cases of filmwise condensation on v e r t i c a l plane s u r f a c e s and tubes. These c o n f i g u r a t i o n s have dominated the l i t e r a t u r e , probably because they are p r a c t i c a l and more r e l e v a n t to most i n d u s t r i a l a p p l i c a t i o n s . The r e l a t i o n s h i p of p a r t i a l p ressure f o r the v e r t i c a l plane c o n f i g u r a t i o n has been i l l u s t r a t e d by Kern (1950) as shown in F i g u r e 1. I t i s b e l i e v e d that i n order f o r the vapour to condense on the condensate f i l m i t has to be d r i v e n a c r o s s the gas f i l m by the d i f f e r e n c e between the p a r t i a l p r e s s u r e s of the vapour i n the main body and the condensate. So the rate at which the steam condenses i s no longer e n t i r e l y dependent on N u s s e l t ' s condensation mechanism, but upon the laws governing d i f f u s i o n . The equation r e p r e s e n t i n g the d i f f u s i o n of the vapour through the gas has been given by Rohsenow and H a r t n e t t (1973) as f o l l o w s : dp v / dy = -w_ R T (p - P y ) / Dc p (9) where w i s the r a t e of vapour flow,and Dc i s the d i f f u s i o n r c o e f f i c i e n t f o r a condensing gas d i f f u s i n g through a noncondensing gas. 17 Pressure Temperature Retort Pouch Substrate \ \ \ \ \ \ \ v \ ^ y \ \ \ \ \ \ \ \ \ \ \ \ \ 5 1 . _ _ ^'Ts Condensate ^ Total Pressure, P / Ti Distance w Gas Layer Tv • Vapour Temperature, P a r t i a l T Pressure, Steam-air mixture Non-condensable Gas P a r t i a l Pressure, p g Direction of Steam-air . Flow Figure 1 : Pressure and temperature relationships for vapours condensing i n presence of noncondensable gases. 18 Dc can be c a l c u l a t e d by an e m p i r i c a l equation that was e s t a b l i s h e d by G i l l i l a n d in Sherwood and R i g f o r d (1952) as f o l l o w s : Dc = C T 1" 5 / p (10) .Where C = 4.2837 x 10"7 {(1/Ma + 1/Mb)0*5 / (Va 1/ 3 + Vb 1/ 3) 2} (11) Where p i s the t o t a l pressure (atmospheres), Va and Vb are the molecular volumes of d i f f u s i n g and i n e r t gases and Ma and Mb are the molecular weights of the two gases. Rohsenow and Har t n e t t (1973) have f u r t h e r i n d i c a t e d that the e f f e c t i v e t h i c k n e s s of the gas, ,-t7'', may be c a l c u l a t e d as f o l l o w s : t' = W R Tav / A p (12) Where W i s the t o t a l mass of gas present, Tav = (1/2) (Tv+Ti), T i i s the condensate temperature, R i s the gas constant and A i s the area of the condensing s u r f a c e . 19 Under dropwise condensation, there has r e c e n t l y been much d i v e r s i t y between the heat t r a n s f e r measurements of d i f f e r e n t o b s e r v e r s . T h i s d i v e r s i t y has been confirmed by Le Fevre and Rose (1967) to be due to the presence of noncondensable gases i n the steam. They have concluded that the presence of noncondensable gases has the e f f e c t of reducing the heat t r a n s f e r c o e f f i c i e n t . G r i f f i t h (1973), for temperature drops, AT, g r e a t e r than 0.5 F°, over which the n u c l e a t i o n e f f e c t s become n e g l i g i b l e , has i n d i c a t e d that the heat t r a n s f e r c o e f f i c i e n t can be c a l c u l a t e d from the equation: 1/h = 1/hi + 1/hdc + 1/hp + 1/hc + 1/hnc . (13) Where h i i s the i n t e r f a c i a l mass t r a n s f e r heat t r a n s f e r c o e f f i c i e n t , hdc i s the drop conduction heat t r a n s f e r c o e f f i c i e n t , hp i s the promoter heat t r a n s f e r c o e f f i c i e n t , he i s the c o n s t r i c t i o n heat t r a n s f e r c o e f f i c i e n t , and hnc i s the noncondensable gas heat t r a n s f e r c o e f f i c i e n t . He has a l s o i n d i c a t e d that hnc i s o f t e n the most important f a c t o r in the equation and at the same time cannot be evaluated f o r an untested system. The reason f o r t h i s he argues i s due to the f a c t that the s p e c i f i c a t i o n of the amount of a i r i n the incoming steam does not f i x the amount of a i r i n the condenser. He a l s o mentions that the v e n t i n g arrangement 20 and the l a r g e s c a l e c i r c u l a t i o n p a t t e r n s i n the condenser are very important. I t would appear that the above holds f o r very low a i r contents s i n c e f o r w e l l mixed steam-air at constant temperature and p r e s s u r e , accumulation of a i r would r e s u l t i n a higher p r e s s u r e . Abdul-Hadi (1979) c a r r i e d out experiments with d i f f e r e n t s u b s t r a t e s and h i s r e s u l t s are summarised in F i g u r e 2. He concluded that noncondensable gases are of a reducing i n f l u e n c e on the o v e r a l l heat t r a n s f e r c o e f f i c i e n t and that the curve tends to assume an asymptotic behaviour as the a i r content i n c r e a s e s . From the l i t e r a t u r e surveyed i t can g e n e r a l l y be concluded that there have been r e l a t i v e l y few s t u d i e s on the heat t r a n s f e r c o e f f i c i e n t f o r steam-air mixtures. T h i s i n f o r m a t i o n i s necessary and d e s i r a b l e f o r the safe and e f f i c i e n t u t i l i s a t i o n of steam-air as a thermal p r o c e s s i n g media. The nature of condensation ( f i l m w i s e or dropwise) can only be e s t a b l i s h e d by t e s t i n g the system. The c o r r e l a t i o n s found between the heat t r a n s f e r c o e f f i c i e n t and a i r r a t i o , are f o r l e s s important c o n f i g u r a t i o n s (predominantly v e r t i c a l ) , mostly e m p i r i c a l and l i m i t e d to small c o n c e n t r a t i o n s of a i r which are of l i t t l e p r a c t i c a l s i g n i f i c a n c e to steam-air p r o c e s s i n g of pouched products. 21 U 0) M-l CO c (0 u -P +J rcj cu (1) CD cn -H •H O g m n cu o o 53 O 9 12 15 18 21 24 27 30 33 36 39 A i r content (PPM) 42»10 Figure 2: Normalised heat trensfer c o e f f i c i e n t against a i r content, (from Abdul-Hadi, 19 79) 22 D. O b j e c t i v e s of t h i s Research The o b j e c t i v e of t h i s r e s e a r c h p r o j e c t was to e s t a b l i s h the f a c t o r s that a f f e c t the heat t r a n s f e r c o e f f i c i e n t f o r steam-air mixtures condensing on the underside of a r e t o r t pouch s u b s t r a t e . The study was a l s o intended to i n v e s t i g a t e the e f f e c t s of steam-air temperature and medium Reynolds number on the heat t r a n s f e r c o e f f i c i e n t . I t was a l s o intended to e s t a b l i s h the nature of condensation that takes p l a c e , and to design and c o n s t r u c t an experimental apparatus with which the above o b j e c t i v e s c o u l d be achieved. 23 MECHANICAL DESIGN OF THE EXPERIMENTAL EQUIPMENT In order to c a r r y out the proposed o b j e c t i v e s , an experimental apparatus was designed. A. F u n c t i o n a l S p e c i f i c a t i o n s The system was designed to be capable of the f o l l o w i n g requirements: 1. A i r r a t i o range of 0.0 to 0.5 2. Reynolds number range of 4,000 - 28,000 3. Maximum temperature of 125°C 4. Heat t r a n s f e r c o e f f i c i e n t measurement of d i f f e r e n t mixtures with a r e t o r t pouch laminate as the s u b s t r a t e f o r condensation. 5. V a r i o u s o r i e n t a t i o n s of the s u b s t r a t e as f o l l o w s : Mixture flow Condensing s u r f a c e o r i e n t a t i o n h o r i z o n t a l - v e r t i c a l - f a c i n g down with g r a v i t y opposing g r a v i t y - f a c i n g up - v e r t i c a l - v e r t i c a l 24 B. Conceptual Design F a c i l i t i e s f o r generating and v a r y i n g the Reynolds number of the d i f f e r e n t steam-air mixtures were a v a i l a b l e and have been d e s c r i b e d elsewhere, i n Tung(l980). So the task was to develop a sensor f o r measuring the heat t r a n s f e r c o e f f i c i e n t . The b a s i c concept that was used i s i l l u s t r a t e d i n F i g u r e 3. With e f f e c t i v e i n s u l a t i o n of the sensor b l o c k , and assuming that the thermal c o n d u c t i v i t y of the sehsor block, k, i s known or can be a c c u r a t e l y determined, i f the sensor i s s u b j e c t e d to a thermal g r a d i e n t ( i . e . one end i n co n t a c t with a steam-air mixture and the other c o o l e d by a low temperature f l u i d ) , the heat f l u x through the block can be c a l c u l a t e d from the equation, q/A = k dT/dx (14) But at the hot end of the sensor, i t can be w r i t t e n t h a t , h(Tv - Ts) = k dT/dx (15) Equating equations (14) and (15) and s o l v i n g f o r , h , the f o l l o w i n g can be obtained 26 h(Tv - Ts) = k dT/dx (16) h = k (dT/dx) / (TV - Ts) (17) The thermal g r a d i e n t dT/dx can be e s t a b l i s h e d from the r e g r e s s i o n equation of the thermocouple temperature measurements with respect to d i s t a n c e , x. Since the thermocouples run i n isothermal s u r f a c e s there i s not l i k e l y to be any s i g n i f i c a n t conduction along the thermocouple l e a d s . The s u r f a c e temperature, Ts, can be obtained by e x t r a p o l a t i o n . _ Measuring i t d i r e c t l y does not o f f e r good prospects s i n c e most experimental temperature measurements in the hydrodynamic boundary l a y e r s are only accurate to w i t h i n 10% ( K r e i t h , 1973). For d i f f e r e n t o r i e n t a t i o n s the e n t i r e condensation chamber can be r o t a t e d and/or i n c l i n e d and h e l d i n p o s i t i o n by an a p p r o p r i a t e support s t r u c t u r e . 27 C. Optimal Design 1. Condensation chamber The chamber l i e s under the "thick-wall cylinder" class, assuming that i t has a constant wall thickness, t, and that i t is to be subjected to uniform maximum internal pressure p!, a uniform maximum external pressure p 2 and a temperature change AT, measured from the inside surface. A schematic configuration i s shown in Figures 4 and 5. The temperature change AT, is a function of the ra d i a l coordinate, r, and the deformation of the cylinder i s symmetrical with respect to the axis of the cylinder (axisymmetric). Also the deformation at a cross-section s u f f i c i e n t l y far removed from the junction of the cylinder and i t s end caps can be considered p r a c t i c a l l y independent of the a x i a l coordinate z. The ra d i a l stress at r, a , the hoop stress at r, a_ , and the a x i a l stress, oz , can be calculated from the following r e l a t i o n s , from Boresi et a l . ( 1978) . r 1 2 AT r d r + ( l ) C + — i r 2 i r 2 (18) r 29 a'E r 2 ( l - v) a'E AT r 2 C AT r d r - i - + (1 '+ — ) C -1 - v l (19) C = r - r {p r 2 2 1 1 a'E r 2 + 2 2 1 - V AT r dr } I (20) C = -p r z 2 - 1 1 (21) 2 p r I I P r2 2 2 a -a'E AT 2a'E l + 1 - v (1 - v) (r 2 - r 2) I AT r dr I (22) Where a' i s the l i n e a r c o e f f i c i e n t of thermal expansion (1/C°), E i s the Young's modulus (kN/m2) and v i s the Poisson's r a t i o . 30 Since the c y l i n d e r i s sub j e c t e d to a s t a t i c l o a d d u r i n g o p e r a t i o n , the o c t a h e d r a l shearing s t r e s s y i e l d c r i t e r i o n was chosen f o r the desi g n . A standard p i p e , 6 inches-schedule 40 was chosen s i n c e i t was found to be most convenient f o r f a b r i c a t i o n purposes. A le n g t h of 1.010 m (40 inches) was t e n t a t i v e l y s e l e c t e d . The h i g h e s t pressure would occur at an a i r r a t i o of 0.5 and maximum temperature of 125°C . For steam at s a t u r a t i o n , .p = m R Tv / M v (23) v s Where m i s the mass (kg) , v g i s the volume (m 3), M i s the molecular weight, R i s the u n i v e r s a l gas constant, p i s the vapour pressure at s a t u r a t i o n , and Tv i s the s a t u r a t i o n temperature. If a q u a n t i t y of compressed a i r i s added, such that the r e s u l t i n g vapour r a t i o i s (1-a) , then i t can be w r i t t e n t h a t , p ( l - a ) v = m R Tv / M (24) ( 1 - a ) = m R T v / M p (25) 31 (1 - a) = p r / p (26) At Tv = 125°C , p = 232.1 kN/m2 . Therefore the maximum pressure was found to be 232.1/0.5 = 464.2 kN/m2. So p, = 464.2 kN/m2 and p 2 = 101.3 kN/m2 . The problem was f u r t h e r s i m p l i f i e d by assuming that AT, f ( r ) i s a l i n e a r f u n c t i o n . At an i n s i d e .temperature of 125°C , an o u t s i d e temperature of 96 °C was computed. T h i s was l a t e r measured to con f i r m the estimate. So at r, = 0.0771 m, AT, = 26 C ° . At r 2 = 0.0842 m, AT, = 29 C°. The r e s u l t i n g f u n c t i o n of AT, was found to be, AT = -4084.5 r + 343.9 (27a) Th i s was found to be equal to 0.0084 C° m2 With the f o l l o w i n g pipe p r o p e r t i e s : OD = 0.1683 m. ID = 0.1541 m. Inside area = 0.01864 m2. Metal area = 0.0036 m 2 . Weight - W = 9.0584 kg. So (27b) 32 Y i e l d p o i n t s t r e s s , a = 4 1 3 , 7 0 0 kN/m2. Poisson r a t i o , v = 0 . 3 . Young's modulus, E = 2 1 0 . 0 x 10 6 kN/m2. Li n e a r C o e f f i c i e n t of thermal expansion, a 1 , = 1 . 0 9 8 x 1 0 ~ 5 / C 0 . C, was c a l c u l a t e d to be 2 5 , 4 0 0 kN/m2. C 2 was c a l c u l a t e d to be - 2 . 8 kN. At r = 0 . 0 7 7 1 , m. a r was found to be - 4 6 4 kN/m2 (compressive) . aa was found to be - 4 4 , 8 0 0 kN/m2 . a _ was found to be - 7 0 , 2 0 0 kN/m2 . At r = . 0 . 0 8 4 2 , m. or was found to be - 1 0 1 kN/m2 . oQ was found to be + 5 0 , 8 0 0 kN/m2 . oz was found to be + 2 5 , 3 6 7 . 9 kN/m2 A sketch of s t r e s s d i s t r i b u t i o n i s given i n F i g u r e 6 . S a t i s f a c t o r y performance of the c y l i n d e r i s expected i f the maximum o c t a h e d r a l shearing s t r e s s , : T m a x t kN/m2 does not exceed 0 . 4 7 1 a /F.S. , where F.S. i s the f a c t o r of yp s a f e t y . In'other words, x < 0 . 4 7 1 a /F.S . 2 max yp B u t W = 1 / 3 { ( a r " V 2 + ( 0 9 ~ ° z ) 2 + K - ar) 2 } Q * 5 ( 2 8 ) At r 0 . 0 7 7 1 , using equation 2 8 , T was found to be ^ ^ ' max 2 3 , 2 0 0 kN/m2. At r = 0 . 0 8 4 2 , using equation 2 8 , T was 33 Stres Figure 6: Sketch of stress distribution in the condensation chamber. 34 found to be 20,800 kN/m2. For a s a f e t y f a c t o r (F.S.) of 3.0, (0.471 a /F.S) was c a l c u l a t e d to be 65,000 kN/m2 . Since x < (0.471 c /F.S), the chamber was max yp t h e r e f o r e c o n s i d e r e d mechanically s a f e . 2. End caps The mechanical design f o r the end caps was based on pressure f o r c e s . Since the r a t i o of the r a d i u s of the cap to the ra d i u s of the hole i n the centre was found to be high, the cap was t r e a t e d as a c i r c u l a r p l a t e , r i g i d l y f i x e d so that there i s no r o t a t i o n or displacement at the edges. In F i g u r e 7 a schematic diagram i s shown. For a c o n f i g u r a t i o n l i k e t h i s , the maximum s t r e s s occurs at the edge and can be c a l c u l a t e d from the equation: Also x < 0.471 a / F.S. max — YP ' But x = 1/3 a max max T h e r e f o r e 1/3 (0.75 p r , 2 / l 2 ) < 0.471 a / F.S. For a yp 35 P I Figure 7: End cap loading. 0 — r0=12.7nm Teflon I n s u l a t i o n I Figure 8: Sensor block loading. 36 f a c t o r of s a f e t y of 3 and a of 413,700 kN/m2 , YP 1 > 0.0046 m. In otherwords 0.0046 m i s the minimum t h i c k n e s s of the end cap that c o u l d be employed without mechanical f a i l u r e . 3. Sensor block The most s u i t a b l e m a t e r i a l f o r the sensor block was found to be s t a i n l e s s s t e e l , mainly because of i t s e x c e l l e n t c o r r o s i o n r e s i s t a n t p r o p e r t i e s and i t s low c o n d u c t i v i t y . For the mechanical design, the sensor block was t r e a t e d l i k e a c i r c u l a r p l a t e . In F i g u r e 8, a schematic diagram of the same i s shown. From Wahl and Lobo (1930). x = k P / l 2 (30) max ' v ' Where k = f ( r , / r 2 ) = f(0.0368/0.0127)= 1.54 P = TT r 2 2 p = TT (0.0191 ) 2 x 464.2 kN = 241,000 kN/m2 B u t 1 / 3 amax^ ° ' 4 7 1 a y p / F - S -For F.S. = 3.0 and a = 241,325.0 kN/m2, 1/3 (1.54 X T T(0.0191) 2 4 6 4 . 2 ) / l 2 < (0.471 x 241,000) /3, Therefore 1 > 0.0027 m. In otherwords 0.0027 m i s the 37 minimum t h i c k n e s s of the sensor i n s u l a t i o n f l a n g e that c o u l d be employed without mechanical f a i l u r e . 4. Sensor i n s u l a t i o n T e f l o n (PTFE) was chosen as an a p p r o p r i a t e m a t e r i a l f o r i n s u l a t i o n purposes, s i n c e i t can perform w e l l without any d e t e r i o r a t i o n up to 250°C . A l s o , i n a d d i t i o n to being r i g i d i t s r e s i s t a n c e to water i s e x c e l l e n t and most important of a l l , i t has a very low thermal c o n d u c t i v i t y . Since the i n s u l a t i o n f i t s on the sensor as shown i n Appendix B, the pressure f o r c e s a c t i n g on i t are t r a n s m i t t e d d i r e c t l y to the sensor. Mechanical f a i l u r e can only occur i f the compressive s t r e s s due to the pressure exceeds the safe performance compressive s t r e s s . The maximum compressive s t r e s s of 232 kN/m2 i s w e l l below the maximum safe s t r e s s of 1,670 kN/m2 (Watson et a l . 1972) The success of T e f l o n as the sensor i n s u l a t i o n i s dependent upon the r a t i o of energy l o s t or gained to the t o t a l energy through the sensor. C o n s i d e r i n g the sensor c o n f i g u r a t i o n as shown i n Appendix B, F i g u r e 25, the s t r u c t u r e can be approximated to a case of two c o n c e n t r i c c y l i n d e r s . The i n s u l a t i o n being the smaller c y l i n d e r and the chamber being the the l a r g e r c y l i n d e r . The s i m p l i f i e d form i s i l l u s t r a t e d i n F i g u r e 9. 38 ' Condensation / / ciiamber / / j V Sensor insulation Figure 9: Sensor configuration approximated to a case of two concentric cylinders. With the above s i m p l i f i c a t i o n the q u a n t i t y of energy l o s t or gained through the i n s u l a t i o n can be c a l c u l a t e d using the equation of c o n c e n t r i c c y l i n d e r s ( K r e i t h , 1973). In (r / r ) In (r / r ) Q = (Ti - To) / { + — • (31) 2TT k 1 2irk 1 1 2 With the f o l l o w i n g p r o p e r t i e s , 1 = 0.0381 m. r, = 0.0127 m. r 2 = 0.0191 m. 39 r 3 •= 0.0241 m. k, = 0.25 W/m °C. k 2 = 24.80 W/m °C. T i = (T, + T 2 ) / 2, and a t y p i c a l value of T, of 30°C , a t y p i c a l value of T 2 of 105°C , a minimum value of T i of 65°C , a maximum value of Tb of 96°C , a maximum value of T i - Tv of 31 C ° , Q was e s t a b l i s h e d , from equation 31, to be equal to -4.6 Watts. Thus the small amount of energy gained by the sensor through the i n s u l a t i o n may be ne g l e c t e d and t h e r e f o r e the performance of T e f l o n was judged to be s a t i s f a c t o r y . D. System D e s c r i p t i o n The complete system d e s c r i p t i o n , by way of working, drawings and schematic diagrams i s shown i n Appendix B. A schematic diagram of the system layout i s shown i n F i g u r e 20. The condensation chamber, the end caps, the sensor and sensor i n s u l a t i o n are shown i n F i g u r e s 21,22,23 and 24 r e s p e c t i v e l y . A s e c t i o n of the assembly drawing i s shown i n Fi g u r e 25. 40 EXPERIMENTAL PROCEDURE The heat t r a n s f e r c o e f f i c i e n t was measured at f i v e temperatures of approximately 105, 110, 115, 121 and 125 °C. The a i r content f r a c t i o n was v a r i e d between 0.0 and 0.5. The a i r flowrate was v a r i e d between 4720 x 10" 6 m3/s and 14200 x 10" 6 m 3/sec. The experimental design i s given i n Table I. Each run c o n s i s t e d of s i x experiments with c o o l i n g water f l o w r a t e s of 37.5, 45.6, 52.7, 78.8, 87.5 and 87.8 g/s. The temperature and pressure c o n t r o l s were set to give the d e s i r e d c o n d i t i o n s . For example at a temperature of 105.0°C, an a i r - f l o w r a t e of 4720 x 10" 6 m3/s and an a i r r a t i o of 0.3, the c o n t r o l system set p o i n t s were c a l c u l a t e d as f o l l o w s . The temperature c o n t r o l l e r had a c o n t r o l range of 0.0 to 150.0°C which corresponds" to a s c a l e of 0% to 100%. So for a temperature of 105.0°C, the c o n t r o l system was set at 105.0/150 x 100% = 70% . The gauge pressure c o n t r o l l e r had a c o n t r o l range of 0.0 to 345 kN/m2, which corresponds to a s c a l e of 0% to 100%. So f o r the above-mentioned c o n d i t i o n s the system pressure was c a l c u l a t e d from equation 26 . With an atmospheric pressure of 101.3 kN/m2, the gauge pressure was c a l c u l a t e d as (120.8/(1-0.3)) -101.3 which equals 73.1 kN/m2. The c o n t r o l system was t h e r e f o r e set at 71.3 / 345 X100% which equals 20.7%. Table I: Experimental design showing temperature, a i r f r a c t i o n and mixing a i r f l o w r a t e . Run A i r Temper- A i r Number Number Flowrate ature R a t i o of x 105 m3/s °C R e p l i -c a t e s 1 051 0 4720 105.0 0.0 3 10512 4720 1 05.0 0.2 3 10513 4720 105.0 0.3 3 1 051 4 4720 1 05.0 0.4 3 1 051 5 4720 1 05.0 0.5 3 10523 9430 105.0 0.3 2 1 0533 1 41 50 1 05.0 0.3 2 11010 4720 110.0 0.0 2 11011 4720 110.0 0.1 1 11012 4720 110.0 0.2 1 11013 4720 110.0 0.3 5 11014 4720 110.0 0.4 2 11015 4720 110.0 0.5 2 11510 4720 115.0 0.0 1 11512 4720 115.0 0.2 1 11513 4720 115.0 0.3 11514 4720 115.0 0.4 1 11515 4720 115.0 0.5 1 12110 4720 121.0 0.0 1 12112 4720 121.0 0.2 1 12113 4720 121.0 0.3 12114 4720 121.0 0.4 1 12115 4720 121.0 0.5 1 1 251 0 4720 1 25.0 0.0 1 1 251 2 4720 1 25.0 0.2 1 1 251 4 4720 125.0 0.4 1 42 The c o o l i n g water f l o w r a t e was set by means of a c a l i b r a t e d v a l v e . Time was allowed f o r the system to s t a b i l i s e , a f t e r which the thermocouple temperature readings were recorded by means of a Kaye Ramp II scanner/processor system, at i n t e r v a l s of one minute f o r a p e r i o d of seven minutes. The gauge pressure readings were tken at i n t e r v a l s of two minutes and were averaged. Then the c o o l i n g water f l o w r a t e was changed to the next d e s i r e d v a l u e , the system was allowed to s t a b i l i s e and the thermocouple readings were recorded. T h i s was repeated u n t i l a l l the d e s i r e d f l o w r a t e s were exhausted. Then the c o n t r o l system was set f o r the next run, and the procedure repeated. 43 RESULTS AND DISCUSSION A. R e s u l t s A l l thermocouples were c a l i b r a t e d a g a i n s t an ASTM mercury i n g l a s s thermometer and the a p p r o p r i a t e c o r r e c t i o n s were made to the data t a b u l a t e d i n Table V I I I , Appendix E. The f o l l o w i n g example f o r Run 10533, Expt. No. 5 w i l l i l l u s t r a t e how the heat f l u x , temperature drop and heat t r a n s f e r c o e f f i c i e n t were c a l c u l a t e d . The c o r r e c t e d data for the experiment are shown in Table II . The r e s u l t s are summarised i n a diagrammatic form i n F i g u r e 10 and the thermocouple p o s i t i o n s r e f e r r e d to are shown i n F i g u r e 3. Table I I : C o r r e c t e d data f o r experiment no.5, run 10533. Time Thermocouple Readings, °C (min.) T51 T52 T53 T56 T57 T58 T59 1 80 .9 105.1 105.1 37.6 46. 1 57.9 67.6 2 81 . 1 1 05.2 1 05. 1 37.7 46.2 57.9 67.7 3 81 .2 105.2 105.1 37.7 46.2 57.9 67.7 4 81 .0 105. 1 105.1 37.6 46. 1 57.9 67.6 5 81 .2 1 05.2 105. 1 37.6 46. 1 57.8 67.6 6 81 . 1 105.2 105.1 37.6 46. 1 57.8 67.6 7 81 .2 1 05.2 105.1 37.6 46. 1 57.8 67.6 Mean 81 . 1 105.2 1 05. 1 37.6 46. 1 57.9 67.6 • Dev. 0. 1 2 0.05 0.00 0.05 0.05 0.05 0.05 44 The r e g r e s s i o n equation that d e s c r i b e s the temperature p r o f i l e was found to be T = 26.8 + 1605,9x, r c = 0.9985. Using t h i s equation Ts was estimated to be 88.0°C . Tv was obtained by t a k i n g the average of T52 and T53 = (105.17 + 105.10)/2 °C. The temperature drop between the s u b s t r a t e and the steam-air mixture was found to be 17.2 C ° . Using the thermal c o n d u c t i v i t y of s t a i n l e s s s t e e l 316 of 17.3 W/m C°, the heat f l u x , Q/A, was found to be 17.3 x 1605.9 = 27,800 W/m2 D i v i d i n g by the temperature drop, AT, the heat t r a n s f e r c o e f f i c i e n t was found to be 1620 W / m 2 ° C . The corresponding Reynolds number was c a l c u l a t e d as i n d i c a t e d i n Appendix C. B. C o r r e l a t i o n of the Data The data were c o r r e l a t e d by means of d e r i v i n g e m p i r i c a l equations. I t was observed that the heat t r a n s f e r c o e f f i c i e n t depends upon the temperature of the steam a i r mixture, the temperature drop from the steam-air to the condensing s u b s t r a t e , AT , and/or the temperature of the condensing s u b s t r a t e . I , I t x^ x^ Xj- x (m) 0.0064 0.0191 0.0381 0.0127 0.025^ Figure 10: Schematic diagram of the sensor showing thermocouple positions and a typical temperature gradient. 46 The e f f e c t s of these v a r i a b l e s were determined e m p i r i c a l l y from the data by p l o t t i n g the experimental values h vs. Ts, h vs. AT, In (h) vs. Ts and In (h) vs. AT. P l o t s of these types are shown in F i g u r e s 11,12,13 and 14, r e s p e c t i v e l y . From F i g u r e s 13 and 14 i t i s to be seen that s t r a i g h t l i n e s are reasonable c o r r e l a t i o n s . T h i s i m p l i e s that f o r a given steam-air temperature, the n a t u r a l l o g a r i t h m of the heat t r a n s f e r c o e f f i c i e n t i s approximately a l i n e a r f u n c t i o n of the s u b s t r a t e temperature and/or the temperature drop. So, a Ts h = a e 2 at a constant Tv (32) l 3 AT h = 3 e 2 at a constant Tv (33) I Where a , a , 3 and - 3 are parameters. . These 1 2 1 2 parameters were estimated by use of a computer program, BMDP3R a v a i l a b l e on UBC computing system, f o r e s t i m a t i n g parameters of n o n l i n e a r models by the method of l e a s t squares. The r e s u l t s are summarised in Tables III and IV . 47 Figure 11 : Plot of h against Ts for steam-air temperature of 105, 110, 115, 121, and 125°C. 48 3Q0QI— 2500 X X TV = 105°C A TV = 110 °C 0 TV = 115 °C • TV = 121 °C s TV - 125 °C o CM 5 2000| 1500 1000 10 Figure 12 "V: •* X * 1 15 20 AT, °C. 25 30 Plot of h against AT for steam-air temperatures of 105, 110, 115, 121, and 125 °C. 49 8.0 X Tv = 105°C A Tv = 110°C #jj <*> TV = 115 °C x • TV = 121°C X TV = 125°C * x £ 7.51 7.0 * X * 4*4 4 . i t • 9 80 85 90 95 Ts, °C. 100 105 110 Figure 13 : Plot of ln(h) against Ts for steam-air temperatures of 105, 110, 115, 121, and 125°C. 50 8.0 X TV = 105°C A TV = 110°C <*> TV = 115 °C • TV = 121 °C X TV = 125°C H 7.5 3 7.0 * 4 • • QV X »«" ^ v ^ * _L 1 10 15 20 25 AT, °C. 30 35 Figure 14 : Plot of ln(h) against AT for steam-air teitiperatures of 105, 110, 115, 121 and 125°C. 51 Table III : Estimated parameters a and a . 1 2 Temp. °C a a S.E. of S.E. of 1 2 (W/nf C) (1 /C) a a 1 2 105 1.2686 0.0813 0.1157 0.0010 110 4.0383 0.0648 0.4896 0.0013 115 6.9137 0.0564 0.7155 0.0011 121 4.1374 0.0589 0.6526 0.0016 125 5.3205 0.0545 1.0895 0.0020 Table IV : Estimated parameters 3 and 3 Temp, 3 3 (W/m2 C) (1/C°) S.E. of 3 S.E. of 1 05 1 1 0 1 1 5 121 1 25 6311 .6 4998.7 4994.2 4768.0 4928.3 -0.0799 •0.067-3 -0.0604 -0.0551 -0.0551 93 98 1 14 68 1 50 1 6 89 30 66 72 0, 0, 0 0 0 001 0 0010 001 1 0007 001 5 S.E. i s the Standard E r r o r . P l o t s of the p r e d i c t e d heat t r a n s f e r c o e f f i c i e n t versus Ts are shown i n F i g u r e s 15. P l o t s of the p r e d i c t e d heat t r a n s f e r c o e f f i c i e n t a g a i n s t AT are shown in F i g u r e 16. 52 4500, 4000 (1) TV = 105°C (2) TV = 110°C (3) TV = 115°C (4) TV = 121°C (5) TV = 125°C 3500 3000 u eg ^ 2500 2000 1500 1000 500 I i I 1 I t 1 . I 80 85 90 95 Ts, °C. 1Q0 105 110 115 Figure 15 Plot of predicted h against Ts for steam-air temperatures of 105, 110, 115, 121 and 125°C. 53 4000 1 1 ' 1 1 1 1 1 1 (1) TV = 105°C 3500 (2) TV = 110°C (3) TV = 115 °C (4) TV = 121°C (5) TV = 125°C 3000 — 2500 — 2000 — \(4) N\\X(5) 1500 — 1000 CD ' < 2 ! (3) 500 i 1 1 I • 1 I 1 1 5 10 15 20 25 30 AT, C°. Figure 16 : Plot of predicted h against AT for steam-air temperatures of 105, 110, 115, 121 and 125°C. 54 The dependence of the heat t r a n s f e r c o e f f i c i e n t on the temperature drop, AT, supports the gas l a y e r - f o r m a t i o n h y p o thesis as proposed by Kern(1950). I t appears that a l a r g e AT corresponds to a t h i c k e r gas l a y e r . T h i s t h i c k e r gas l a y e r seems to occur at low s u b s t r a t e temperatures. T h i s i s probably because the temperature of the s u b s t r a t e i s w e l l below the s a t u r a t i o n temperature of the steam, which causes steam, adjacent to the s u b s t r a t e to condense, l e a v i n g a t h i c k gas l a y e r . A l s o a l a r g e p r essure d i f f e r e n t i a l between the t o t a l pressure and the vapour p a r t i a l pressure at the s u b s t r a t e i s c r e a t e d as a r e s u l t of condensation of the adjacent steam. T h i s p r essure d i f f e r e n t i a l a c t s as the p o t e n t i a l f o r the d i f f u s i o n of steam through the gas l a y e r . As more steam d i f f u s e s through the gas l a y e r , g i v i n g up i t s l a t e n t heat by condensing on the s u b s t r a t e , the temperature of the s u b s t r a t e r i s e s , reducing the pressure p o t e n t i a l and reducing the gas l a y e r t h i c k n e s s as there i s l e s s d i f f u s i o n . O v e r a l l , the gas l a y e r seems to act as a thermal r e s i s t a n c e to heat t r a n s f e r ; hence, there i s a higher heat t r a n s f e r c o e f f i c i e n t at l a r g e AT ' s which correspond to t h i c k e r gas l a y e r s . So i t appears that f o r steam-air up to an a i r r a t i o of 0.5, the r e l a t i o n s h i p s d e p i c t e d by equations 32 and 33 h o l d . The a i r r a t i o i s t i e d up i n Ts or AT such that at a high a i r r a t i o the r a t e of change of e i t h e r Ts or AT i s expected to be low and at a low a i r r a t i o the r a t e of change of e i t h e r Ts or AT i s expected to be high as there would be 55 more steam in the l a t t e r case to d i f f u s e through the gas l a y e r and give up more l a t e n t heat at the s u b s t r a t e . If the above argument i s reasonable then there should be a r e l a t i o n s h i p between AT and the gas l a y e r t h i c k n e s s . Rohsenow and H a r t n e t t (1973) i n d i c a t e d that the e f f e c t i v e t h i c k n e s s of the gas l a y e r , t' can be c a l c u l a t e d by equation 12. Although Rohsenow and H a r t n e t t (1973) i n d i c a t e d that W, the t o t a l mass of the gas present, should be used i n s t e a d of the gas to vapour mass r a t i o , because the q u a n t i t y of the gas to vapour r a t i o i s a f u n c t i o n of the system volume, in t h i s work, only one s i z e of condensation chamber was used, t h e r e f o r e i t appears that the gas to vapour r a t i o can be employed. The problem i s that T i can not be estimated. But s i n c e most of the experiments were c a r r i e d out at high Reynolds numbers i t i s l i k e l y that the flow of the condensate was t u r b u l e n t , so T i can be assumed approximately equal to Ts. If the gas to vapour mass r a t i o i s designated by m, f o r a known condensation chamber volume, Vsa, the volume of the a i r component can be c a l c u l a t e d as ( a x Vsa ). The mass of the a i r would be (a x Vsa p ). a For steam,the mass would be ( (1-a) x Vsa p )-. Ks So m = a Vsa p / (1-a) Vsa p . Given that W i s cl S p r o p o r t i o n a l t o t ' , then t.'would be p r o p o r t i o n a l to { a( p = )(2Tv-AT) / (1-a) P„ p } ,designated by SL , or a. to r e f e r r e d to as the apparent gas l a y e r t h i c k n e s s . A l i n e a r 56 r e g r e s s i o n of I a g a i n s t AT y i e l d e d a c o r r e l a t i o n c o e f f i c i e n t of 0.646 . The p l o t i s shown in F i g u r e 17. A high c o r r e l a t i o n c o e f f i c i e n t suggests a trend where T i n c r e a s e s with the apparent gas l a y e r t h i c k n e s s . Since the steam from the main body can only condense by d i f f u s i n g through the gas l a y e r and s i n c e there appears to be a r e l a t i o n s h i p between the gas l a y e r t h i c k n e s s and the temperature drop i t was decided to check the r e l a t i o n s h i p between the d i f f u s i o n c o e f f i c i e n t of steam through the gas l a y e r and the temperature drop, AT. The d i f f u s i o n c o e f f i c i e n t was c a l c u l a t e d u sing G i l l i l a n d ' s equation in Sherwood and R i g f o r d (1952) as shown in Appendix D. A p l o t of AT vs. Dc i s shown in F i g u r e 18. From t h i s i t i s to be seen that a s t r a i g h t l i n e i s a reasonable c o r r e l a t i o n , the c o r r e l a t i o n c o e f f i c i e n t was found to be 0.816. It i s n o t i c e a b l e that at high AT there i s l e s s v a r i a b i l i t y but as AT decreases, v a r i a b i l i t y i n c r e a s e s . T h i s i s probably due to the f a c t that as AT decreases the gas l a y e r decreases, the d i f f e r e n t i a l pressure p o t e n t i a l decreases and the motion of steam vapour i s l e s s dependent on d i f f u s i o n . If equations 33 and 34 are combined the heat t r a n s f e r c o e f f i c i e n t can be p r e d i c t e d by an equation of the form: Y Dc h. = y e 2 (35) l 57 .300 CNJ-,200 6 I o .100 x w *Nx * x x * xx*<x* «xx X 10 15 20 25 30 AT, C° Figure 13: Plot of Dc against AT for steang-air temperature range of 105 - 125 C. 59 From equation 10 i t i s noteworthy that Dc i s a f u n c t i o n of the steam-air temperature and the t o t a l p r e s s u r e . A l s o , from equation 26, s i n c e the s a t u r a t i o n pressure i s a f u n c t i o n of the steam-air temperature, i t can be presumed that the a i r content i s a f u n c t i o n of temperature and p r e s s u r e . So i t can be i n f e r r e d that Dc i s r e l a t e d to the a i r c o ntent. A c c o r d i n g l y , the parameters y and y were 1 2 estimated f o r a l l the data. y^  was estimated to be 792, I with S.E. of 34.0, y was estimated to be 42100, with S.E. 2 of 2390 . I t was observed that at high d i f f u s i o n c o e f f i c i e n t s which correspond to low AT" s there i s a l a r g e amount of v a r i a b i l i t y , which supports the hypothesis that the movement of vapour through the gas l a y e r at low AT" s i s l e s s dependent on the d i f f u s i o n mechanism. A p l o t of the p r e d i c t e d heat t r a n s f e r c o e f f i c i e n t versus the d i f f u s i o n c o e f f i c i e n t i s shown in F i g u r e 19. C. I n f l u e n c e of Reynolds Number on the Parameters Kusak (1958) showed that the parameters i n h i s model depended on the geometry of the system and the Reynolds number. Therefore to i n v e s t i g a t e the i n f l u e n c e of Reynolds number on the parameters, m u l t i p l e r e g r e s s i o n was employed assuming models of the form: 6 6 Ts h = 6 Re 2 e 3 (36a) 60 61 6 6 AT h = 6 Re 2 e 2 (36b) For equation 36a, Re was shown to have a p a r t i a l c o r r e l a t i o n of -0.0043, and f o r equation 36b, Re was shown to have a p a r t i a l c o r r e l a t i o n of -0.0269. The reason f o r t h i s i s not wel l understood, but a l s o the p o s s i b i l i t y of a poor estimate of the Reynolds number cannot be r u l e d out. D. Mode of Condensation The heat t r a n s f e r c o e f f i c i e n t obtained f o r the a i r content set at 0.0 ranged between 1228 and 3041 w/m2K. These values were found to be p r e d i c t a b l e by the i n d i c a t e d models which assume the presence of noncondensable gases. T h i s seems to i n d i c a t e that when the system was set at zero a i r content, there must have been a s u b s t a n t i a l amount of a i r s t i l l p resent. Coulson and Richardson (1977) have i n d i c a t e d that the average value of the heat t r a n s f e r c o e f f i c i e n t f o r condensation of pure vapours on h o r i z o n t a l tubes ranges from 10,000 to 28,000 W/m2K for AT range of 1 -11 C° and 18,000 to 37,000 W/m2K f o r AT range of 4 - 37 C° . 62 They have estimated the dropwise condensation heat t r a n s f e r c o e f f i c i e n t to l i e between 40,000 and 114,000 W/m2K. As i n d i c a t e d e a r l i e r , Othmer (1929) found that the presence of 0.5% a i r by volume would decrease the heat t r a n s f e r c o e f f i c i e n t by 50%. And as the a i r content i n c r e a s e s the normalised heat t r a n s f e r c o e f f i c i e n t tends towards an asymptote. For a temperature of 110°C and a i r content range of 0% to 7%, the asymptote by i n s p e c t i o n i s about 0.12. Using t h i s v a l u e , and, assuming that the a i r content of the steam with the system set at zero to be about 5%, the heat t r a n s f e r c o e f f i c i e n t of the pure steam can be shown to l i e between 10,200 and 25,300 W/m2K. The asymptotic nature of the normalised heat t r a n s f e r c o e f f i c i e n t has been observed by Abdul-Hadi (1979) as w e l l . As shown i n Fi g u r e 2 the asymptote i s approximately 0.1 f o r the range of a i r content up to 4.2%. T h i s value p l a c e s the heat t r a n s f e r c o e f f i c i e n t i n the range 12,300 to 30,000 W/m2K. Since the heat t r a n s f e r c o e f f i c e n t s f o r a i r content approaching zero are c o n s i d e r a b l y lower than the range e s t a b l i s h e d f o r dropwise condensation, i t can be concluded that the mode of condensation i s l i k e l y to be f i l m w i s e . 6 3 E. Average Heat T r a n s f e r C o e f f i c i e n t f o r Steam-air Thermal Processes The e x p o n e n t i a l r e l a t i o n s h i p s developed i n t h i s study are based on steady s t a t e experimental c o n d i t i o n s . In other words the heat t r a n s f e r c o e f f i c i e n t i s measured at a constant AT and Ts. Making these measurements over a range of AT's or Ts's p o r t r a y s how h may vary, d u r i n g thermal p r o c e s s i n g . For high B i o t number thermal process c o n d i t i o n s , where AT r a p i d l y f a l l s to a very low value, the average heat t r a n s f e r c o e f f i c i e n t would approximately be equal to 8 , s i n c e h tends towards 0 as AT tends towards 0. For low 2 B i o t number thermal process c o n d i t i o n s , where AT g r a d u a l l y f a l l s to a low value, the average heat t r a n s f e r c o e f f i c i e n t may be computed by i n t e g r a t i n g h, a f u n c t i o n of time, with respect to time, over the e n t i r e p rocess. 64 CONCLUSIONS In t h i s s t u d y , t h e e f f e c t s on t h e 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 o f t h e d i f f u s i o n c o e f f i c i e n t ( w h i c h i s a f u n c t i o n o f t h e a i r c o n t e n t o f a g i v e n s t e a m - a i r m i x t u r e ) , t h e s t e a m - a i r t e m p e r a t u r e , t h e c o n d e n s a t i o n s u b s t r a t e t e m p e r a t u r e , t h e t e m p e r a t u r e d r o p a n d t h e R e y n o l d s number" were i n v e s t i g a t e d . The r e s u l t s o f t h i s work s u p p o r t t h e f o l l o w i n g c o n c l u s i o n s : (1) The c o n d e n s a t i o n m e c h a n i s m of s t e a m f r o m t h e s t e a m - a i r m i x t u r e , on a r e t o r t p o u c h s u b s t r a t e i s f i l m w i s e . (2) F o r a g i v e n s t e a m - a i r t e m p e r a t u r e , 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 c a n be d e t e r m i n e d e m p i r i c a l l y f r o m m o d e l s o f t h e f o r m : a Ts h = a e 2 I 3 AT h. = B. e 2 where a - , a , 8 , a n d 6 a r e p a r a m e t e r s . 1 2 1 2 (3) . A t h i g h A T ' s 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 c a n be 65 p r e d i c t e d by a model of the form : Y Dc h = Y e 2 1 where y and y are parameters and Dc i s the 1 2 d i f f u s i o n c o e f f i c i e n t . (4) The Reynolds number w i t h i n the range of 4,000 to 28,000 as used i n t h i s study does not seem to have a s i g n i f i c a n t e f f e c t on the parameters a and 3 I i 66 SUGGESTIONS FOR FURTHER STUDY A l t h o u g h some of t h e f a c t o r s t h a t a f f e c t 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 f o r s t e a m - a i r m i x t u r e s h a v e been i d e n t i f i e d i n t h i s s t u d y , , t h e e x t e n t t o w h i c h t h i s h a s been done i s n o t c o m p l e t e . The f o l l o w i n g i n v e s t i g a t i o n s a r e t h e r e f o r e p r o p o s e d f o r f u t u r e s t u d y : ( 1 ) The 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 s u r f a c e t e m p e r a t u r e s c l o s e t o t h e s t e a m - a i r t e m p e r a t u r e s h o u l d be e s t a b l i s h e d . (2) S i m i l a r s t u d i e s t o t h i s s h o u l d be c a r r i e d o u t f o r o t h e r o r i e n t a t i o n s s i g n i f i c a n t t o r e t o r t p o u c h p r o c e s s i n g , s u c h a s a r r a n g i n g t h e p o u c h e i t h e r v e r t i c a l l y o r i n a p o s i t i o n f a c i n g u p w a r d s , w h i l e m a i n t a i n i n g a h o r i z o n t a l m i x t u r e f l o w , a s w e l l a s c h a n g i n g t h e m i x t u r e f l o w i t s e l f f r o m h o r i z o n t a l t o v e r t i c a l , b o t h w i t h a n d a g a i n s t g r a v i t y . ( 3 ) The t h e o r e t i c a l l y d e t e r m i n e d t r a n s p o r t p r o p e r t i e s f o r s t e a m - a i r m i x t u r e s , n a m e l y d e n s i t y a n d v i s c o s i t y s h o u l d be v e r i f i e d e x p e r i m e n t a l l y f o r a b e t t e r e s t i m a t e o f t h e R e y n o l d s n u m b e r . (4) I n c r e a s e i n 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 a s a r e s u l t o f u s i n g p r o m o t e r s s u c h a s o l e i c a c i d , s t e a r i c a c i d , d i o c t a d e c y l d i s u l p h i d e a n d c u p r i c o l e a t e , s h o u l d be i n v e s t i g a t e d i n c a s e o f r e t o r t pouch p r o c e s s i n g . 67 LITERATURE CITED Abdul-Hadi, M. I. 1979. Dropwise condensation of d i f f e r e n t steam-air mixtures on v a r i o u s s u b s t r a t e m a t e r i a l s . Can. J . Chemical Engineers. 57(4):451. B o r e s i , A. P., Sidebottom, 0. M., Seedy, F. B., Smith, J . 0. 1978. "Advanced Mechanics of M a t e r i a l s " , 3rd ed., John W i l l e y & Sons, New York, NY. Copley, D. I. 1978. The r e t o r t pouch - the way ahead with aluminum f o i l . I n t . J . F l a v o u r s and Food A d d i t i v e s . 9 ( 1 ) : 2 8 . Coulson, J . M., Richardson, J . F. 1977. "Chemical E n g i n e e r i n g " , 3rd ed. v o l . I, Robert Maxwell, Pergamon Press, Oxford, U.K. Davis, R. B., Long, F. E. and Robertson, W. F. 1972. E n g i n e e r i n g c o n s i d e r a t i o n s i n r e t o r t pouch p r o c e s s i n g of f l e x i b l e packages. Food Technol. 26(8):65. F a t i c a , N i c h o l a s and Katz, Donald, L. 1949. Dropwise condensation. Chemical E n g i n e e r i n g Prog. 45(11):661. Gerstmann, J . and G r i f f i t h , P. 1967. E f f e c t of s u r f a c e i n s t a b i l i t y on laminar f i l m condensation. I n t . J . Heat Mass T r a n s f e r 10:567. G r i f f i t h , P. 1973. Dropwise condensation. "Handbook of Heat T r a n s f e r " , McGraw-Hill Book Co., Inc., New York, NY. Heldman, Dennis R. 1975. "Food Process E n g i n e e r i n g " , Avi P u b l i s h i n g Co., I n c . , Westport, CT. Kern, D. Q. 1950. "Process Heat T r a n s f e r " , McGraw-Hill Book Co., Inc., New York, NY. K r e i t h , F. 1973. " P r i n c i p l e s of Heat T r a n s f e r " , 3rd ed. Harper and Row, New York, NY. Kusak, L l o y d , J . 1958. "The Condensation of Vapours from Noncondensing Gases", Ph.D. T h e s i s , C o r n e l l U n i v e r s i t y . Le Fevre, E. J . and Rose, J . W. 1967. A theory of heat t r a n s f e r by dropwise condensation. Proc. T h i r d I n t . Heat T r a n s f e r Conf. v o l . I I : 755. 68 Meisenburg, S. J . , Boarts, R. M. and Badger, W. L. 1934/35. The i n t e r f e r e n c e of small c o n c e n t r a t i o n s of a i r i n steam on the steam f i l m c o e f f i c i e n t of heat t r a n s f e r . Trans. American S o c i e t y of Chemical Engineers. v o l . XXXI:622. Mermelstein, N. H. 1978. R e t o r t pouch earns 1978 I FT Food Technology I n d u s t r i a l Achievement Award: Food Technol. 32(6):22. M i k i c , B. B. 1969. On mechanism of dropwise condensation. I n t . J . Mass Heat T r a n s f e r . 12:1311. Mohsenin, Nuri N. 1980. "Thermal P r o p e r t i e s of Food and A g r i c u l t u r a l M a t e r i a l s " , Gordon and Beach Science P u b l i s h e r s , Inc., New York, NY. Nieboer, S. F. T. 1974. Where do r e t o r t pouches go from here? Food Manufacture. 49(9) :31. N u s s e l t , W. 1916., VDI Z e i t s c h r i f t . 60:541,569. Othmer, D. F. 1929. The condensation of steam. Ind. Eng. Chem. 21(6):576. P f l u g , I. J . 1975. "Procedure f o r C a r r y i n g out a Heat P e n e t r a t i o n Test and A n a l y s i s of the R e s u l t i n g Data", U n i v e r s i t y of Minnesota. P f l u g , I. J . , B l a i s d e l , I. L. and Kopelmann, I. J . 1965. Developing temperature-time curves, f o r o b j e c t s that can be approximated by a sphere, i n f i n i t e p l a t e or i n f i n i t e c y l i n d e r . Part I. ASHRE. Trans.71. P f l u g , I. J . and Borrero, C. 1967. " E v a l u a t i o n of the Heating Media f o r P r o c e s s i n g S h e l f - s t a b l e Foods i n F l e x i b l e Packages i n Commercial P r o c e s s i n g Equipment", F i n a l report of part II of Quartermaster P r o j e c t No. IK 6433 D587. Rees, J . A. G, 1974 , P r o c e s s i n g Heat S t e r i l i z a b l e F l e x i b l e Packs. Jan. FMC Review. Rha, ChoKyun. 1975. "Theory, Determination and C o n t r o l of P h y s i c a l P r o p e r t i e s of Food M a t e r i a l s " , D. Reider P u b l i s h i n g Co., Boston, MA. Rohsenow, W. M. and H a r t n e t t , J . P, 1973. "Handbook of Heat T r a n s f e r " , McGraw-Hill Book Co., Inc., New York, NY. 69 Rose, J . W. 1967. On the mechanism of dropwise condensation. I n t . J . Heat Mass T r a n s f e r . 10:755. Sherwood, T. K. and R i g f o r d , R. 1952. "Absorption and E x t r a c t i o n " , McGraw-Hill Book Co., Inc., New York, NY. Steam T a b l e s . 1967. E l e c t r i c a l Research A s s o c i a t i o n . Edward Arnold P u b l i s h e r s , L i m i t e d , London, U.K. Sugawara, Sugao and M i c h i y o s h i , I t a r u . 1956. Dropwise condensation. Fac. Eng. J . , Kyoto U n i v e r s i t y . 18(11):84. Tung, M. A. 1980. Thermophysical s t u d i e s f o r improved food p r o c e s s e s . A f i r s t q u a r t e r r e p o r t . (16th June to 15th September.) f o r the A g r i c u l t u r e Canada PDR Program. T u r t l e , B. I. and Alderson, 1971. S t e r i l i z a b l e f l e x i b l e packaging. Food Manufacture. 46(9):23. Umur, A. and G r i f f i t h , P. 1965. Mechanism of dropwise condensation. J . Heat T r a n s f e r (Trans. ASME). 87(6):275. Vasserman, A. A., K a z a v c h i n s k i i , Z. and Rabinovich, V. A. 1971. "Thermal P h y s i c a l P r o p e r t i e s of A i r and A i r Components", I s r a e l Program for S c i e n t i f i c T r a n s l a t i o n s L t d . (IPST Cat No. 5794). Wahl, A. M. and Lobo, G. 1930. S t r e s s and d e f l e c t i o n in f l a t c i r c u l a r p l a t e s , with c e n t r a l h o l e s . Trans. American S o c i e t y of Mechanical Engineers. 52:29. Watson, A. M., Lund, P. G. and Todd, J . D. 1972. "Engineering Tables and Data", Chapman and H a l l , London, U.K. Yamano, Y. Komatsu, Y. and Ikogami, Y. 1969. S t e r i l i s a t i o n of foods in f l e x i b l e packages, p a r t II -Measurements of heat t r a n s f e r r a t e and storage tasks of s e v e r a l packaged foods. J . Food Sc. Technol. 16(3):119. 70 APPENDIX A Bio t Numbers f o r some r e t o r t a b l e products. For the heat t r a n s f e r c o e f f i c i e n t , a value of 3410 W/m2K was used f o r steam and a value of 1700 W/m2K was used f o r water. Both values were obtained from P f l u g and Borrero (1967). For the sma l l e s t dimension a value of 5 mm was used. 71 Table V: Estimates of Bi o t numbers f o r some food products in t h i n p r o f i l e c o n f i g u r a t i o n s . Food m a t e r i a l Thermal- Temp- Bi o t B i o t References conducti era no. no. v i t y t ure W/m.K °C steam water Egg White 0. 5539 38. 2 30. 8 1 5 .3 Mohsenin( Egg York 0. 3393 34. 8 50. 3 25 . 1 B r o i l e r Muscle 0. 4120 26. 7 41 . 4 20 .6 II Beef(0.8% f a t , 7 8 . 9% 0. 4760 6. 9 35. 8 1 7 .9 Rha(1975) moi sture) 0. 4676 36. 3 36. 5 18 .2 II 0. 4864 62. 0 35. 1 1 7 .5 Beef(1.4% f a t , 7 8 . 7% 0. 4310 7. 9 39. 6 19 .7 II moi sture) 0. 4293 32. 1 39. 7 19 .8 Pork(7.8% f a t , 7 5 . 1% 0. 4431 60. 9 38. 5 1 7 .4 II Pork(6.7% f a t , 7 5 . 9% 0. 4881 6. 0 34. 9 1 7 .4 H moisture) 0. 5072 21 . 4 33. 6 16 .8 II 0. 5401 59. 3 31 . 6 1 5 .7 Pork(7.8% f a t , 7 5 . 1% 0. 4518 6. 1 37. 7 18 .8 II moisture) 0. 4847 42. 9 35. 2 1 7 .5 H 0. 4899 60. 7 34. 8 1 7 .4 H V e a l ( 2 . 1 % f a t , 7 5 . 0% 0. 4760 5. 9 35. 8 1 7 .9 H moisture) 0. 4778 42. 3 35. 7 17 .9 II 0. 4899 62. 4 34. 8 17 .8 II Lamb(8.7% f a t , 7 1 . 8% 0. 4483 10. 6 38. 1 19 .0 II moi sture) 0. 4691 46. 4 36. 3 18 . 1 II 0. 4778 61 . 1 35. 7 17 .8 II Lamb(9.6% f a t , 7 1 . 0% 0. 4483 10. 4 43. 6 21 .7 II moi sture) 0. 4691 48. 5 40. 5 20 .2 II 0. 4778 51 . 4 40. 4 20 . 1 n APPENDIX B System D e s c r i p t i o n ( A l l dimensions i n inches) Temperature Alternate Vertical Position of the Condensation Chamber Coolant .fly.tl.e_t_. Cold Water Inlet Steam Inlet Regulator TJ-LK><3—0 Filter Pressurised Air Inlet Condensation Chamber Support Structure Condensate Outlet 6 Muffler -1X3—© Condensate Outlet Data Acquisition Systern (Kaye Instruments) Figure 20: Schematic layout of the steam-air mixing systero.ocndensation charter and the data, aoqusition system. 'to.o Figure 21a : Condensation charter. 0.1 Figure 22: Coolant end cap for the cold end of the Jsr 00 79 APPENDIX C C a l c u l a t i o n s f o r Reynolds number, Re. 80 The Reynolds number a s s o c i a t e d with f l u i d flow i n a c i r c u l a r pipe may be computed by the. f o l l o w i n g equation: Re = v D/u = p D v / n sa ' Ksa K s a s a ' sa where v i s the mean v e l o c i t y of the steam-air mixture, D sa i s the i n t e r n a l diameter of the condensation chamber (0.1541 m.), u i s the kinematic v i s c o s i t y of the steam-K s a a i r mixture, ^ i s the d e n s i t y of the steam-air mixture, S3. and n i s the absolute v i s c o s i t y of the steam-air mixture, sa C a l c u l a t i o n f o r mean v e l o c i t y . The c a l c u l a t i o n was based on the assumption that the mixture i s homogeneous and that at steady s t a t e the a i r content at the i n l e t to the condensation chamber i s equal to that at the o u t l e t . Using the gas law, the a i r f l o w r a t e , CMSa, was c a l c u l a t e d from the equation : SCMSa= p,T 2 SCMSa/p.T, where SCMSa i s the standard f l o w r a t e , m 3/s, as measured by the flowmeter, p, i s the standard p r e s s u r e , a b s o l u t e (kN/m 2),. p 2 i s the steam-air pressure, a b s o l u t e (kN/m 2), T, i s the standard temperature (°K), and T 2 i s the steam-air temperature (°K). Knowing the a i r f l o w r a t e , and the a i r 81 r a t i o , the steam-air f l o w r a t e , CMSsa was c a l c u l a t e d from the equation: CMSsa = CMSa/a Then using the c o n t i n u i t y equation, the steam-air v e l o c i t y , v was c a l c u l a t e d . f r o m the equation: sa v = CMSsa/A, m/s S3. where A i s the chamber c r o s s - s e c t i o n area, m2. For an example, take a = 0.3, T 2 = 105°C and SCMSa = 4716.7 x IO" 6 m 3/s. From equation 26, p 2 = 120.8/0.7 = 172.6 kN/m2, T, = 15.56°C = 288.7 °K, and p, = 101.3 kN/m2. Ther e f o r e CMSa = 3626.4 x 10' 6 m 3/s. And CMSsa = 3626.4 x l0 " 6 / 0 . 3 = 12088.4 x 10" 6 m3/s Therefore v s a - = 12,088.4 x 10" 6/0.01864 = 0.65 m/s 82 C a l c u l a t i o n f o r the steam-air d e n s i t y . The d e n s i t y of steam was obtained from Steam Tables (1967). For example, at a temperature of 105°C (221 °F), for a = 0.3 (the corresponding steam-air pressure i s 172.6 kN/m2 (25.0 p s i ) , a s p e c i f i c volume of 1.4193 m 3/kg (22.74 f t 3 / l b ) can be read, the r e c i p r o c a l of which i s the steam d e n s i t y . So p g = 1/1.4193 = 0.7046 kg/m3. The d e n s i t y of a i r was obtained, using the gas law, from which i t can be shown that p = p 2 p /p^ , at a a i constant temperature, where p i s the a i r d e n s i t y at a I known pr e s s u r e , p,, and p 2 i s the steam-air p r e s s u r e . At atmospheric pressure of 101.3 kN/m2, and temperature of ,105°C, p = 0.934 kg/m3 ( K r e i t h , 1973). So f o r a = 0.3, at T = 105°C, p = 172.6(0.934)/l01.3 = 1.591 kg/m 3. 2 The equation used f o r c a l c u l a t i n g p was d e r i v e d as sa f o l l o w s : iP a/Va = P a ma = Va P a Hg/Vs = p s 1 1 ^ = Vs P s For a known q u a n t i t y of steam-air weighing m kg, = V s a psa 83 But Va = a Vsa Vs = (1 - a) Vsa m s a = m a + m s Therefore m = Vsa p = Va p + Vs p sa Ksa M a " = a Vsa p +(1 - a) Vsa p So p s a = a p a + (1-a) p s For a = 0.3, T 1.15 kg/m3 . C a l c u l a t i o n f o r steam-air kinematic v i s c o s i t y . From Steam Tables (1967) the kinematic v i s c o s i t y of steam was ob t a i n e d . For example at 105°C and an a i r r a t i o of 0.3 a value of 10.45 m2/s was obtained. From Vasserman et a l . (1971) the v i s c o s i t y of a i r was obtained. Assuming that the v a r i a t i o n of the absolute v i s c o s i t y between one and ten bars can be approximated by a l i n e a r r e l a t i o n s h i p , an equation of the form: n = /I 0" 8 =1 .2556 p +2203.1 , was e s t a b l i s h e d , f o r a temperature of 105 °C. = 105°C, p _ = 0.3 (1.5913) + 0.7 (0.9660) = 84 For a = 0.3, T = 105 °C, ^ was found to be equal to 2205.3 • 3. x 10" 8 Ns/m2.. • ' D i v i d i n g by the corresponding a i r d e n s i t y , t h e kinematic v i s c o s i t y was obtained as: ]x = 2205.3 x 1 0~8/1 .5913. cl =13.86 x 10" 6 m2/s The v i s c o s i t y of the steam-air mixture was assumed to be a l i n e a r f u n c t i o n of composition, s i n c e there i s no in f o r m a t i o n found i n l i t e r a t u r e as regards the v i s c o s i t y of mixtures of steam and a i r . For example f o r a =0.3 and T 105 °C , u = {(13.86 - 10.45)0.3 + 10.45} x l0- 6,m 2/s. S a =11.47 x 10" 6 m2/s C a l c u l a t i o n f o r the Reynolds number,Re. For a = 0.3, T = 105°C and SCMSa=4720x10" 6, m3/s Re = 0.65 x 0.1541 /11.47 x 10" 6 = 8720 . The r e s t of the c a l c u l a t e d values are presented i n the f o l l o w i n g Table VI. Table V I : Calculated Reynolds numbers for inves t igat ing the ve loc i ty e f fec ts of the heat transfer c o e f f i c i e n t . Temp- A i r SCMSa Absolute Gauge CMSa CMSsa Steam-air Density Density Kinematic Kinematic Kinematic Reynolds e r a t - Ratio (Air) Pressure Press (Air) (Steam Ve loc i ty of of V i s c o s i t y V i s c o s i t y V i s c o s i t y of Number ure (m 3/s) (kN/m 2) -ure (m 3 /s) - a i r ) (m /s ) Steam A i r of A i r of Steam Steam-air ( ° C ) x lO 6 (kN/m2) x l O 6 (m'/s) (kg/ms) (kg/m J) <m 2 /s)xl0 6 (m/ sJxIO 6 (mV s)xlO* x l O 6 105 0.0 4720 120.7 19.4 0.7046 1.1134 19.60 14.35 14.35 105 0.1 4720 134.5 33.2 4670 46700 2.50 0.7046 1.2367 17.83 12 .99 13.47 28620.0 105 0.2 4720 151.0 49.7 4150 20700 1.11 0.7046 1.3921 15.84 11.19 1 2 . 1 2 14150.0 105 0.3 4720 172.4 71.1 3630 12100 0.65 0.7046 1.5913 13.86 10 .45 11 .47 8720.0 105 0.4 4720 201 .3 100.0 3110 7780 0.42 0.7046 1 . 8 5 5 1 11.89 9 . 01 10 .16 6340.0 105 0.5 4720 243.4 142.1 2550 5140 0.23 0.7046 2.2476 9.82 7.60 8.71 4900.0 105 0.0 9430 120.7 19.4 0.7046 1.1134 19.80 14.35 14.35 105 0.1 9430 134.5 33.9 9340 93300 5.01 0.7046 1.2367 17.83 12.99 13.47 57290.0 105 0.2 9430 151.0 49.7 8300 41500 2.23 0.7046 1 .3921 15.84 11.19 1 2 . 1 2 28290.0 105 0.3 9430 172.4 71.1 7260 24200 1 .30 0.7046 1.5906 13.86 10.45 11 .47 17440.0 105 0.4 9430 201.3 100.0 6230 15600 0.84 0.7046 1.8551 11.89 9 . 01 10.16 12660.0 105 0.5 9430 243.4 142.1 5190 10400 0.56 0.7046 2.2476 9.82 7.60 8.71 9820.0 105 0.0 14200 120.7 19.4 0.7046 1.1134 19.80 14.35 14.35 105 0.1 14200 134.5 33.9 14000 139000 7.51 0.7046 1.2367 17.83 12 .99 13.47 85920.0 105 0.2 14200 171.0 49.7 12500 62200 3.34 0.7046 1.3921 15.64 11 .19 1 2 . 1 2 42440.0 105 0.3 14200 172.4 71.1 10900 36300 1 .95 0.7046 1.5908 13.86 10 .45 11 .47 26170.0 105 0.4 14200 201.3 1 0 0 . 0 9340 23300 1 .25 0.7046 1.8551 11.69 9.01 10.16 19000.0 105 0.5 14200 243.4 142.1 7690 15400 0.83 0.7046 2.2476 9.82 7.60 8.71 14610.0 110 0.0 4720 143.3 42.0 0.8265 1 .3040 17.08 12.31 12 .31 110 0.1 4720 159.2 57.9 3980 40000 2.14 0.8265 1.4498 15.36 11.31 11 .72 28100.0 1 10 0.2 4720 179.1 77.8 3540 17700 0.95 0.8265 1.6308 13.66 10.15 10 . 85 13510.0 110 0.3 4720 204.7 103.4 3100 10300 0.55 0.8265 1.8647 1 1 .95 8.95 9.85 8670.0 110 0.4 4720 238.8 137.5 2660 6640 0.36 0.8265 2.1755 10.24 7.80 8.78 6270.0 110 0.5 4720 286.5 185.2 2210 4430 0.24 0.8265 2.6097 8.54 6.73 7.64 4800.0 115 0.0 4720 169.1 67.8 0.9660 1.5203 14.72 10.70 10 .70 115 0.1 4720 187.8 86.5 3420 34200 1.84 0.9660 1.6885 13.26 9.88 10 .22 27700.0 115 0.2 4720 211 .3 110.0 3100 15500 0.83 0.9660 1.9000 11.78 8.89 9.47 13550.0 115 0.3 4720 241.5 140.2 2660 8870 0.48 0.9660 2.1667 10.24 7.76 8.50 9450.0 115 0.4 4720 281.8 180.5 2280 5700 0.31 0.9660 2.5344 8.84 6.79 7.61 6200.0 115 0.5 4720 338.1 236.8 1900 3800 0.20 0.9660 3.0406 7.37 5.78 6.58 4780.0 121 0.0 4720 205.6 104.3 1.1592 1.8199 12.51 9.06 9.06 121 0.1 4720 228.5 127.2 2860 28600 1.53 1.1592 2.0217 1 1.26 8.32 8.61 27440.0 121 0.2 4720 257.1 155.7 2540 10600 0.57 1.1592 2.2476 10 .13 7.54 8.06 10900.0 121 0.3 4720 293.8 192.5 2220 7400 0.40 1.1592 2.6000 8.76 6.66 7.43 8250.0 121 0.4 4720 342.7 241.4 1900 4760 0.26 1.1592 3.0342 7.51 5.78 6.47 6100 .0 121 0.5 4720 411.3 310.0 1570 3170 0.17 1.1592 3.6413 6.26 4.91 5.59 4690 .0 125 0.0 4720 232.1 130.8 1.2984 2.0329 11.29 8.20 8.20 125 0.1 4720 257.9 156.6 2560 25600 1 .37 1.2984 2.2588 10. 16 7.60 7.86 26900.0 125 0.2 4720 290.1 188.8 2270 11400 0.61 1.2984 2.5408 9.03 6.82 7.26 12950.0 125 0.3 4720 331 .6 230.3 1990 6600 0.36 1.2984 2.9044 7.90 5.97 6.55 8380.0 125 0.4 4720 386.8 285.5 1700 4260 0.23 1.2984 3.3882 6.78 5 . 21 5.84 6040.0 125 0.5 4720 464.2 362.9 1420 2840 0.15 1.2984 4.0659 5.65 4.51 5.08 4650.0 00 Ln APPENDIX D C a l c u l a t i o n s f o r the D i f f u s i o n C o e f f i c i e n t , Dc. 87 From G i l l i l a n d i n Sherwood and R i g f o r d (1952), an e m p i r i c a l equation f o r determining the d i f f u s i o n c o e f f i c i e n t , Dc, of one gas through another i s given as : T 3 / 2 ± 1 Dc = 0.0166 : { — + — I 1 / 2 p (Va 1/ 3 +Vb 1/ 3) 2 Ma iMb Where Dc i s the d i f f u s i o n c o e f f i c i e n t , f t 2 / h r . p i s the t o t a l pressure in atmospheres. Va and Vb are the molecular volumes of d i f f u s i n g and i n e r t gases computed from the data on atomic volumes, given i n Table V I I . T i s the absolute temperature, °K , and Ma and Mb are the molecular weights of the d i f f u s i n g and i n e r t gases r e s p e c t i v e l y . For steam, H 20, Va = 2 (3.7) + 7.4 = 14.80 Ma = 2 x 1 + 16 =18.00 For A i r 79% N 2 and 21% 0 2, Vb = 29.90 Mb = (79/100)(28)+(21/100)(32) = 28.84 So Dc = (T 1' 5/p) 0.00598635/(2.4272 + 3. 1038) 2 = 0.00016299 T" 5/p f t 2 / h r = (0.0929 x 0.00016299/3600) T 1 , 5/p m2/s = 4.2060 x 10" 9 ( T u 5 / p ) m2/s For an example take Run 10520, Experiment No. 1. Dc = 4.2060 x 10" 9 x ( 378 . 1 5 ) 1 , 5 / I - 1 # 2 = 2.5947 x 10"" m2/s = 2.59 x 10-" m2/s . Table V I I : Atomic volumes , f o r some gases employed i n c a l c u l a t i n g f o r Dc Bromine 27.0 S u l f u r 25.0 Oxygen 7.4 In methyl e s t e r s 9.1 In higher e s t e r s and ether s 11.0 In ac ids 12.0 Carbon 14.8 C h l o r i n e 24.6' Hydrogen 3.7 Nitrogen 15.6 In primary amines 10.5 In secondary amines 12.0 For the hydrogen molecule 14.3 For a i r 29.9 89 APPENDIX E Table VIII: Experimental and Calculated Data. 90 \ • Table V I I I : Experimental and c a l c u l a t e d data. Run Expt. Steam A i r Heat Sub- Temp. Heat T o t a l D i f f u - Rey-No. No. A i r R a t i o S t r a t e Drop Trans- Press s i o n nolds Temp. Flux Temp. f e r ure C o e f f . No. C o e f f . (°C) (W/m2) (°C) (C°) (W/m2C) (atm) (nf/s) x 10 5 1 0520 01 105 . 0 0 .0 28790 9 5 . 3 9 . 7 2 9 6 8 . 0 1 .19 2 . 6 1 0520 02 105 . 0 0 .0 29420 9 5 . 2 9 . 8 3 0 0 2 . 0 1 .19 2 . 6 1 0520 03 104 . 9 0 .0 29800 9 5 . 2 9 . 8 3041 . 0 1.19 2 . 6 1 0520 04 104 . 9 0 .0 301 50 9 4 . 9 10 . 0 3 0 1 5 . 0 1 .19 2 . 6 1 0520 05 104 . 9 0 .0 30180 9 4 . 8 10 . 1 2 9 8 8 . 0 1.19 2 . 6 1 0520 06 104. 9 0 .0 30070 9 4 . 6 10 . 3 2 9 1 9 . 0 1 .19 2 . 6 1 0530 07 104. 9 0 .0 28820 9 4 . 1 10 . 8 2 6 6 8 . 0 1 .19 2 . 6 10530 08 1 0 4 . 8 0 .0 29120 9 4 . 0 10 . 8 2 6 9 6 . 0 1 .19 2 . 6 1 0530 09 1 0 4 . 9 0 .0 29420 9 4 . 0 10 . 9 2 6 9 9 . 0 1.19 2 . 6 1 0530 1 0 1 0 4 . 9 0 .0 29690 9 3 . 9 1 1 . 0 2 6 9 9 . 0 1 .19 2 . 6 10530 1 1 1 0 4 . 9 0 .0 29660 9 3 . 7 1 1 . 2 2 6 4 9 . 0 1 .19 2 . 6 1 0530 1 2 1 0 4 . 9 0 .0 29660 9 3 . 8 1 1 . 1 2 6 7 2 . 0 1 .19 2 . 6 1 0540 13 1 0 5 . 0 0 .0 26090 8 8 . 5 16 . 5 1 581 . 0 1.19 2 . 5 10540 14 1 0 4 . 8 0 .0 2601 0 8 8 . 2 16. 6 1 5 6 7 . 0 1 .19 2 . 6 1 0540 1 5 1 0 4 . 7 0 .0 26560 8 8 . 2 16. 5 1610 . 0 1 .19 2 . 6 1 0540 16 1 0 4 . 9 0 .0 26700 8 8 . 5 16. 4 1628 . 0 1 .19 2 . 6 1 0540 1 7 1 0 4 . 9 0 .0 271 50 8 8 . 8 16. 1 1687 . 0 1 .19 2 . 6 1 0540 18 1 04 . 8 0 .0 271 50 8 8 . 7 16. 1 1687 . 0 1.19 2 . 6 1 0522 1 9 1 0 4 . 8 0 .2 28790 9 2 . 8 12 . 0 2 3 9 9 . 0 1 .15 2 . 0 14150 1 0522 20 104 . 8 0 .2 29010 9 2 . 6 J 2 . 2 2 3 7 8 . 0 1 .15 2 . 0 14150 1 0522 21 1 0 4 . 8 0 .2 27590 9 3 . 2 1 1 . 6 2 3 7 8 . 0 1 .15 2 . 0 1 41 50 1 0522 22 104 . 8 0 .2 28710 9 2 . 6 12 . 2 2 3 5 4 . 0 1 .15 2 . 0 1 41 50 1 0522 23 104 . 8 0 .2 29390 9 2 . 6 12 . 2 2 4 0 9 . 0 1 .15 2 . 0 141 50 1 0522 24 104 . 8 0 .2 29470 9 2 . 7 12 . 1 2 4 3 6 . 0 1 .15 2 . 0 14150 1 0532 25 1 0 5 . 0 0 .2 28000 91 . 5 13 . 5 2 0 7 4 . 0 1 . 4 9 2 . 0 14150 1 0532 26 1 0 4 . 8 0 .2 28270 91 . 3 13 . 5 2 0 9 4 . 0 1 .48 2 . 0 141 50 10532 27 1 0 4 . 9 0 .2 28140 9 0 . 8 14 . 1 1996 . 0 1 . 4 9 2 . 0 141 50 1 0532 28 104 . 8 0 .2 28740 91 . 1 13 . 7 2 0 9 8 . 0 1 . 48 2 . 0 14150 10532 29 1 0 4 . 9 0 .2 28850 91 . 0 13 . 8 2 0 9 0 . 0 1 . 4 9 2 . 0 1 41 50 1 0532 30 1 0 4 . 8 0 .2 28850 91 . 0 13 . 8 2 0 9 0 . 0 1 . 48 2 . 0 1 41 50 1 0542 31 105 . 0 0 .2 26420 8 9 . 1 15 . 9 1 661 . 0 1 . 4 9 2 . 0 1 41 50 1 0542 32 104 . 9 0 .2 26720 8 9 . 0 15 . 9 1680 . 0 1 . 4 9 2 . 0 1 41 50 1 0542 33 104 . 9 0 .2 26880 8 8 . 9 16 . 0 1680 . 0 1 . 4 9 2 . 0 14150 10542 34 104 . 9 0 .2 27260 8 8 . 7 16. 2 1683 . 0 1 . 4 9 2 . 0 14150 1 0542 35 1 0 4 . 9 0 .2 27370 8 8 . 7 16. 2 1690 . 0 1 . 4 9 2 . 0 14150 1 0542 36 104 . 9 0 .2 27460 8 8 . 8 16. 1 1705 . 0 1 . 4 9 2 . 0 14150 91 T a b l e V I I I : C o n t i n u e d . Run E x p t . S t e a m A i r H e a t S u b - T e m p . H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s T e m p . F l u x T e m p . f e r u r e C o e f f . N o . C o e f f . ( ° C ) (W/m 2 ) ( C C ) ( C ° ) ( W / n f C ) (a tm) ( m 2 / s ) x 105 1 0523 37 1 0 5 . 0 0. 3 27180 9 0 . 2 14. 8 1836. 0 1 .70 1 .8 8720 1 0523 38 105 . 1 0. 3 27560 9 0 . 0 15 . 1 1825. 0 1 .71 1 .8 8720 1 0523 39 1 0 5 . 1 0 . 3 28130 8 9 . 7 15 . 4 1827. 0 1.71 1 .8 8720 1 0523 40 1 0 5 . 1 0 . 3 281 90 8 9 . 7 15 . 4 1831 . 0 1.71 1 .8 8720 1 0523 41 1 0 4 . 9 0 . 3 28220 9 0 . 0 15 . 1 1869 . 0 1 .70 1 .8 8720 1 0533 42 1 0 5 . 2 0 . 3 27260 8 8 . 8 16. 4 1662. 0 1.71 1 .8 8720 1 0533 43 1 0 5 . 1 0 . 3 27450 8 8 . 8 16 . 4 1 6 7 4 . 0 1.71 1 .8 8720 1 0533 44 1 0 5 . 2 0 . 3 27560 8 8 . 6 16 . 6 1 6 6 0 . 0 1.71 1 .8 8720 1 0533 45 1 0 5 . 1 0 . 3 27840 8 8 . 3 16 . 8 1 6 5 7 . 0 1.71 1 .8 8720 1 0533 46 105 . 2 0 . 3 27780 8 8 . 0 1 7 . 2 1615 . 0 1.71 1 .8 8720 1 0533 47 1 0 5 . 1 0 . 3 27780 8 7 . 9 17 . 2 1615 . 0 1.71 1 .8 8720 1 0543 48 1 0 5 . 2 0 . 3 25760 8 7 . 2 18 . 0 1 431 . 0 1 .72 1 .8 8720 1 0543 49 1 0 4 . 8 0 . 3 26030 8 7 . 5 18 . 3 1 4 2 3 . 0 1 . 6 9 1 .8 8720 1 0543 50 1 0 4 . 7 0 . 3 26060 8 6 . 2 18 . 5 1 4 0 9 . 0 1 . 6 9 1 .8 8720 1 0543 51 1 0 4 . 6 0 . 3 26750 8 6 . 7 17 . 9 1 4 9 4 . 0 1 .68 1 .8 8720 1 0543 52 1 0 4 . 6 0 . 3 26720 8 5 . 7 18 . 9 1414. 0 1 .68 1 .8 8720 1 0543 53 1 0 5 . 6 0 . 3 26800 8 7 . 9 17 . 7 1 4 3 3 . 0 1 .74 1 .7 8720 SC201 54 1 0 5 . 2 0 . 3 28850 9 2 . 6 12 . 6 2 2 6 5 . 0 1 .72 1 .8 1 7440 SC201 55 1 0 5 . 2 0 . 3 28850 9 2 . 6 12 . 6 2 2 8 9 . 0 1 .72 1 .8 1 7440 SC201 56 1 0 5 . 2 0 . 3 2901 0 9 2 . 3 12 . 9 2 2 4 9 . 0 1 .72 1 .8 1 7440 SC201 57 1 0 5 . 2 0 . 3 291 70 9 2 . 5 12 . 7 2 2 9 7 . 0 1 .72 1 .8 1 7440 SC201 58 105 . 2 0 . 3 29090 9 2 . 3 12 . 9 2 2 5 5 . 0 1 .72 1 .8 1 7440 SC201 59 1 0 5 . 2 0 . 3 28540 9 2 . 6 12 . 6 2 2 6 5 . 0 1 .72 1.8 1 7440 SC202 60 1 0 4 . 9 0 . 3 27290 8 9 . 5 15 . 4 1 7 7 2 . 0 1 . 6 9 1 .8 1 7440 SC202 61 105 . 0 0 . 3 27560 8 9 . 5 15 . 5 1 7 7 8 . 0 1 .70 1 .8 1 7440 SC202 62 1 0 5 . 0 0 . 3 27650 8 9 . 3 15 . 7 1 761 . 0 1 .70 1 .8 1 7440 SC202 63 1 0 5 . 1 0 . 3 281 40 8 9 . 5 15 . 6 1804. 0 1 .71 1 .8 1 7440 SC202 64 1 0 5 . 2 0 . 3 28220 8 9 . 4 1 5 . 8 1 7 8 6 . 0 1 .72 1 .8 1 7440 SC202 65 1 0 5 . 2 0 . 3 28220 8 9 . 3 15 . 9 1775 . 0 1 .72 1 .8 1 7440 SC301 66 1 0 4 . 8 0 . 3 27890 9 2 . 3 12 . 5 2231 . 0 1 . 6 9 1 .8 261 70 SC301 67 1 0 4 . 7 0 . 3 28270 9 2 . 4 12. 3 2 2 9 9 . 0 1 .69 1 .8 261 70 SC301 68 1 0 4 . 7 0 . 3 28330 9 2 . 1 12. 6 2 2 4 8 . 0 1 . 6 9 1 .8 261 70 SC301 69 1 0 4 . 7 0 . 3 28760 9 2 . 1 12 . 6 2 2 8 3 . 0 1 . 6 9 1 .8 26170 SC301 70 1 0 4 . 7 0 . 3 28870 9 2 . 0 12 . 7 2274 . 0 1 .69 1 .8 261 70 SC301 71 1 0 4 . 7 0 . 3 28820 91 . 9 12. 8 2251 . 0 1 . 6 9 1 .8 26170 SC302 72 1 0 4 . 9 0 . 3 26720 8 8 . 9 16 . 0 1 6 7 0 . 0 1 .70 1 .8 261 70 92 T a b l e V I I I : C o n t i n u e d . Run E x p t . S t e a m A i r H e a t S u b - Temp. H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s T e m p . F l u x Temp. f e r u r e C o e f f . N o . ( ° C ) (W/m 2 ) C O (C° ) C o e f f . (W/m 2 C) (atm) (m2/s) x 10 5 SC302 73 1 0 4 . 9 0 . 3 27020 8 8 . 8 1 6 . 1 1678 . 0 1 .70 1 .8 261 70 SC302 74 1 0 4 . 8 0 . 3 2721 0 8 8 . 7 1 6 . 1 1690 . 0 1 . 6 9 1 .8 261 70 SC302 75 1 0 4 . 8 0 . 3 27400 8 8 . 4 1 6 .4 1 671 . 0 1 .69 1 .8 261 70 SC302 76 1 0 4 . 8 0 . 3 27650 8 8 . 6 1 6 .2 1 7 0 7 . 0 1 .69 1 .8 261 70 SC302 77 1 0 4 . 8 0 . 3 27540 8 8 . 4 1 6 .4 1679 . 0 1 .69 1 .8 261 70 1 0524 78 104 . 6 0. 4 2601 0 8 7 . 0 1 7 .6 1 4 7 8 . 0 1 . 96 1 . 5 6340 1 0524 79 1 0 4 . 6 0 . 4 26290 8 6 . 7 1 7 . 9 1468 . 0 1 . 96 1 . 5 6340 1 0524 80 1 0 4 . 7 0 . 4 26390 8 6 . 5 18 .2 1450 . 0 1 .97 1 . 5 6340 1 0524 81 1 0 4 . 8 0 . 4 26740 8 6 . 8 18 .0 1 4 8 6 . 0 1 .97 1 . 5 6340 1 0524 82 1 0 4 . 8 0 . 4 27020 8 6 . 8 18 .0 1 501 . 0 1 .97 1 .5 6340 1 0524 83 1 0 4 . 9 0 . 4 26850 8 6 . 6 18 .3 1467 . 0 1 .98 1 . 5 6340 1 0534 84 1 0 5 . 3 0 . 4 25820 8 5 . 1 20 .2 1278. 0 2 .01 1 . 5 6340 1 0534 85 1 0 5 . 3 0 . 4 25950 8 4 . 9 20 .4 1272 . 0 2 .01 1 . 5 6340 1 0534 86 1 0 5 . 3 0 . 4 2601 0 8 4 . 8 20 . 5 1269 . 0 2 .01 1 . 5 6340 1 0534 87 1 0 5 . 2 0 . 4 2631 0 8 4 . 5 20 .7 1271 . 0 2 .01 1 . 5 6340 1 0534 88 1 0 5 . 1 0. 4 23360 8 4 . 4 20 .7 1274 . 0 1 . 9 9 1 . 5 6340 1 0534 89 1 0 5 . 2 0 . 4 26200 8 5 . 1 20 . 1 1 242 . 0 2 .00 1 . 5 6340 1 0544 90 1 0 5 . 0 0. 4 25030 8 4 . 6 20 .4 1227 . 0 1 . 9 9 1 .5 6340 1 0544 9 1 105 . 1 0 . 4 25330 8 4 . 7 20 .4 1241 . 0 1 . 9 9 1 .5 6340 1 0544 92 1 0 5 . 1 0 . 4 25350 8 4 . 4 20 .7 1225 . 0 1 . 9 9 1 . 5 6340 1 0544 93 1 0 5 . 1 0 . 4 2571 0 8 4 . 3 20 .8 1 2 3 6 . 0 1 . 9 9 1 . 5 6340 1 0544 94 1 0 5 . 1 0 . 4 25790 8 4 . 1 21 .0 1 2 2 8 . 0 ] . 99 1 . 5 6340 1 0544 95 1 0 5 . 0 0 . 4 25900 8 4 . 2 20 .8 1 2 4 5 . 0 1 . 9 9 1 . 5 6340 1 0525 96 1 0 4 . 9 0 . 5 24590 8 2 . 9 22 .0 1118. 0 2 .38 1 .3 4900 1 0525 97 1 0 4 . 9 0 . 5 24700 8 2 . 5 22 .4 1102 . 0 2 .38 1 .3 4900 10525 98 1 0 4 . 9 0 . 5 24890 8 2 . 4 22 . 5 1 1 0 6 . 0 2 .38 1 .3 4900 1 0525 99 1 0 5 . 0 0 . 5 25270 8 2 . 3 22 .7 1113 . 0 2 .38 1 .3 4900 1 0525 100 1 0 5 . 0 0 . 5 25330 8 2 . 3 22 .7 1116 . 0 2 .38 1 .3 4900 1 0525 101 1 0 5 . 0 0 . 5 25330 8 2 . 3 22 .7 1116 . 0 2 .38 1 .3 4900 1 0535 102 1 0 5 . 1 0 . 5 2391 0 8 0 . 8 24 .3 9 8 4 . 0 2 . 3 9 1 .2 4900 1 0535 103 105 . 2 0 . 5 241 50 8 0 . 6 24 .6 9 8 2 . 0 2 .40 1 .2 4900 1 0535 1 04 1 0 5 . 5 0 . 5 24530 81 . 0 24 . 5 1 001 . 0 2 .43 1 .2 4900 1 0535 105 105 . 3 0 . 5 24660 8 0 . 7 24 .6 1002. 0 2 .41 1 .2 4900 1 0535 1 06 1 0 5 . 6 0 . 5 24730 8 0 . 7 24 . 9 9 9 3 . 0 2 .44 1 .2 4900 1 0535 1 07 1 0 5 . 7 0 . 5 24840 81 . 0 24 . 7 1 0 0 6 . 0 2 . 4 5 1 .2 4900 1 0545 108 1 0 5 . 1 0 . 5 24620 8 0 . 9 24 .2 1017 . 0 2 . 3 9 1 .2 4900 93 T a b l e V I I I : C o n t i n u e d . Run E x p t . S team A i r H e a t S u b - T e m p . H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s Temp. F l u x Temp. f e r u r e C o e f f . N o . ( ° C ) (W/m 2 ) C O (c°) C o e f f . (W/m 2 C) (atm) ( m 2 / s ) x 10 5 1 0545 109 105 . 8 0 . 5 24230 81 . 8 2 4 . 0 1010 . 0 2 . 4 6 1 .2 4900 10545 1 10 1 0 5 . 8 0 . 5 24340 81 . 6 2 3 . 2 1 0 4 9 . 0 2 . 3 7 1 .3 4900 1 0545 1 1 1 104 . 6 0 . 5 2421 0 8 0 . 9 2 3 . 7 1021 . 0 2 . 3 5 1 .3 4900 1 0545 1 1 2 1 0 5 . 6 0 . 5 24890 81 . 5 2 4 . 1 1 033 . 0 2 . 4 4 1 .2 4900 10545 1 1 3 1 0 6 . 1 0 . 5 24840 81 . 5 2 4 . 6 1010 . 0 2 . 4 8 1 .2 4900 1 1 030 1 1 5 1 10 . 1 0 . 0 26280 8 8 . 7 21 . 4 1 2 2 8 . 0 1 .42 2 .2 1 1 030 1 16 110 . 2 0 . 0 26550 8 8 . 9 21 . 3 1 2 4 7 . 0 1 .42 2 . 2 1 1 030 1 1 7 1 10 . 2 0 . 0 26750 8 8 . 8 21 . 4 1250 . 0 1 .42 2 . 2 1 1 030 1 18 1 10 . 2 0 . 0 27290 8 9 . 3 2 0 . 9 1 3 0 6 . 0 1 .42 2 . 2 1 1 030 1 1 9 1 10 . 1 0 . 0 27370 8 9 . 3 2 0 . 8 1316 . 0 1 .42 2 . 2 1 1 030 1 26 1 10 . 1 0 . 0 27480 8 9 . 3 2 0 . 8 1321 . 0 1 .42 2 .2 1 1 040 121 110 . 0 0 . 0 26280 9 2 . 6 21 . 4 1 5 7 8 . 0 1.41 2 . 2 1 1 040 1 22 109 . 8 0 . 0 26550 9 2 . 8 21 . 3 1 6 4 2 . 0 1 .23 2 . 2 1 1 040 1 23 109 . 6 0 . 0 26750 9 2 . 6 21 . 4 1652 . 0 1 . 40 2 . 2 1 1 040 1 24 109 . 6 0 . 0 27290 9 2 . 6 2 0 . 9 1681 . 0 1 . 40 2 . 2 1 1 040 1 25 109 . 6 0 . 0 27370 9 2 . 5 2 0 . 8 1 681 . 0 1 . 40 2 . 2 1 1 040 1 26 109 . 6 0 . 0 27480 9 2 . 3 2 0 . 8 1 6 5 8 . 0 1 .40 2 .2 1 1 041 1 27 110 . 1 0 . 1 28490 9 4 . 3 15 . 8 1803 . 0 1 .58 2 . 0 28120 1 1 041 1 28 110 . 1 0 . 1 28760 9 4 . 4 15 . 7 1832 . 0 1 .58 2 . 0 281 20 1 1 041 129 1 10 . 0 0 . 1 28850 9 4 . 3 15 . 7 1 837 . 0 1 .58 2 . 0 281 20 1 1 041 130 1 10 . 0 0 . 1 2931 0 9 4 . 2 15 . 8 1855 . 0 1 .58 2 . 0 281 20 1 1 041 131 110 . 0 0 . 1 29500 9 4 . 1 15 . 9 1855 . 0 1 .58 2 . 0 281 20 1 1 041 1 32 109 . 9 0 . 1 29500 9 4 . 0 15 . 9 1855 . 0 1 .57 2 . 0 281 20 1 1 032 1 33 110 . 0 0 . 2 27180 9 0 . 7 19 . 3 1 4 0 4 . 0 1 .77 1 .7 1 3500 1 1 032 1 34 1 10 . 0 0 . 2 2721 0 9 0 . 2 19 . 8 1 3 7 4 . 0 1 .77 1 .7 1 3500 1 1 032 1 35 1 10 . 3 0 . 2 27650 9 0 . 8 19 . 5 1418 . 0 1 . 7 9 1 .7 1 3500 1 1 032 1 36 110 . 5 0 . 2 281 1 0 91 . 0 19 . 5 1 441 . 0 1 . 80 1 .7 1 3500 1 1 032 1 37 1 10 . 2 0 . 2 281 1 0 9 0 . 5 19 . 7 1 4 2 7 . 0 1 .78 1 .7 1 3500 1 1 032 1 38 1 10 . 2 0 . 2 281 40 9 0 . 6 19 . 6 1 4 3 6 . 0 1 .78 1 .7 1 3500 11013 139 1 10 . 0 0 . 3 28850 9 4 . 7 15 . 3 1885 . 0 2 . 0 2 1 . 5 8670 11013 140 109 . 9 0 . 3 28950 9 4 . 4 15 . 5 1868 . 0 2.01 1 . 5 8670 11013 141 109 . 9 0 . 3 29040 9 4 . 2 15 . 7 1849 . 0 2.01 1 .5 8670 11013 1 42 1 10 . 0 0 . 3 29550 9 4 . 2 15 . 8 1870 . 0 2 . 0 2 1 . 5 8670 11013 143 110 . 0 0 . 3 29470 9 4 . 0 16. 0 1842 . 0 2 . 0 2 1 . 5 8670 11013 144 110 . 0 0 . 3 29560 9 4 . 1 15 . 9 1859 . 0 2 . 0 2 1 . 5 8670 1 1 023 1 45 1 10 . 9 0 . 3 28300 91 . 9 19 . 0 1 4 9 0 . 0 2 . 0 9 1 .5 8660 94 T a b l e V I I I : C o n t i n u e d . Run E x p t . S team A i r H e a t S u b - Temp. H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s Temp. F l u x Temp. f e r . u r e C o e f f . N o . ( °c) (W/m 2 ) ( ° C ) (C° ) C o e f f . (W/m 2 C) (atm) ( m 2 / s ) x 10 5 1 023 1 46 1 10 . 9 0 . 3 2841 0 91 . 7 19 . 2 1480 . 0 2 . 0 9 1 . 5 8660 1 023 1 47 1 10 . 9 0 . 3 28570 91 . 6 19 . 3 1 481 . 0 2 . 0 9 1 . 5 8660 1023 1 48 1 10 . 8 0 . 3 29070 91 . 5 19. 3 1 5 0 6 . 0 2 . 0 8 1 . 5 8660 1 023 149 1 10 . 8 0 . 3 29070 91 . 5 19 . 3 1 5 0 6 . 0 2 . 0 8 1 . 5 8660 1 023 150 110 . 8 0 . 3 29070 91 . 5 19 . 3 1 5 0 6 . 0 2 . 0 8 1 . 5 8660 1 023 151 1 10 . 8 0 . 3 28950 91 . 3 19 . 5 1 4 8 5 . 0 2 . 0 8 1 . 5 8660 1 033 1 52 1 10 . 8 0 . 3 27180 9 0 . 1 2 0 . 7 1313 . 0 2 . 0 8 1 . 5 8660 1 033 1 53 110 . 3 0 . 3 27290 8 9 . 8 2 0 . 5 1331 . 0 2 . 0 4 1 . 5 8660 1 033 154 1 10 . 3 0 . 3 27370 8 9 . 4 2 0 . 9 1 31.0. 0 2 . 0 4 1 . 5 8660 1 033 1 55 110 . 4 0 . 3 27870 8 9 . 7 2 0 . 7 1 3 4 6 . 0 2 . 0 5 1 . 5 8660 1 033 1 56 1 10 . 4 0 . 3 28060 8 9 . 8 2 0 . 6 1 3 6 2 . 0 2 . 0 5 1 . 5 8660 1 033 1 57 1 10 . 5 0 . 3 27890 8 9 . 8 2 0 . 7 1 3 4 7 . 0 2 . 0 6 1 . 5 8660 1 043 158 1 10 . 8 0 . 3 281 1 0 9 2 . 9 17 . 9 1570 . 0 2 . 0 8 1 . 5 8660 1 043 1 59 110 . 7 0 . 3 28300 9 2 . 6 18. 1 1 5 6 3 . 0 2 . 0 7 1 . 5 8660 1 043 160 110 . 8 0 . 3 28570 9 2 . 8 18 . 0 1587 . 0 2 . 0 8 1 . 5 8660 1 043 161 111 . 0 0 . 3 2901 0 9 2 . 7 18 . 3 1 5 8 5 . 0 2 . 0 9 1 . 5 8660 1 043 1 62 110 . 9 0 . 3 29170 9 2 . 8 18 . 1 1612. 0 2 . 0 9 1 . 5 8660 1 043 1 63 1 10 . 3 0 . 3 28850 91 . 9 18 . 4 1 5 6 8 . 0 2 . 0 4 1 . 5 8660 1 053 1 64 109 . 9 0 . 3 261 20 8 9 . 1 2 0 . 8 1 2 5 6 . 0 2.01 1 . 5 8660 1 053 1 65 1 10 . 2 0 . 3 26200 8 8 . 8 21 . 4 1 2 2 4 . 0 2 . 0 3 1 . 5 8660 1 053 1 66 109 . 8 0 . 3 26800 8 9 . 4 2 0 . 4 1314 . 0 2.01 1 . 5 8660 1 053 1 67 1 10 . 1 0 . 3 27200 8 9 . 8 2 0 . 3 1 3 4 4 . 0 2 . 0 3 1 . 5 8660 1 053 168 109 . 9 0 . 3 25700 8 7 . 0 2 2 . 9 1 1 2 5 . 0 2.01 1 . 5 8660 1 053 1 69 109 . 9 0 . 3 27670 9 0 . 1 19 . 8 1389 . 0 2.01 1 . 5 8660 1 034 1 70 1 10 . 7 0 . 4 26550 8 8 . 4 2 2 . 3 1191 . 0 2 . 4 2 1 .3 6270 1 034 171 110 . 5 0 . 4 26580 8 7 . 7 2 2 . 8 1 1 6 6 . 0 2 . 4 0 1 .3 6270 1 034 1 72 110 . 2 0 . 4 26750 8 7 . 8 2 2 . 4 1 1 9 4 . 0 2 . 3 7 1 .3 6270 1 034 1 73 1 10 . 2 0 . 4 26940 8 7 . 1 2 3 . 1 1 1 6 6 . 0 2 . 3 7 1 .3 6270 1 034 1 74 110 . 3 0 . 4 27130 8 7 . 4 2 2 . 9 1185 . 0 2 . 38 1 . 3 6270 1 034 1 75 1 10 . 3 0 . 4 2721 0 8 7 . 4 2 2 . 9 1 188 . 0 2 . 3 8 1 .3 6270 1 044 176 109 . 7 0 . 4 26800 8 8 . 9 2 0 . 8 1288 . 0 2 . 3 3 1 .3 6270 1 044 1 77 109 . 9 0 . 4 27260 8 9 . 5 2 0 . 4 1 3 3 6 . 0 2 . 3 5 1 .3 6270 1 044 178 109 . 7 0 . 4 27240 8 9 . 0 2 0 . 7 1316 . 0 2 . 3 3 •1 .3 6270 1 044 1 79 109 . 7 0 . 4 27480 8 8 . 5 21 . 2 1296 . 0 2 . 3 3 1 .3 6270 1 044 180 109 . 4 0 . 4 27540 8 8 . 2 21.. 2 1299 . 0 2.31 1 .3 6270 1 044 181 109 . 9 0 . 4 27620 8 8 . 3 21 . 6 1279 . 0 2 . 3 5 1 .3 6270 95 T a b l e V I I I : C o n t i n u e d . Run E x p t . S team A i r H e a t S u b - T e m p . ' H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s Temp. F l u x Temp. f e r u r e C o e f f . N o . ( ° C ) (W/m 2 ) ( ° C ) ( C ° ) C o e f f . (W/m2 C) (atm) ( m 2 / s ) x 10 5 1 1 035 182 111 . 1 0 .5 25520 8 5 . 2 2 5 . 9 9 8 5 . 0 2 . 8 4 1 . 1 4800 1 1 035 183 110 . 6 0 .5 25520 8 4 . 7 2 5 . 9 9 8 5 . 0 2 . 8 9 1 .0 4800 1 1035 184 111 . 0 0 .5 25820 8 3 . 9 2 6 . 1 9 8 9 . 0 2 . 8 3 1 . 1 4800 1 1 035 185 110 . 7 0 . 5 25930 8 4 . 4 2 6 . 3 9 8 6 . 0 2 . 9 0 1 .0 4800 1 1 035 186 1 10 . 4 0 . 5 25840 8 4 . 0 2 6 . 4 9 7 9 . 0 2 . 8 7 1 . 1 4800 1 1 035 187 1 10 . 4 0 . 5 25930 8 4 . 0 2 6 . 4 9 8 2 . 0 2 . 8 7 1 . 1 4800 1 1 045 1 88 110 . 1 0 . 5 25900 8 6 . 4 2 3 . 7 1093 . 0 2 . 8 4 1 . 1 4800 1 1 045 189 1 10 . 1 0 . 5 26010 8 5 . 8 2 4 . 3 1070 . 0 2 . 8 4 1 . 1 4800 1 1 045 190 110 . 0 0 . 5 26170 8 5 . 7 2 4 . 3 1077 . 0 2 . 8 3 1 . 1 4800 1 1 045 191 109 . 9 0 . 5 26530 8 5 . 5 2 4 . .4 1087 . 0 2 . 8 2 1 . 1 4800 1 1 045 1 92 110 . 3 0 . 5 26690 8 5 . 2 2 5 . 1 1063 . 0 2 . 8 6 1 . 1 4800 1 1 045 1 93 1 10 . 1 0 . 5 26610 8 5 . 2 2 4 . 9 1 0 6 9 . 0 2 . 8 4 1 . 1 4800 1 1 530 194 114. 4 0 .0 29530 9 6 . 1 18 . 3 1 6.1 4. 0 1 .64 1.9 1 1 530 195 114 . 7 0 .0 29610 9 6 . 2 18. 5 1 601 . 0 1 . 6 5 1 . 1 1 1 532 196 1 15 . 4 0 .2 291 20 9 5 . 7 19 . 7 1 4 7 8 . 0 2.11 1 . 5 1 3550 1 1 532 197 115 . 0 0 .2 291 50 9 5 . 6 19 . 4 1 5 0 2 . 0 2 . 0 9 1 . 5 1 3550 1 1 532 198 1 15 . V" 0 .2 29690 9 6 . 1 • 19 . 0 1563 . 0 2 . 0 9 1 .5 1 3550 1 1 532 1 99 115 . 1 0 .2 29940 9 5 . 9 19 . 2 1 5 5 9 . 0 2 . 0 9 1 . 5 1 3550 1 1 532 200 1 15 . 1 0 .2 30050 9 6 . 0 19 . 1 1 5 7 3 . 0 2 . 0 9 1 . 5 1 3550 1 1 532 201 115 . 0 0 .2 30050 9 5 . 9 19 . 1 1 5 7 3 . 0 2 . 0 9 1 .5 1 3550 11513 202 116 . 0 0 .3 30510 9 9 . 3 16. 7 1827 . 0 2 . 4 7 1 .3 9450 11513 203 1 16. 1 0 .3 30700 9 9 . 2 16 . 9 1817 . 0 2 . 4 7 1 .3 9450 11513 204 116 . 1 0 .3 30890 9 9 . 1 17 . 0 1817 . 0 2 . 4 7 1 .3 9450 11513 205 116 . 0 0 .3 31 300 9 9 . 1 16. 9 1852 . 0 2 . 4 7 1 .3 9450 11513 206 1 15 . 9 0 .3 31270 9 8 . 7 17 . 2 1818 . 0 2 . 4 6 1 .3 9450 11513 207 1 15 . 9 0 .3 31 270 9 8 . 6 17 . 3 1808 . 0 2 . 4 6 1 .3 9450 1 1 523 208 1 15 . 8 0 .3 29420 9 5 . 6 2 0 . 2 1 4 5 6 . 0 2 . 4 5 1 .3 9450 1 1 523 209 1 15 . 5 0 .3 2931 0 9 4 . 4 21 . 1 1 3 8 9 . 0 2 . 4 3 1 .3 9450 1 1 523 210 115 . 1 0 .3 29500 9 4 . 4 2 0 . 7 1 4 2 5 . 0 2 . 3 9 1 .3 9450 1 1 523 21 1 114 . 9 0 .3 29690 9 3 . 7 21 . 2 1401 . 0 2 . 3 8 1 .3 9450 1 1523 212 115 . 4 0 .3 29880 9 3 . 0 21 . 4 1396 . 0 2 . 4 2 1 .3 9450 1 1 523 213 115 . 4 0 .3 29860 9 4 . 0 21 . 4 1 3 9 5 . 0 2 . 4 2 1 .3 9450 1 1 533 214 114 . 7 0 .3 28570 9 4 . 2 2 0 . 5 1 3 9 4 . 0 2 . 3 6 1 .3 9450 1 1533 215 1 15 . 2 0 .3 28850 9 4 . 1 21 . 1 1367 . 0 2 . 4 0 1 .3 9450 1 1 533 216 1 15 . 4 0 .3 29200 9 4 . 5 2 0 . 9 1397 . 0 2 . 4 2 1 .3 9450 1 1 533 217 1 15 . 4 0 .3 29470 9 4 . 3 21 . 1 1 3 9 7 . 0 2 . 4 2 1 .3 9450 96 T a b l e V I I I : C o n t i n u e d . Run E x p t . S team A i r H e a t S u b - Temp. H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s Temp. F l u x Temp. f e r u r e C o e f f . N o . ( ° C ) (W/m 2 ) ( ° C ) (C °) C o e f f . (W/m 2 C ) (atm) ( m 2 / S ) x 10 5 1 533 218 1 15 . 3 0 . 3 29450 9 4 . 1 21 . 2 1389 . 0 2 . 41 1.3 9450 1 533 219 1 15 . 3 0 . 3 29470 9 4 . 1 21 . 2 1390 . 0 2 . 41 1 .3 9450 1 534 220 114 . 9 0 . 4 27560 91 . 2 2 3 . 7 1 1 6 3 . 0 2 . 77 1 • 1 6200 1534 221 115 . 0 0 . 4 27840 91 . 5 2 3 . 5 1 185 . 0 2 . 78 1 . 1 6200 1 534 222 1 15 . 3 0 . 4 28000 91 . 5 2 3 . 8 1 1 7 6 . 0 2 . 81 1 . 1 6200 1 534 223 115 . 4 0 . 4 28300 91 . 4 2 4 . 0 1 1 7 9 . 0 2 . 82 1 . 1 6200 1 534 224 1 15 . 6 0 . 4 28220 91 . 8 2 3 . 8 1 1 8 6 . 0 2 . 84 1 • 1 6200 1 534 225 115 . 0 0 . 4 28380 91 . 2 2 3 . 8 1 1 9 3 . 0 2 . 78 1 . 1 6200 1 535 226 1 15 . 5 0 . 5 26250 8 8 . 3 2 7 . 2 9 6 5 . 0 3 . 40 0 . 9 4780 1 535 227 114 . 9 0 . 5 26530 8 8 . 0 2 6 . 9 9 8 6 . 0 3 . 33 0 . 9 4780 1 535 228 114 . 9 0 . 5 26470 8 7 . 4 2 7 . 5 9 6 2 . 0 3 . 33 0 . 9 4780 1 535 229 1 15 . 0 0 . 5 26530 8 6 . 9 2 8 . 1 9 4 4 . 0 3 . 34 0 . 9 4780 1 535 230 1 15 . 8 0 . 5 2721 0 8 7 . 9 2 7 . 9 9 7 5 . 0 3 . 43 0 . 9 4780 1 535 231 115 . 8 0 . 5 27290 8 8 . 2 2 7 . 6 9 8 9 . 0 3 . 43 0 . 9 4780 2030 232 1 2 0 . 5 0 . 0 31 470 1 0 2 . 4 18 . 1 1 7 3 9 . 0 1 . 99 1.6 2030 233 1 2 0 . 8 0 . 0 31810 1 0 2 . 7 18. 1 1 7 5 7 . 0 2 . 01 1 .6 2030 234 1 2 0 . 6 0 . 0 31 740 1 0 2 . 4 18 . 2 1744 . 0 1 . 96 1 .6 2030 235 1 2 0 . 3 0 . 0 32090 1 0 2 . 2 18 . 1 1 7 7 3 . 0 1 . 98 1 .6 2030 236 1 2 0 . 0 0 . 0 32090 101 . 9 18. 1 1773 . 0 1 . 96 1 .6 2030 237 119 . 6 0 . 0 31 900 101 . 5 18. 1 1 7 6 3 . 0 1 . 94 1 .7 2032 238 121 . 5 0 . 2 30890 101 . 3 2 0 . 2 1 5 4 5 . 0 2 . 49 1 .3 1 0890 2032 239 1 2 0 . 9 0 . 2 31 270 101 . 7 19 . 2 1629 . 0 2 . 52 1 .3 1 0890 2032 240 1 2 0 . 8 0 . 2 31 360 101 . 4 19 . 4 1619 . 0 2 . 51 1 .3 10890 2032 241 121 . 5 0 . 2 31 900 101 . 8 19 . 7 1619 . 0 2 . 57 1 .2 10890 2032 242 121 . 4 0 . 2 31630 101 . 6 19 . 9 1 5 8 9 . 0 2 . 57 1 .2 10890 2032 243 121 . 5 0 . 2 31 930 101 . 6 19 . 9 1 6 0 5 . 0 2 . 57 1 .2 1 0890 2023 244 121 . 5 0 . 3 30380 9 8 . 8 2 2 . 7 1338. 0 2 . 94 1 . 1 8250 2023 245 121 . 4 0 . 3 30540 9 8 . 6 2 2 . 8 1 3 3 9 . 0 2 . 93 1 .2 8250 2023 246 121 . 4 0 . 3 30650 9 8 . 5 2 2 . 9 1 3 3 8 . 0 2 . 93 1 .2 8250 2023 247 121 . 4 0 . 3 31 000 9 8 . 4 2 3 . 0 1 3 4 8 . 0 2 . 93 1 .2 8250 2023 248 121 . 4 0 . 3 31080 9 8 . 3 2 3 . 1 1 3 4 6 . 0 2 . 93 1 .2 8250 2023 249 121 . 4 0 . 3 31110 9 8 . 4 2 3 . 0 1 3 5 3 . 0 2 . 93 1 .2 8250 2013 250 121 . 0 0 . 3 31990 102. 9 18 . 1 1756 . 0 2 . 90 1 . 1 8250 2013 251 121 . 1 0 . 3 321 50 102. 4 18 . 7 1719 . 0 2 . 90 1 . 1 8250 201 3 252 121 . 1 0 . 3 32070 1 0 2 . 4 18. 7 1715 . 0 2 . 90 1 . 1 8250 201 3 253 121 . 1 0. 3 32340 102 . 3 18. 8 1 720 . 0 2 . 90 1 . 1 8250 97 T a b l e V I I I : C o n t i n u e d . Run E x p t . S t e a m A i r H e a t S u b - Temp. H e a t T o t a l D i f f u - R e y -N o . N o . A i r R a t i o S t r a t e D r o p T r a n s - P r e s s s i o n n o l d s T e m p . F l u x Temp. f e r u r e C o e f f . N o . ( ° C ) (W/m 2 ) (° C) ( C « ) C o e f f . (W/m 2 C) ( atm) ( m 2 x / s ) 10 s 1 201 3 254 121 . 1 0 . 3 32530 1 0 2 . 1 19 . 0 1712. 0 2 . 90 • 1 8250 1 201 3 255 121 . 0 0 . 3. 32420 1 0 2 . 1 18 . •9 1715 . 0 2 . 90 1 . 1 8250 1 2033 256 121 . 0 0 . 3 30540 9 8 . 9 2 2 . 1 1 3 8 2 . 0 2 . 90 1 . 1 8250 1 2033 257 121 . 0 0 . 3 30810 9 9 . 0 2 2 . 0 1 401 . 0 2 . 90 1 . 1 8250 1 2033 258 121 . 0 0 . 3 30810 9 8 . 7 2 2 . 3 1 3 8 2 . 0 2 . 90 1 8250 1 2033 259 1 2 0 . 9 0 . 3 31 030 9 8 . 1 2 2 . 8 1361 . 0 2 . 89 1 . 1 8250 1 2033 260 1 2 0 . 9 0. 3 31 360 9 8 . 4 2 2 . 5 1 3 9 4 . 0 2 . 89 1 8250 1 2033 261 1 2 0 . 9 0 . 3 31 360 9 8 . 3 2 2 . 6 1 3 8 8 . 0 2 . 89 1 . 1 8250 1 2034 262 121 . 3 0 . 4 29720 9 7 . 4 2 3 . 9 1 2 4 3 . 0 3 . 41 0 . 9 61 00 1 2034 263 121 . 1 0 . 4 29750 9 6 . 9 2 4 . 2 1 2 2 9 . 0 3 . 39 0 . 9 6100 1 2034 264 121 . 9 0 . 4 301 60 9 7 . 4 2 4 . 5 1 231 . 0 3 . 48 0 . 9 . 61 00 1 2034 265 121 . 5 0 . 4 30270 9 6 . 7 2 4 . 8 1 2 2 0 . 0 3 . 43 0 .9 61 00 1 2034 266 121 . 8 0 . 4 3051 0 9 6 . 9 2 4 . 9 1 2 2 5 . 0 3 . 46 0 .9 6100 1 2034 267 121 . 9 0 . 4 30540 9 6 . 9 2 5 . 0 1 2 2 2 . 0 3 . 48 0 .9 61 00 1 2035 268 121 . 1 0 . 5 281 1 0 9 2 . 6 2 8 . 5 9 8 6 . 0 4 . 06 0 .8 4690 12035 269 1 2 0 . 8 0 . 5 28000 9 2 . 0 2 8 . 8 9 7 2 . 0 4 . 03 0 .8 4690 1 2035 270 121 . 9 0 . 5 28550 9 3 . 2 2 8 . 7 9 9 4 . 0 4 . 1 7 0 .7 4690 1 2035 271 121 . 3 0 . 5 28680 9 2 . 7 2 8 . 6 1 0 0 3 . 0 4 . 09 0 .8 . 4690 1 2035 272 1 2 0 . 9 0 . 5 28410 91 . 8 2 9 . 1 9 7 6 . 0 4 . 04 0 .8 4690 1 2035 273 121 . 5 0 . 5 28660 9 2 . 2 2 9 . 3 9 7 8 . 0 4 . 1 2 0 .8 4690 1 251 0 274 1 2 5 . 5 0 . 0 32370 106. 5 18 . 8 1 7 2 2 . 0 2 . 31 1 .4 1 251 0 275 1 2 5 . 2 0 . 0 32670 1 0 6 . 3 18. 9 1 7 2 8 . 0 2 . 30 1 .4 1 2510 276 1 2 4 . 9 0 . 0 31 430 105 . 5 19 . 4 1 6 2 0 . 0 2 . 29 1 .4 12510 277 1 2 4 . 9 0 . 0 32990 105 . 9 19 . 0 1 7 3 7 . 0 2 . 28 1 .4 1 251 0 278 1 2 4 . 9 0 . 0 33490 1 0 5 . 9 19 . 0 1 7 6 2 . 0 2 . 28 1 .4 1 251 0 279 1 2 5 . 0 0 . 0 33460 1 0 5 . 7 19 . 3 1 7 3 4 . 0 2 . 29 1 .4 1 251 2 280 125 . 3 0 . 2 32480 105 . 4 19 . 9 1 6 3 2 . 0 2 . 89 1 . 1 1 2950 12512 281 1 2 5 . 2 0 . 2 331 30 1 0 6 . 2 19 . 0 1 7 4 4 . 0 2 . 89 1 . 1 1 2950 12512 282 1 2 5 . 2 0 . 2 32750 1 0 5 . 0 2 0 . 2 1 621 . 0 2 . 89 1 . 1 1 2950 1 251 2 283 1 2 5 . 1 0 . 2 331 30 104. 9 2 0 . 2 1 6 4 0 . 0 2 . 89 1 • • 1 2950 1 251 2 284 1 2 5 . 1 0 . 2 33100 104. 6 2 0 . 5 1615 . 0 2 . 89 1 . 1 1 2950 12512 285 1 2 5 . 1 0 . 2 331 00 1 0 4 . 6 2 0 . 5 1615 . 0 2 . 89 1 . 1 12950 1 251 4 286 125 . 7 0 . 4 29990 9 9 . 6 2 6 . 1 1 149 . 0 3 . 91 0 .8 6040 1 251 4 287 1 2 5 . 3 0 . 4 29990 9 9 . 0 2 6 . 3 1 1 4 0 . 0 3 . 86 0 .8 6040 1 251 4 288 1 2 5 . 1 0 . 4 30070 9 8 . 5 2 6 . 6 1 130. 0 3 . 83 0 .8 6040 12514 289 1 2 4 . 8 0 . 4 30350 9 7 . 8 2 7 . 0 1 1 2 4 . 0 3 . 80 0 .8 6040 1 2514 290 1 2 4 . 7 0 . 4 30430 9 7 . 7 2 7 . 0 1 1 2 7 . 0 3 . 79 0 .8 6040 12514 291 124 . 8 0 . 4 30460 9 7 . 8 2 7 . 0 1 128 . 0 3 . 80 0 .8 6040 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0095268/manifest

Comment

Related Items