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Numerical and experimental study of orientation dependency of free convection heat sinks Rana, Md. Ruhul Amin 2015

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NUMERICAL AND EXPERIMENTAL STUDY ON ORIENTATION DEPENDENCY OF FREE CONVECTION HEAT SINKS by Md Ruhul Amin Rana  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in  THE COLLEGE OF GRADUATE STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)   April 2015  © Md Ruhul Amin Rana, 2015 ii  ABSTRACT The flow momentum in free convection heat transfer is generally lower than forced convection, and the flow direction is determined by the gravitational direction. Hence, the thermal performance of heat sinks relying on free convection could vary significantly depending on the mounting orientation. This is confirmed by the present work, a computational fluid dynamics and heat transfer study with focus on the relation between the design of heat sinks and their thermal performance under varied mounting orientations. A heat sink with rectangular straight fins, a very commonly used type of heat sink, is first studied. The results show poor thermal performance when the heat sink is placed vertically and fin length horizontally to the ground. The fluid dynamics analysis indicates interruption of buoyancy flow by the horizontally placed fins, which in turn impedes heat transfer. An experimental work on straight fin heat sink is also performed, and with the help of infrared camera and thermocouples the orientation dependencies are observed for a wide range of orientation angles. In order to minimize the negative effect of mounting orientations, two other types of heat sinks are studied. One is angled-fin heat sink, which has plate fins parallel to the diagonal rather than the side of the heat sink base. The other type is pin-fin heat sinks. The two types of heat sinks are shown to provide similar thermal performances for both horizontal and vertical orientations, and the low orientation dependency is attributed to the low orientation effect on the buoyancy flow. The fin thickness, fin spacing and number of fins are varied for both the heat sinks. The purpose is to study the effect of these changes on thermal performance for different mounting orientations. For angled-fin, the effects of fin interruptions are also studied, where horizontal orientation shows better cooling performance than the vertical. In case of pin fin heat sink, the temperature iii  differences between the vertical and horizontal orientations show that, the fin spacing plays an important role in the selection of mounting orientation. This study is useful for designing free convection heat sinks for orientation-independent cooling performance. iv  PREFACE Some portions of this research have been submitted for the possible publication in journal and some were presented in conference (see below). The author conducted all the experimental works, simulation analysis and writing of this thesis. His research supervisor has great contribution in providing guidance, advices and supportive involvement throughout the research for successful outcome.  Journal and Conference Publications R.A. Rana and R. Li, “Orientation Dependency of Free Convection Heat Sinks,” Submitted to Journal of Thermal Science and Engineering Applications, 2015. R.A. Rana and R. Li, “Design of Heat Sink for Orientation-Independent Free Convection,” has been presented at CSME International Congress, 2014. v  TABLE OF CONTENTS ABSTRACT .................................................................................................................................... ii PREFACE ...................................................................................................................................... iv TABLE OF CONTENTS ................................................................................................................ v LIST OF TABLES ....................................................................................................................... viii LIST OF FIGURES ....................................................................................................................... ix LIST OF SYMBOLS ................................................................................................................... xiv ACKNOWLEDGEMENTS ......................................................................................................... xvi DEDICATION ............................................................................................................................ xvii CHAPTER 1: INTRODUCTION AND THESIS ORGANIZATION ........................................... 1 1.1 GENERAL ................................................................................................................ 1 1.2 OBJECTIVE OF THE STUDY ................................................................................ 2 1.3 RESEARCH SIGNIFICANCE ................................................................................. 3 1.4 THESIS OUTLINE ................................................................................................... 4 CHAPTER 2: LITERATURE REVIEW ........................................................................................ 6 2.1 HEAT TRANSFER MECHANISM ......................................................................... 6 2.2 FREE CONVECTION AND RADIATION HEAT TRANSFER ............................ 7 2.2.1 Different Types of Heat Sinks ............................................................................... 7 2.2.2 Thermal Performance Analysis ............................................................................. 8 2.2.3 Free Convection Flow ......................................................................................... 10 2.2.4 Parametric Study of Heat Sinks .......................................................................... 11 2.2.5 Mounting orientation of Heat Sinks .................................................................... 13 CHAPTER 3: NUMERICAL ANALYSIS OF STRAIGHT FIN HEAT SINK .......................... 18 3.1 NUMERICAL METHODOLOGIES...................................................................... 18 3.1.1 Thermal Model .................................................................................................... 19 3.2 Thermal Performance.............................................................................................. 27 vi  3.3 Free Convection Flows ........................................................................................... 31 CHAPTER 4: EXPERIMENT ON STRAIGHT FIN HEAT SINK ............................................. 35 4.1 HEAT SINK SELECTION AND MAKING .......................................................... 35 4.2 EXPERIMENTAL SETUP ..................................................................................... 36 4.3 UNCERTAINTY ANALYSIS ............................................................................... 41 4.4 EMISSIVITY CALIBRATION .............................................................................. 43 4.5 THERMAL ANALYSIS ........................................................................................ 45 4.5.1 Thermal Readings ............................................................................................... 45 4.5.2 Heat Loss ............................................................................................................. 47 4.5.3 Thermal Distribution ........................................................................................... 49 4.5.4 Orientation Dependency ...................................................................................... 52 4.5.5 Heat Sink Performance........................................................................................ 54 4.6 NUMERICAL STUDY .......................................................................................... 57 CHAPTER 5: ANGLED-FIN HEAT SINK ................................................................................. 60 5.1 NUMERICAL MODEL.......................................................................................... 60 5.2 THERMAL PREFORMANCE ............................................................................... 61 5.3 FREE CONVECTION FLOW ............................................................................... 63 5.4 PARAMETRIC STUDY ........................................................................................ 64 5.4.1 Change in Fin Thickness and Fin Spacing .......................................................... 65 5.4.2 Change in Fin Numbers and Spacing .................................................................. 67 5.5 ANGLED-FIN WITH INTERrUPTIONS .............................................................. 69 CHAPTER 6: PIN FIN HEAT SINK ........................................................................................... 72 6.1 NUMERICAL MODEL.......................................................................................... 72 6.2 THERMAL PERFORMANCE ............................................................................... 73 6.3 FREE CONVECTION FLOW ............................................................................... 74 6.4 PARAMETRIC STUDY ........................................................................................ 75 CHAPTER 7: RESULT AND DISCUSSION .............................................................................. 80 vii  7.1 ORIENTATION DEPENDENCIES ....................................................................... 80 7.2 THERMAL PERFORMANCES OF DIFFERENT HEAT SINKS ....................... 81 CHAPTER 8: CONCLUSIONS AND RECOMMENDATIONS ................................................ 84 8.1 CONCLUSIONS..................................................................................................... 84 8.2 LIMITATIONS OF THIS STUDY ........................................................................ 84 8.3 FUTURE RECOMMENDATIONS ....................................................................... 85 REFERENCES ............................................................................................................................. 86 viii   LIST OF TABLES Table 3.1: Flow-pressure boundaries of the numerical domain for varied gravity vectors. ......... 21 Table 3.2: Thermal boundaries of the numerical domain for varied gravity vectors ................... 21 Table 4.1: Experimental sets for different mounting orientations ................................................ 39 Table 4.2: Uncertainties in experimental test ............................................................................... 42 Table 4.3: Insulation materials and their thermal properties ........................................................ 47 Table 6.1: Designs of pin-fin heat sinks with varied pin diameters and number of pins.............. 76  ix  LIST OF FIGURES Figure 2.1: Contour temperature variation with orientation for straight fin heat sink: (a) horizontal orientation; (b) vertical orientation where fin lengths are parallel to gravity direction; (c) vertical orientation where fin lengths are perpendicular to gravity direction. ........................................................................................................ 16 Figure 3.1: Thermal model of heat sink: (a) straight-fin heat sink (dimensions are in mm); (b) heat sink in the domain where gravity can be applied in g-1, g-2 or g-3 orientation; (c) finite element meshing of domain; (d) meshing of heat sink inside the domain. ...................................................................................................... 20 Figure 3.2: Mesh independency of numerical model to thermal performance: (a) meshing with 1 mm minimum cell size; (b) meshing with 0.5 mm minimum cell size........... 24 Figure 3.3: Flat plate with domain where gravity ‘g’ is perpendicular to plate surface ............... 26 Figure 3.4: Temperature contour on the bottom surface of the straight-fin heat sink placed horizontally (g-1 orientation). .................................................................................... 28 Figure 3.5: Temperature contour on the bottom surface of the straight-fin heat sink placed vertically with fins parallel to gravity vector (g-2 orientation). ................................. 29 Figure 3.6: Temperature contour on the bottom surface of the straight-fin heat sink placed vertically with fins orthogonal to gravity vector (g-3 orientation). ........................... 31 Figure 3.7: Observation plane for observing the fluid dynamics of buoyancy flow. ................... 32 Figure 3.8: Velocity vector on the observation plane for the g-2 orientation of the straight-fin heat sink shown in Figure 3.4. .............................................................................. 33 x  Figure 3.9: Velocity vector on the observation plane for the g-3 orientation of the straight-fin heat sink shown in Figure 3.5. .............................................................................. 34 Figure 4.1: Making of heat sink: (a) cutting of heat sink block using Water Jet; (b) forming of rectangular shape fins on the block using CNC machine. ..................................... 36 Figure 4.2: Thermal model of heat sink; (a) straight fin heat sink (dimensions are in mm); (b) orientation of heat sink made by rotating about the three sides ‘A’, ’B’ and ’C’; (c) schematic of the heat sink (all dimensions are in mm). ................................ 37 Figure 4.3: Experimental setup, (a) Insulation layers of heat sink; (b) Heat sink rotation mechanism ................................................................................................................. 38 Figure 4.4: Orientation of the heat sink; (a) rotation about side ‘A’ (b) rotation about side ‘B’; (c) rotation about the diagonal ‘C’ ..................................................................... 40 Figure 4.5: Experimental setup for straight fin heat sink thermal reading ................................... 41 Figure 4.6: Emissivity calibration by black painted flat plate ...................................................... 44 Figure 4.7: Average Emissivity of black painted calibration plate ............................................... 45 Figure 4.8: Infrared camera readings accuracy compared to thermocouples. .............................. 46 Figure 4.9: Thermal resistance of insulation materials ................................................................. 48 Figure 4.10: Thermal analysis of heat sink: (a) thermal image from IR camera for α=60° orientation; (b) heat sink orientation for α=60°(c) temperature distribution along the channel length for the orientation shown in figure (b) ............................... 50 Figure 4.11: Channel average temperature plot at different orientation angle ............................. 51 Figure 4.12: Gravity force component parallel to the heat sink base ........................................... 52 xi  Figure 4.13: Average base temperature for different mounting orientation ................................. 54 Figure 4.14: Comparison of experimental results with the numerical simulations. ..................... 58 Figure 4.15: Velocity vector at observation plane (Figure 3.6) for the experimental heat sink specimen: (a) for θ=90°, rotation about diagonal side C; (b) for α=90°, rotation about side A .................................................................................................. 59 Figure 5.1: (a) Angled-heat sink placed horizontally (g-1 orientation); (b) Temperature contour on the bottom surface of the angled-fin heat sink in g-1 orientation. ........... 62 Figure 5.2: Temperature contour on the bottom surface of the angled-fin heat sink placed vertically (g-2, g-3 orientations). ............................................................................... 63 Figure 5.3: Velocity vectors of buoyancy flow on the observation plane of the angled-fin heat sink placed in g-2 or g-3 orientation shown in Figure 5.2. ................................ 64 Figure 5.4: Thermal performance of vertically orientated angled-fin heat sink versus fin thickness for the constant number of fins. ................................................................. 66 Figure 5.5: Average heat transfer coefficient of vertically oriented angled-fin heat sink versus fin thickness .................................................................................................... 67 Figure 5.6: Variations of angled-fin base plate temperature with fin spacing for 1 mm thick fin ............................................................................................................................... 68 Figure 5.7: Variations in average heat transfer coefficient with fin spacing for vertically oriented 1mm thick angled-fin heat sink .................................................................... 69 Figure 5.8: Angled-fin with interruptions: (a) 3 interruptions (b) 5 interruptions ........................ 70 xii  Figure 5.9: Variations in average base temperature with interruptions for angled-fin heat sink ............................................................................................................................. 71 Figure 6.1: (a) Pin-fin heat sink with 12×12 pin fins with 5 mm in diameter. (b) Temperature contour on the bottom surface of the pin-fin heat sink placed horizontally (g-1 orientation). .................................................................................... 73 Figure 6.2: Temperature contour on the bottom surface of the pin-fin heat sink (12×12 pins, 5 mm in diameter) placed vertically (g-2, g-3 orientations). ............................. 74 Figure 6.3: Velocity vectors of buoyancy flow on the observation plane of the pin-fin heat sink (12×12 pins, 5 mm in diameter) placed in g-2 or g-3 orientation shown Figure 6.2. .................................................................................................................. 75 Figure 6.4: Variations in average heat transfer coefficient of different heat sinks for vertical orientations. (S-g2: straight-fin heat sink with g-2 orientation; S-g3: straight-fin heat sink with g-3 orientation; A: angled-fin heat sink; P-D: pin-fin heat sinks with pin diameter 8.57 mm; P-d: pin-fin heat sinks with pin diameter 6.56 mm; P-dd: pin-fin heat sinks with pin diameter 5 mm). The x-axis values for pin-fin heat sinks are the number of pin rows........................................................................ 78 Figure 7.1: Average temperature on the bottom surface of the heat sink (base average temperature) versus orientation for the three types of heat sinks. ............................. 81 Figure 7.2: Variations in average heat transfer coefficient of different heat sinks for vertical orientations. (S-g2: straight-fin heat sink with g-2 orientation; S-g3: straight-fin heat sink with g-3 orientation; A: angled-fin heat sink; P-D: pin-fin heat sinks with pin diameter 8.57 mm; P-d: pin-fin heat sinks with pin diameter 6.56 mm; xiii  P-dd: pin-fin heat sinks with pin diameter 5 mm). The x-axis values for pin-fin heat sinks are the number of pin rows........................................................................ 83  xiv  LIST OF SYMBOLS g Gravity force LRa  Rayleigh number LuN  Nusselt number a  Diffusivity a  Thermal expansion coefficient   Kinematic viscosity L  Fin height cL  Corrected fin length chL  Characteristic length A  Area P  Perimeter sT  Heat sink surface temperature T  Ambient temperature fT  Film temperature avgT  Average temperature Pr  Prandtl number k Thermal conductivity S Fin Spacing h  Average heat transfer coefficient ch  Corrected avg. heat transfer coefficient eh  Effective heat transfer coefficient f  Fin efficiency q  Heat transfer rate q   Heat transfer rate per unit area cq  Corrected heat transfer rate xv  D Diameter btA .  Total base area t Fin thickness R   Thermal resistance per unit area ftA .  Total fin surface area   Angle of rotation about side A   Angle of rotation about side B   Angle of rotation about side C ε Emissivity   View factor   Stefan-Boltzmann constant V Voltage I Current   Density  xvi  ACKNOWLEDGEMENTS I would like to convey my profound gratitude to the Almighty Allah who has given me the strengths and blessings to pursue my MASc and conduct the thesis works easy and smoothly. My heartiest gratitude goes to my supervisor Dr. Sunny Li for providing me the opportunity to conduct my MASc under his wise supervision. I am thankful to him in every possible way for his endless supports and directions. Without his guidance and motivation it was not possible to fulfill my goal. His valuable directions and advice made this thesis works productive and my graduate experience wonderful.  I would also like to thank my thesis dissertation committee members for their valuable comments, feedbacks and directions that made this research work a successful one. I am also grateful to my family members who are the key source of all my inspirations and motivations in every successful achievement.  xvii  DEDICATION    To my family who supported me all the way long 1  CHAPTER 1: INTRODUCTION AND THESIS ORGANIZATION 1.1 GENERAL In this modern civilized world, people are experiencing more and more new devices and electronics equipment day by day. As those have been an essential part of their life, failure of proper working of those devices is unimaginable. One of the main reasons of failure is the generated heat by the devices. This generated heat must be dissipated to the surrounding to protect the devices from being burnt out and for the proper function. Proper methods of heat dissipation must be employed to the device to protect them. The selection of proper method depends on the application, manufacturing capability, required performance, efficiency and cost.  Two popular methods of heat transfer are forced and free convection. Force convection requires an external fan or blower to generate and increase the fluid motion. This external addition of devices requires power to drive as well as space to install which might be insufficient in many situations. The other very common free convection heat transfer is caused by buoyancy force of fluid due to the density variation within the surrounding fluid which results from the temperature difference. This passive cooling method is noiseless and trouble-free, and features simplicity and low cost, as no parasitic power is required for running a circulating device or fan. However, free convection usually has low heat transfer capability due to its low heat transfer coefficient. So there are needs for some innovative and efficient ways to increase the convection heat transfer. Free convection cooling can be enhanced by increasing heat transfer area, and the most common approach is attaching a plate with fins on it to the hot surface of the device. The finned 2  plate is a heat sink, which can be commonly seen in the thermal management solutions for many cooling applications. Different types of fin configurations are used depending on the application, required performance, manufacturing constraints, and costs. Among these, some configurations show high orientation dependency to mounting orientations which may cause high temperature rise that leads to device failure. Other configurations might perform very well in response to free convection in any mounting orientations.  Due to compact, small, and ever-shrinkage nature of modern devices, it has become increasingly challenging to develop an effective thermal management system. Such a system should meet the required performance minimizing the manufacturing cost. As portability of devices has added a new dimension to the user flexibility, so orientation dependency to thermal performance of this system must be considered. To enhance the thermal performance with low orientation dependency and ensure efficient use of suitable heat sink, the numerical and experimental study is necessary which will help to overcome the difficulties of free convection heat transfer. 1.2 OBJECTIVE OF THE STUDY For the thermal management of equipment and electronic devices, use of heat sink has become very common due to its easy, low cost solution. The effective use of the heat sink requires low dependency on mounting orientation, which can only be achieved through the combination of proper design and selection of fin configuration. This study seeks to investigate the effect of orientation angle on thermal performance for free convection heat sink. The study is conducted to achieve the following objectives: 3  1. Understand the use of different heat sinks for free convection heat transfer. 2. Study the heat sink design with different fin configurations sensitive to mounting orientations. 3. Investigate the effect of different orientation angles on thermal performance of heat sink. 4. Investigate the parametric effects on cooling performance and explore the effective heat sink design for free convection. 5. Validate the numerical results with practical experience. 1.3 RESEARCH SIGNIFICANCE Extensive research has been conducted on heat sink for free convection heat transfer. Different types of heat sinks with different fin configurations have been studied previously. The main focus of those works was on the effects of changing fin configurations on flow patterns and heat sink thermal performance. Not much attention has been paid to the mounting orientation effect. The present work explores the effect of mounting orientations by investigating different fin configurations under varied mounting orientations. For the heat sinks with low orientation-dependency, detailed parametric studies are done to investigate better cooling performance. The flow dynamics of these models are also studied to investigate the buoyancy effects of orientation angles. This study addresses high orientation dependency of some heat sink for certain orientation angles which could cause ultimate device failure. The relation between fin parameters and orientation angle variations for different heat sink are analysed. This study offers a new dimension to the heat sink design considering the orientation dependency of free convection. The results are useful for developing effective heat sinks with low orientation dependency. 4  1.4 THESIS OUTLINE This study is organized with seven different chapters. Each chapter includes specific part of the dissertation in the following manner: Chapter-1 covers the short preface and objective of this study. The research significance and thesis outline are also discussed in this section Chapter-2 includes the details literature review of the previous works done related to this work. This chapter also includes the thermal performance of different heat sinks with different fin configurations. The effects of fin spacing, fin thickness, fin height and base to ambient temperature difference on heat transfer performance are discussed. Chapter-3 presents the numerical analysis of orientation dependency for straight fin heat sink under free convection. The thermal distributions and flow dynamics of different heat sink orientations are analysed.  Chapter-4 comprises the experimental findings on straight fin heat sink. In this chapter, the orientation dependency is studied with more orientation angles experimentally. The thermal performance and orientation dependency are compared with the numerical results for different orientations. Chapter-5 provides the thermal performance and flow dynamics of angled fin heat sink for different orientations. The effects of variation of fin spacing and thickness on cooling performance are analysed. The thermal performance of interruption cuts on angled fin heat sink is also studied.  5  Chapter-6 demonstrates the orientation dependency of pin fin heat sink. Using the numerical methodologies, the thermal performance of pin fin configurations with different pin diameter and varied number of fins are analysed.  Chapter-7 discusses the results of thermal performances of different heat sinks and their orientation dependencies.  Chapter-8 presents the conclusions and summary derived from this study. Some recommendations are also noted for further research works. 6  CHAPTER 2: LITERATURE REVIEW This chapter aims to present the previous works related to free convection heat transfer from heat sinks and their thermal performance variations with varied parameters. The existing knowledge and detailed summary of available literatures are also discussed. 2.1 HEAT TRANSFER MECHANISM Heat transfer has three modes: conduction, convection and radiation. Convection heat transfer is the most popular mode for cooling and thermal management. For high heat flux applications, forced convection of using liquid or air is very popular. Forced air cooling has the benefit of not using circulating loop. Usually heat sinks are used to forced-air-cooling for surface extension. Here, the design of heat sink is also important and need to be optimized by selecting optimum fin parameters in addition to the required size and power of fan or blower [1]. For relatively low heat flux applications, free convection air cooling is ideal. Because of low heat transfer efficiency, heat sinks must be needed to extend surface so that the cooling performance is sufficient. However, the heat transfer coefficient is very sensitive to the heat sink design and orientation. Spray cooling is another approach of heat transfer mechanism widely used in industrial application and cooling of electronic equipment [2, 3]. It is mostly used in high heat transfer and requires external arrangements and larger space to install. 7  Another effective cooling mechanism of vertical hot surface is by falling cold liquid film [4]. Cooling of very hot surface by this film wetting phenomenon is very convenient in some applications.  2.2 FREE CONVECTION AND RADIATION HEAT TRANSFER For free convection, the temperature gradient of the fluid causes density gradient, and the density gradient then causes net buoyancy force, which drives the fluid to flow [5]. Buoyancy flow from heated heat sink is also governed by the heat sink geometry and mounting orientation.  For radiation heat transfer, emissivity is an important factor which depends on the surface condition. Several works have been conducted on free convection and radiation for different heat sinks focusing on thermal improvement and optimum design for different applications. The findings from those literatures are observed which have been very helpful for the new direction and appropriate selection of the present work.  2.2.1 Different Types of Heat Sinks Different types of heat sinks were studied previously. The selection of a particular heat sink depends on the required thermal performance and application. Various cooling methods are also involved depending on the size and speed of the circuit and other non-thermal parameters [6].  Lee [7] summarized different types of heat sinks and their application with cost range. The parameters influence the thermal performance were also noted with discussing the design and selection of optimum heat sink for specific cases.  Among the literature, the most common and much studied heat sink has been the rectangular cross section straight fin heat sink. Starner and McManus [8] showed that for free convection, 8  incorrect use of rectangular fins on heated surfaces may reduce thermal performance even lower than the bare plate. Studies on pin fin heat sink are also common. A new type of pin fin heat sink was studied by Chapman and Lee [9] which was of elliptical shape and the thermal performance was compared with two other heat sink configurations of cross-cut and extruded fin. It was found that, although cross-cut heat sink shows increased air flow, better thermal performance is observed for elliptical pin heat sink with less vortex flow.  For the study of natural convection and radiation heat transfer from vertical surface, Guglielmini at el. [10] used staggered array of fins. The geometric configuration of the staggered fins of discrete plates were varied and compared with the same bulk volume rectangular fin heat sink. It was found that staggered array heat sink has higher heat transfer capability. Two compact models of extruded and pin fin heat sinks were studied numerically and analytically by Narasimhan and Majdalani [11]. To reduce the computational time, compact models were considered instead of analysing large arrays of heat sinks. The findings from analysis were compared with respect to actual model under free convection and good agreement was found for both the detailed and compact 3-D model.  A fully different type of approach was taken by Yu at el. [12] to improve the thermal performance from heat sink by using both plate fin and pin fin on the same base plate. This plate-pin fin heat sink was thermally compared with the plate fin and 30% less thermal resistance was achieved. Both the numerical and experimental results were taken to compare the performances.  2.2.2 Thermal Performance Analysis The purposes of all the literatures are to ensure better thermal performance and appropriate use of various methods. Different approaches were taken to improve heat transfer from vertical 9  plate by different authors. Changing the surface geometry with transverse roughness is one of the technique was used by Bhavnani [13]. Under natural convection and in the laminar regime, it was found that 23.2% increase in heat transfer coefficient is possible by introducing stepped geometry on the surface. But for ribbed surface geometry degrading nature of thermal performance was noticed. Heat transfer from different heated fin configurations were analysed with two different optical methods by Rao at el [14]. Using both the optical methods of deferential interferometer and Mach Zehnder interferometer, thermal performance of vertical plane, one finned, and three finned horizontal plate were studied.  Free convection from rectangular, square and circular plates positioned horizontally were investigated by Al-Arabi and El-Reidy [15]. Thermal performance for both laminar and turbulent regions were studied and compared the results with Fishenden & Saunders [16] and Bosworth’s [17] equations and also with Mikheyev’s [18] recommendation. The contributions in heat transfer performance by edges and corners of plates of different shapes were also studied in the literature. The Influence of chimney effect on natural convection heat transfer from shrouded vertical fin arrays was studied numerically by Karki and Patankar [19]. The effects were analysed by evaluating the Nusselt number for varied clearance space. Another analytical study on design of heat sinks and their thermal performance under chimney effect was performed by Fisher and Torrance [20]. It was shown that, heat sink height has negligible effect in temperature rise and is invariant relative to the total height of the system. Aihara at el. [21] investigated pin fin performance for convection and radiation heat transfer with a vertical base plate. For different pin fin dissipators the Nusselt number and Rayleigh 10  number were correlated for thermal performance characteristics. An experimental approach was taken by Sobhan at el [22] to investigate the free convection from horizontal based fin arrays. Optical method was used to determine the thermal performance, and depending on the material properties optimum fin spacing was evaluated. 2.2.3 Free Convection Flow The fluid velocity and thermal boundary layers formed on the vertical plate and the horizontal plate are different [5]. A number of studies have been reported to investigate the free convection flow and heat transfer from different surfaces at various operating conditions. Huang and Wong [23] studied flow dynamics of free convection for varied fin lengths and fin height of horizontal rectangular fin arrays. A relation between the pattern of buoyancy flow and fin lengths was observed in respect to the thermal performance. It was found that, for short fin length the type of buoyancy flow is different than that of increased fin length, which consequently affects the thermal performance. The flow pattern was also characterized by the ratio of fin height and fin length.  Another study on free convection flow was reported by Mobedi and Yuncu [24] using finite difference code in a three dimensional system. The effects of fin spacing, fin height and fin length on flow dynamics were investigated. Two different types of buoyancy flow were found by them which are up and down type flow and single chimney type flow. The height to length ratio of the fin was found important for affecting the flow pattern. Experimental efforts were taken by Warner and Arpaci [25] to verify the existing correlations of natural convection from heated vertical plate in the region of turbulent flow. A good agreement of their experimental results was found with the correlations. Heat transfer from a 11  vertical isothermal plate under free convection was investigated and correlations are presented over a wide range of Rayleigh and Prandtl number [26]. This study was done to understand the heat and mass transfer correlations and their experimental anomalies.  Free convection from a plate of arbitrary inclination was observed by Fujii and Imura [27]. Expression of flow conditions for different plate angle were deduced and compared. Flow pattern was used to explain the changes in heat transfer coefficient. 2.2.4 Parametric Study of Heat Sinks Effects of fin parameters on heat transfer performance have been studied widely. Selection of fin thickness of rectangular fin heat sink is an important parameter to maximize the free convection thermal performance. Bar-Cohen [28] found that thicker fin shows better thermal performance and would be maximum if the thickness is equal to the optimum fin spacing. Using least material and thermally efficient rectangular plate fin heat sink design was studied by Bar-Cohen at el. [29]. In another study Bar-Cohen and Rohsenow [30] investigated the isothermal and isoflux cases for parallel plates fin under free convection cooling. For natural convection heat transfer from rectangular fin arrays in horizontal orientation, selection of fin length is important. Harahap and McManus [31] revealed that, heat sink with smaller fin length shows larger heat transfer coefficient. Flow field for the horizontal orientation around the rectangular fin heat sink was also studied. Their proposed correlation shows that, high thermal performance can be achieved by choosing high ratio of fin spacing and fin length. Although the effects of fin spacing, height and temperature difference on thermal performance show a good agreement with the work of Jones and smith [32], the fin length effect was questioned. 12  Heat sink with rectangular fin was studied for non-uniform base temperature for both short and long fins with varied fin spacing [33]. Another study for horizontal orientation of thick fin with short length heat sink was conducted under free convection heat transfer by Dialameh at el. [34]. From this study it was found that, heat transfer coefficient is sensitive to fin spacing, fin length and temperature difference. Higher fin temperature and fin spacing increase the heat transfer coefficient which was also confirmed by Mittelman at el. [35] and the work was verified theoretically, experimentally and numerically. Their findings are important in optimum design of heat sink. Welling and Wooldridge [36] studied the relationship between fin geometry and heat transfer for vertical rectangular fins. An optimum ratio of fin height to fin channel width was found for free convection. A relation was also observed between this geometric ratio and fin temperature. Chen at el. [37] investigated the accuracy of thermal results obtained from plate fin heat sink for various fin spacing. Good agreement between numerical and experimental data was also observed. Zografos and Sunderland [38] conducted a parametric study on the free convection heat transfer of pin fin arrays. It was found that thermal performance is greatly dependent on the ratio of fin diameter to center-to-center spacing, and is best for the ratio of 1/3. This prediction was done based on experimenting a wide range of data from varied geometries and Rayleigh numbers. Yuncu and Anber [39] investigated the distinct role and performance of fin spacing, height and base-to-ambient temperature difference under free convection from horizontal based rectangular fins. It was found that fin height has strong effect on thermal performance and for a specific height there is an optimum fin spacing, which is invariant to temperature difference. 13  Morrison [40] studied heat sink geometry optimization for natural convection. It was found that the lowest average heat sink temperature can be achieved by finding the optimum combination of fin spacing, fin thickness and baseplate thickness. Zhang and Liu [41] took a numerical approach to find out the optimum spacing between fins for vertical rectangular fins under free convection. It was found that for free convection heat transfer the optimum spacing is related to boundary layer formation along the fins. This effect was determined by simulating a wide range of fin configurations. 2.2.5 Mounting orientation of Heat Sinks Depending on the fin orientation, fins have significant effect on the fluid dynamics of the buoyancy flow, which eventually affects heat transfer. Since the fin orientation is determined by the mounting orientation of the heat sink, the free convection heat transfer performs differently depending on the device’s orientation. One major concern of electronic components manufacturers is the device orientation effects on heat transfer performance. This performance is related to how the device is mounted during operation: horizontal, vertical or others. Several works were found on heat sink tested for different orientation angles. Effect of inclination angle of heat sink of rectangular cross section under free convention heat transfer was studied by Mehrtash and Tari [42]. They came up with a new correlation which is the replacement of their previous predicted three sets of correlations. Here the inclination angles were chosen by rotating the heat sink only in one direction. Another attempt by the same author was taken to investigate the plate fin heat sink orientation effect for horizontal and slightly-inclined orientations [43]. In another of their works it was found that fin height and spacing have great effect on thermal performance, and change in inclination angles does not have effect on 14  optimum fin spacing [44]. Rectangular block of fluid which is similar to the fluid block in between two consecutive fins of heat sink was studied using the two dimensional equations of motion by Catton at el. [45]. Arbitrary angle of orientations was used under free convection heat transfer. With the change in tilting angle and aspect ratio, variations in fluid flow and heat transfer were observed. Pin fin heat sink was studied by Sparrow and Vemuri [46] for three different orientations. Though the numbers of pin fins were varied for different base temperatures, the fin diameters were kept constant. The experiment was done by inserting the individual fin rod into the holes drilled on the base plate, which may have some effect on thermal performance due to the contact resistance which was neglected. A comparison of heat transfer was done between this pin fin and plate fin results from other literatures which is also limited to only one orientation. Another orientation effect analysis for free convection heat transfer from pin fin of square shape was done by Huang at el. [47]. Three different orientations were considered with varied number of fin arrangements. Thermal performances for these orientations were compared considering the finning factor (At/Ab) and heat sink porosity. Sertkaya at el. [48] investigated the thermal performance of pin fin heat sink experimentally. They changed the orientation angles from up-facing horizontal to down-facing horizontal. The study was done for only one configuration without changing the fin parameters, and the best thermal performance was found for vertical orientation. Starner and McManus [8] showed that the variations in inclination angle have effect on heat transfer coefficient. They found that for the vertical orientation the coefficient is maximum, which may reduce with the increase of fin height. The effect of inclination angle on local Nusselt 15  number for the heat transfer from inclined enclosure was first experimentally and numerically investigated and matched by Hamady at el. [49]. Nowadays, orientation-independent use of many devices has become more common as it provides more flexibility in operation. One example is the electrical vehicle (EV) battery charger. It is one of the critical components [50] which needs to provide fast, reliable, and efficient charging to vehicle batteries. This has become increasingly challenging as the EV makers are moving chargers on-board the vehicle. Due to the variety of mounting schemes of different vehicles, this on-board charger enclosure faces different thermal problems during charging operation. This includes the rise of enclosure surface temperature beyond expected limits, which become even worse for vertical orientation of the charger enclosure. To understand the orientation dependency of heat sink, let’s consider the Figure 2.1. In this figure, the temperature contours of straight fin heat sink are shown from ANSYS simulated results for three different orientations. The first figure (Figure 2.1a) is for horizontal orientation, where the maximum contour temperature is 109°C. The second figure (Figure 2.1b) shows the vertical orientation for fin length positioned parallel to gravity direction. Here, the maximum temperature is 111°C, which is close to the horizontal orientation. Now, if the orientation of that same heat sink is changed for another vertical orientation (Figure 2.1c) where fin lengths become perpendicular to gravity direction, a large increase in contour temperature is observed. For this orientation, a temperature rise of around 75°C more than the other two orientations is seen, which clearly indicates to the orientation dependency of thermal performance.  16   Figure 2.1: Contour temperature variation with orientation for straight fin heat sink: (a) horizontal orientation; (b) vertical orientation where fin lengths are parallel to gravity direction; (c) vertical orientation where fin lengths are perpendicular to gravity direction.  From the above studies it can be concluded that, different approaches were taken to analyze the thermal performance of heat sinks of the various configurations. The purposes of those analyses are to understand the effect of different parameters and achieve better cooling performance. For that, different heat sinks were studied varying different parameters, changing different conditions and introducing new techniques. The present study represents a broad picture of orientation dependencies of three different heat sinks with more possible mounting angles. Orientation angles are selected by rotating the heat sinks about three sides. A new design that is angled-fin heat sink is introduced which was absent in the previous works. The orientation dependency of the three type of heat sinks are compared on the basis of thermal performance for wide range of inclination angles. Simulation results are verified with experimental works and good agreement is observed. This study explores the fin design of heat sinks for the minimization 17  of orientation-dependency and improvement of heat transfer performance with reduced operational constraints.  18  CHAPTER 3: NUMERICAL ANALYSIS OF STRAIGHT FIN HEAT SINK In this chapter, focus will be first put on the baseline heat sink, a conventional type heat sink that is widely used due to its simple design and easy manufacturing capabilities with low cost. This baseline heat sink is rectangular straight fin heat sink and its thermal performance and fluid dynamics will be discussed using numerical simulation. For this simulation model and orientation dependency check, three different orientations will be used as shown in Figure 3.1b. After that, an experimental study will be performed in chapter 4 with more orientation angles to validate and understand the orientation dependency.  The thermal performance of heat sink will be evaluated based on the temperature distribution on the backside of the base plate, where the heat sink is in contact with the heat source. In addition to temperature distribution, the maximum temperature and average temperature are also useful. The maximum temperature has practical use as it ensures that the device cooled by the heat sink is within its safe temperature limit. The average temperature is useful for evaluating the overall heat transfer performance. In order to understand the thermal results, air flow through the fins will be discussed. 3.1 NUMERICAL METHODOLOGIES The orientation dependency of conventional straight fin heat sink is studied numerically using ANSYS Fluent. Under free convection heat transfer, the thermal performance and fluid dynamics of buoyancy flow are discussed for different mounting orientations. For this numerical analysis, a thermal model will be built and this similar type of thermal model will also be used 19  for the numerical analysis of the other two types of heat sinks, which are discussed in chapter 5 and 6. 3.1.1 Thermal Model For the numerical simulation, the dimensions of heat sink were selected to match with the most common sizes used in different applications and also with some previous literatures. The baseline heat sink configuration has rectangular straight fins as shown in Figure 3.1a. This heat sink has a base plate dimension of 130 mm × 130 mm with a plate thickness of 2.5mm. The fins attached with the base plate are of rectangular shape and positioned parallel to the base plate side. A 4 mm fin thickness with a fin height of 60 mm is used in this case. This leaves a spacing of 5mm between two consecutive fins. From this design the total area attained for convection heat transfer is 0.259 m2, while the backside of the heat sink base is insulated. Die-cast Aluminum 413 is considered as the heat sink material, which has thermal conductivity of 121 W⁄(m∙k). For the radiation heat transfer the surface emissivity is considered as 0.3.  20   Figure 3.1: Thermal model of heat sink: (a) straight-fin heat sink (dimensions are in mm); (b) heat sink in the domain where gravity can be applied in g-1, g-2 or g-3 orientation; (c) finite element meshing of domain; (d) meshing of heat sink inside the domain.  Numerical model of the heat sink under steady state of convection and radiation heat transfer is built and simulated using the commercial software ANSYS-Fluent. The domain is shown in Figure 3.1b. As shown in Figure 3.1b, the gravity vector is varied for three directions, and the flow-pressure boundary conditions for the six sides of the domain will change accordingly. Detailed flow-pressure conditions are provided in Table 3.1. For example, for g-1 direction, the side 1a is pressure outlet, the bottom side 1b is insulated and the other remaining sides 2a, 2b, 3a, 3b are pressure inlet. For this four pressure inlet sides, the gauge total pressure is considered zero 21  and this boundary condition is useful when inlet pressure is known but the fluid velocity is unknown. For pressure outlet side the gauge static pressure is considered zero. For all the gravitational directions, the side #1b is kept thermally insulated as there is no heat transfer and no air flow across that side. Table 3.1: Flow-pressure boundaries of the numerical domain for varied gravity vectors. Gravitational direction Side 1a Side 1b Side 2a Side 2b Side 3a Side 3b g-1 P - Outlet* Insulated P - Inlet P - Inlet P - Inlet P - Inlet g-2 P - Inlet** Insulated P- Outlet P- Inlet P - Inlet P - Inlet g-3 P - Inlet Insulated P - Inlet P - Inlet P - Outlet P - Inlet *: pressure outlet; **: pressure inlet.  A constant heat load of 90 watts is applied uniformly on the backside of the base plate. The heat transfer process can be described as follows. The heat from the bottom of the base plate is conducted through the base material and fins and then transfer to the ambient air and surroundings by convection and radiation. For the two heat transfer modes, both air and surrounding temperatures are considered as 40˚C, as ambient temperature higher than room temperature is commonly required for the thermal design of many power electronic devices. Detailed thermal boundary conditions are provided in Table 3.2. For simulating the free convection, constant air density at 40˚C is used except for the buoyancy term in the momentum equation, for which the Boussinesq approximation is used. For radiation heat transfer surface-to-surface (S2S) model is used to group faces together to form surface clusters. This is to reduce the computational effort by reducing the number of radiating surfaces. Table 3.2: Thermal boundaries of the numerical domain for varied gravity vectors  Gravitational direction Side 1a Side 1b Side 2a Side 2b Side 3a Side 3b Heat sink back g-1, g-2, g-3 40°C Insulated 40°C 40°C 40°C 40°C 90W  22  For the ANSYS simulation of free convection flow, continuity equation, momentum equation and energy equations are important. These come from the conservation laws of mass, momentum and energy. Although the free convection is due to density change, the air is treated here as incompressible fluid. The change of density is important only for pressure and body force terms.  The continuity equation of fluid flow is  0yx zVV Vx y z      (3.1) where xV , yV and zV  are velocity component in the direction x, y and z respectively.  Applying Boussinesq approximation, the momentum equation for free convection can be expressed as    21u u g up       (3.2) where 𝐮 = [𝑉𝑥, 𝑉𝑦, 𝑉𝑧] and g are velocity vector and gravity vector. And the density has the following relation with temperature   1 T T         (3.3) where   is the thermal expansion coefficient, and   is density of air at ambient temperature. If the gravity is in −𝑥 direction, i.e. the body force vector 𝐠 = [−𝑔, 0, 0], the momentum equations are 23   2 2 22 2 21x x x x x xx y zV V V V V VpV V V gx y z x x y z                      2 2 22 2 21y y y y y yx y zV V V V V VpV V Vx y z y x y z                     2 2 22 2 21z z z z z zx y zV V V V V VpV V Vx y z z x y z                          (3.4) The approximation can be used until the changes in density are small. This approximation is also helpful for faster convergence of the simulation. For incompressible fluid, the energy equation can be expressed in the form of a thermal equation for the static temperature:     T T   u  (3.5) For heat transfer inside the heat sink, the governing equation is    0T    (3.6) The surface-to-surface (S2S) radiation model is used in the present study, and all surfaces are gray-diffuse surfaces. For S2S method, only “surface-to-surface” radiation is considered for analysis, and any other absorption, emission, or reflection of radiation are ignored.  Figure 3.1(c) and 3.1(d) shows that, a non-uniform mesh grid size is used. For the selection of meshing size, proximity and curvature size function is considered. For better meshing at the fluid-metal interface, inflation layer is considered. Mesh independency study is performed for 24  this study. Figure 3.2 shows two different meshing of numerical model, which are created using ANSYS Fluent. The first figure is for meshing with minimum cell size 1 mm while the second figure shows mesh generation using 0.5 mm minimum cell size. After simulating the models of both meshing sizes the maximum temperatures are observed. It is found that, selection of meshing size less than 1 mm has very less effect on temperature variation. For both the meshing sizes the maximum temperature is about 109.3°C. Finer meshing only increases the computational cost without further changes in maximum temperatures. As the solutions show mesh independency, so 1 mm meshing size is selected for all the ANSYS simulations in this study.   Figure 3.2: Mesh independency of numerical model to thermal performance: (a) meshing with 1 mm minimum cell size; (b) meshing with 0.5 mm minimum cell size  3.1.1.1 Model Accuracy The thermal model considered in this study is used to simulate free convection heat transfer from three different heat sinks: rectangular straight fin, angled-fin and pin fin heat sink. ANSYS 25  Fluent software is used to simulate and analyze the results. As no direct correlation exists for specific heat sink fin configurations, the verification of the obtained simulation results became difficult. That’s why, a heated flat plate was considered for which free convection correlations are known. Free convection from this flat plate is simulated using the software. Then the simulation results are compared with the theoretical findings of correlations.  Square aluminum plate of 0.5mm thick and 50mm long sides is considered. For the ANSYS simulation, a considerably large fluid domain is taken around the plate, considering the domain vertical sides as pressure inlet and domain top as pressure outlet (Figure 3.3). The back of the plate is considered insulated as no heat transfer or fluid flow take place across this side. A constant plate temperature of 100°C is considered which is exposed to an ambient of 20°C. The material properties are considered same as above. The similar convection approximation of Boussinesq and surface-to-surface model for radiation are used. For the simulation non-uniform mesh grid and inflation layers are also used here. The model is simulated for horizontal orientation for constant plate temperature considering the plate surface as full black body (ε=1). 26   Figure 3.3: Flat plate with domain where gravity ‘g’ is perpendicular to plate surface  After simulating the perfectly meshed model using ANSYS fluent the total heat transfer rate is found to be 4.04 Watts. Deducting the radiation heat transfer rate of 1.695 W, the final rate of convection heat transfer is calculated as 2.35 W.  For the free convection flow from the hot horizontal plate, the flow condition can be determined by the Rayleigh number. Here, all the fluid properties are calculated at film temperature, Tf =(Ts+T∞)/2.   achsaLLTTgRa3 (3.7) 27  where characteristic length, PAL sch . The calculated LRa  number for that size of plate is found to be 0.874×104. Hence, the correlation for buoyancy driven flow from the upper hot horizontal surface is  4154.0 LL RauN       (3.8) From that correlation, the calculated Nusselt number is, LuN = 5.22. Then the average heat transfer coefficient and heat transfer rate can be calculated using  ,chLLkuNh  (3.9)    TThAq ss  (3.10) The convection heat transfer coefficient is calculated to be 12 W/(m2.k) and the heat transfer rate is calculated to be 2.40 W. The theoretical results show 2.08% difference from the ANSYS simulated result, which can be considered good agreement.   3.2 THERMAL PERFORMANCE In real life application, the heat sink base is attached with the electronic device to be cooled, so temperature profile of base is important. The thermal performance of heat sink can be evaluated observing the temperature distribution on base plate bottom. After the numerical simulation of straight fin heat sink, the thermal distribution is observed. At first, the simulation is done for a position where the baseline heat sink is placed such that its base plate is parallel with 28  the ground. This horizontal mounting orientation corresponds to the g-1 gravity vector is shown in Figure 3.1(b). The heat load is applied on the backside of the base plate and transfer through the heat sink by conduction and then by free convection and radiation to the ambient and surroundings. Figure 3.4 shows the temperature contour on the bottom surface of the heat sink.  Figure 3.4: Temperature contour on the bottom surface of the straight-fin heat sink placed horizontally (g-1 orientation).  The sides A and B of the contour match the sides of heat sink. Symmetric temperature distribution with hot spot located at the center region can be seen for this mounting orientation. As the periphery is in constant contact with the fresh cold air, temperature is low here. The temperature ranges from 105˚C to 109˚C, and the average temperature is 108°C.  29  Then, the orientation of the heat sink is changed to vertical where g acts parallel to the fin length (g-2 shown in Figure 3.1b). Temperature contour is shown in Figure 3.5. The temperature distribution is symmetric across the fins. Along the fins, the temperature is low at the lower edge and high at the upper edge. The maximum temperature is 110˚C, slightly higher than the horizontal orientation. The minimum temperature is 104˚C, slightly lower than the horizontal orientation. The average temperature is 108.5˚C. Comparison between the two orientations g-1 and g-2 shows similar cooling performance for both orientations. The only major difference is the location of hot spot for the two orientations. For g-1, the hot spot is located at the center, and for g-2 the hot spot moves to the upper edge.  Figure 3.5: Temperature contour on the bottom surface of the straight-fin heat sink placed vertically with fins parallel to gravity vector (g-2 orientation).  30  If the heat sink in Figure 3.5 is rotated either clockwise or counter-clockwise by 90˚, the gravity force acts perpendicular to the fin length (g-3 in Figure 3.1b). The temperature contour is plotted in Figure 3.6. The distribution is symmetric in the direction perpendicular to gravity. Along the gravity direction, the distribution is almost symmetric with hotspot located in the center, except that the upper region is around one or two degrees higher than the lower region. The temperature ranges from 177˚C to 186˚C, and the average is 184˚C.  Compared with the two previous orientations, the current orientation causes the maximum temperature to increase by more than 70˚C. This higher increase in temperature indicates that for this g-3 orientation thermal performance reduces significantly which ultimately may cause device failure in many situations. This thermal behavior clearly shows that the performance of straight fin heat sink greatly depends on mounting orientation. In addition to the temperature difference, the two vertical orientations, g-2 and g-3, are different in terms of the location of hot spot. 31   Figure 3.6: Temperature contour on the bottom surface of the straight-fin heat sink placed vertically with fins orthogonal to gravity vector (g-3 orientation).  3.3 FREE CONVECTION FLOWS The fluid dynamics of buoyancy flow is discussed to explain the orientation effects on temperature variations. To observe the flow dynamics, an observation plane at 5 mm above the fin base and parallel to base plate is used as shown in Figure 3.7. On this observation plane, air velocities across the entire simulation domain are obtained and presented. 32   Figure 3.7: Observation plane for observing the fluid dynamics of buoyancy flow.  For the vertical orientation g-2 shown in Figure 3.5, air flow velocity vectors on the observation plane across the simulation domain is shown in Figure 3.8. The locations of free space and the heat sink can be easily identified based on the velocity vectors.  Here the fins lengthwise are parallel to the gravity force, air flows upward along the channels between fins. The fresh cold air enters from the bottom, and gets heated up as it travels through the fins with increasing velocity. The maximum velocity is 0.38m/s, which occurs in the upper region above the heat sink. Observation plane located 5mmabove the fin baseHeat sink33   Figure 3.8: Velocity vector on the observation plane for the g-2 orientation of the straight-fin heat sink shown in Figure 3.5.  The buoyancy flow for another vertical orientation g-3 is shown in Figure 3.9, which corresponds to the thermal results shown in Figure 3.6. For this orientation, the fins are horizontal, and buoyancy force acts normal to the fin surface. Apparently, the upward fluid motion is interrupted by the horizontal fins, and as a result air can move only horizontally between fins. Comparison of Figure 3.8 and 3.9 shows that, although air velocities outside the heat sink are comparable, the air velocities confined between fins are much lower for the g-3 orientation than for the g-2 direction. So buoyancy flow is significantly reduced, resulting in weak convection heat transfer and high surface temperature. 34   Figure 3.9: Velocity vector on the observation plane for the g-3 orientation of the straight-fin heat sink shown in Figure 3.6.  The numerical analysis of straight fin heat sink shows that, although horizontal and one vertical (g-2) orientations respond well to thermal performance, it shows orientation dependency for another vertical orientation (g-3). The buoyancy flow also clarifies the reason of this low performance for that g-3 orientation. This straight fin heat sink needs to be analysed experimentally to understand the orientation dependencies more extensively. The next chapter represents an experimental analysis of straight fin with more mounting orientations. 35  CHAPTER 4: EXPERIMENT ON STRAIGHT FIN HEAT SINK As shown in the ‘Model Accuracy’ subsection (3.1.1.1), the numerical simulation was in good agreement with the existing correlations of convection heat transfer. But for further verification and to gain practical knowledge, some experimental works on straight fin heat sink are also done. Another purpose of this experimental work is to observe and analyze the orientation dependency with more mounting angles. Here, 28 different angles of orientation are studied experimentally and their thermal performances are observed under free convection heat transfer. 4.1 HEAT SINK SELECTION AND MAKING For this experimental work, the material and dimensions used are different from that used in the forgoing numerical simulation. This is because of the material unavailability and limitation of proper tools needed. For example, to make a heat sink in laboratory with larger fin height not only requires longer and stronger drill bits or cutting tools but also involves higher manufacturing precision. So, for easy manufacturing process smaller size heat sink is made with the available lab equipment. Numerical simulations are also run to validate the thermal performance of the new experimental design. The heat sink used in this experiment is made of aluminum 6061-T651 which is a good general type of material of most applications. This material has a density of 2700 kg/m3 and thermal conductivity of 167 W/(m.k). A rectangular block of this material is cut using jet water machine at a dimension of 100×100×29 mm (Figure 4.1a). Using CNC machine, rectangular cross section straight fins are formed on the material block with a manufacturing precision of 0.1 36  mm (Figure 4.1b). The detailed dimensions and heat sink geometry is shown at Figure 4.2c. The heat sink base thickness, fin thickness and fin spacing are considered to be 4 mm. A fin height of 25 mm is considered for this. The final appearance of the straight fin heat sink is shown in Figure 4.2a. To get the actual reading of temperature at different locations of the heat sink back and also to ensure the steady state condition seven T-type thermocouples are placed. Seven grooves of 0.6 mm depth and 1mm wide are engraved at the back of the heat sink (Figure 4.2b). These grooves are made to fit the thermocouple wires to ensure no gap exist between the heater and heat sink back. To ensure uniform heat flux at the heat sink back these grooves are important.   Figure 4.1: Making of heat sink: (a) cutting of heat sink block using Water Jet; (b) forming of rectangular shape fins on the block using CNC machine.  4.2 EXPERIMENTAL SETUP After cleaning and smoothening the roughness of the heat sink surface, the thermocouples are attached using high thermal conductivity paste into the grooves. For the heat load Kepton heater 37  of same size as the heat sink base is attached at the back of the heat sink. Insulation composed of multiple layers of low thermal conductive material like medium dense fiber (MDF) wood, flexible fiberglass insulation and Acrylic plastic is placed beneath the heater to reduce heat loss from the back (Figure 4.3a). For further reduction of heat loss plastic screws are used to hold the insulation layers together. As a bonding agent between heater back and insulation, low thermal conductive epoxy is used.    Figure 4.2: Thermal model of heat sink; (a) straight fin heat sink (dimensions are in mm); (b) orientation of heat sink made by rotating about the three sides ‘A’, ’B’ and ’C’; (c) schematic of the heat sink (all dimensions are in mm).  38   Figure 4.3: Experimental setup, (a) Insulation layers of heat sink; (b) Heat sink rotation mechanism  During experimental test, the thermal readings are taken at various orientations of the heat sink. These orientations are made rotating the heat sink with respect to three different sides of the heat sink as shown in Figure 4.2b. In the figure, ‘A’ and ‘B’ are two sides of the heat sink where fin length is parallel to side ‘A’ and perpendicular to side ‘B’. Line ‘C’ is the diagonal of the heat sink. Rotational angles are varied from horizontal to vertical orientation that is from 0° to 90° with an angle step of 10°. That means, for the rotation about each side there are 10 different positions of heat sink mounting (Table 4.1). From these orientation settings, the horizontal orientation where α=β=θ=0° is common for the rotation about any sides.   39  Table 4.1: Experimental sets for different mounting orientations Horizontal α,  β and θ 0° Rotation about side A form angle α when side A kept horizontal 10° 20° 30° 40° 50° 60° 70° 80° 90° Rotation about side B form angle β when side B kept horizontal 10° 20° 30° 40° 50° 60° 70° 80° 90° Rotation about side C form angle θ when side C kept horizontal 10° 20° 30° 40° 50° 60° 70° 80° 90°  Figure 4.4a shows orientation about the side ‘A’. Here the rotational axis is parallel to fin length and gravitational force ‘g’ acts always perpendicular to ground. During rotation about the side ‘A’, the line ‘A’ is kept always parallel to ground. It produces the rotational angle ‘α’, which is the angle between side ‘B’ and horizontal.  Angle ‘α’ is gradually increased from 0° to 90° at an angle interval of 10°. The rotation about the side ‘B’ is shown in Figure 4.4b, where the line ‘B’ is kept parallel to ground. Here ‘β’ is the rotational angle between side ‘A’ and horizontal. This angle is also increased gradually at 10° interval from 0° to 90°. The diagonal side ‘C’ is kept parallel to ground and the heat sink is rotated about this diagonal (Figure 4.4c). In this case, ‘θ’ is the rotational angle, which is the angle formed between the other diagonal ‘d’ and projection of this diagonal on ground. The changes of orientation angles about this diagonal are same as the other two rotations. In this experiment, all these rotations are made using a tripod. A holder attached with the heat sink is used to clamp with the tripod and rotate the heat sink about the three sides as shown in Figure 4.3b. The tripod is very helpful to rotate the heat sink in any desired position. Its good design has very little effect on the free convection buoyancy flow. 40   Figure 4.4: Orientation of the heat sink; (a) rotation about side ‘A’ (b) rotation about side ‘B’; (c) rotation about the diagonal ‘C’  The heat sink is tested at different orientations for the same heat load of 29.7 watts that is supplied by a DC power supply (Figure 4.5). To get the thermal reading from the attached thermocouples at desired sampling rate and to convert the sensors signals, signal conditioner and multifunction data acquisition modular are used. Infrared Camera from FLIR (Model SC660) is used to get the extensive thermal readings and images from the experiment. The thermocouples and IR Camera readings are processed and presented by a computer. The air and surrounding temperatures are kept at 20° C which is also measured by a T-type thermocouple. A90°αgYBZXB90°βXZAgYCdProjection of d on groundθg(a) (b)(c)41   Figure 4.5: Experimental setup for straight fin heat sink thermal reading  4.3 UNCERTAINTY ANALYSIS The uncertainty analysis for the experimental test is done. The total uncertainty of a system is the sum of uncertainties associated with all the measurements. For example, uncertainty in y is the sum of all the uncertainties of its components.     1 2,  ,  ..... ny f x x x   0.522 21 21 2...... nny y yy x x xx x x                             (4.1)  (4.2) In the present study, the sources of uncertainty include measuring the temperatures by thermocouples, IR camera measurement and DC power supply and the details are shown in Table 4.2.  ComputerSignal conditionerMultifunction data acquisitionHeat SinkInfrared CameraDC Power SupplyThermocouples42  Table 4.2: Uncertainties in experimental test Sources of Uncertainty Uncertainty/Error Current supplied to DC power supply 1% Voltage supplied to DC power supply 1% IR Camera reading, ∆𝑻𝒂𝒗𝒈 ±0.5°C Thermocouple measurement, ∆𝑻∞ ±1°C  For heater power, uncertainty lies within measuring the voltage and current. Hence, the uncertainty can be estimated as  0.52 20.52 2q VIq qq V IV Iq V Iq V I                                     (4.3)   (4.4) For 1% uncertainties in calculating both voltage and current, the uncertainty of heater power is %4.1 qqqq . During test the average temperature, avgT  is measured by IR camera and ambient temperature, T  is measured by T-type thermocouple. Error associated with the IR camera measurement is CTavg  5.0 . For thermocouple measurement in our test .1 CT    The average heat transfer coefficient for the convection heat transfer from the heat sink is   TTqhavg (4.5) The uncertainty associated with the heat transfer coefficient measurement can be calculated using [51] 43   0.52 220.52 22avgavgavgavg avgh h hh q T Tq T TT Th qh q T T T T                                                           (4.6) Considering the average temperature of all the tests 90°C and ambient temperature 20°C, the overall uncertainty in the free convection cooling for the experimental work is found to be 2.12%.  4.4 EMISSIVITY CALIBRATION The thermal energy also dissipates in the form of radiation to the surrounding. The infrared camera uses this infrared radiation to map the thermal image. To get the exact thermal reading from infrared camera it is important to know the emissivity of the surface as the radiation energy dissipation greatly depends on surface emissivity.  The emissivity of the heat sink aluminum surface is low and unknown. To enhance the emissivity of the surface, it is painted black with barbecue paint whose emissivity is close to black body. Now, to get the accurate thermal reading from the infrared camera it is essential to know the surface emissivity of the black painted heat sink surface.  To evaluate the emissivity of a black painted surface, a thin aluminum plate is considered. A T-type thermocouple is attached at the center of the plate using epoxy. For the nice fit of the thermocouple wire a channel is also cut on the surface. Then the surface is painted black with the 44  barbecue paint. To heat up the plate at different temperatures a heater of adjustable power is used. The detailed experimental setup is shown at Figure 4.6.  Figure 4.6: Emissivity calibration by black painted flat plate  At steady state, the temperature reading of the heated plate is taken from the thermocouple reading. Knowing the thermal reading, the emissivity of the painted surface can easily be determined with the help of IR Camera. Emissivity of the surface is calibrated and calculated at different plate temperatures changing the heater power. The temperature range is selected within the operation range of this experiment.  The emissivity of the surface at this temperature range is plotted with the plate surface temperature (Figure 4.7). From the graph, the average emissivity of the black painted surface is found to be 0.96. Hence, the emissivity of the black painted heat sink surface is known and can be used to evaluate the thermal readings by infrared camera. Heater Black painted calibration plateInfrared cameraMultifunction data acquisitionSignal conditioner45   Figure 4.7: Average Emissivity of black painted calibration plate  4.5 THERMAL ANALYSIS To understand the orientation dependency of the heat sink, thermal analysis is needed for different mounting angles. The thermal distribution on heat sink surface and effect of orientation angles are observed. Heat loss during the test is calculated and heat sink thermal performances are discussed. An uncertainty analysis is done for the overall enhancement of free convection.  4.5.1 Thermal Readings For each mounting orientation, the thermal readings are taken when the system reach at steady state condition. It took ~3 hours to reach steady state for each test. If the temperature change over the previous 30 minutes is found to be less than 0.5°C, the steady state condition is assumed, which is confirmed by observing the temperature readings of the thermocouples. 50 60 70 80 90 100 1100.9400.9450.9500.9550.9600.9650.9700.975 Emissivity Avg. emissivityEmissivityCalibration Plate Temp (°C)46  The thermocouples attached with the heat sink back measure the temperatures at different points of the back surface. The average of these readings is the average temperature of the base plate back. The infrared camera measures the average temperature of the opposite surface of the plate. For each orientation angle there are two average temperatures from the two opposite surfaces: one is measured by thermocouples and the other is by IR camera. For the seven orientation angles formed by rotation about side B, the average temperatures are plotted as shown in the Figure 4.8. It shows that, for all the orientations the thermocouple readings are little bit higher than the IR camera readings. Because thermocouples measure temperature upstream in the thermal path, where they are closer to the heater. Whereas, Infrared camera measures the temperature of the outside surface of the heat sink which is under convection heat transfer. So, this little variation in temperatures is expected and practical.   Figure 4.8: Infrared camera readings accuracy compared to thermocouples.  47  4.5.2 Heat Loss The experiment is performed assuming that the back of the heat sink is insulated by layers of insulation materials. For every insulation materials there is some heat loss. In this experiment four layers of different materials are stacked together to reduce the heat loss. This includes 1 mm thick low thermal conductive epoxy, 3 mm thick medium dense fiber (MDF) wood, 25.4 mm thick flexible fiberglass insulation and 2 mm thick acrylic plastic sheet. Their thermal conductivities are also shown in Table 4.3.  Table 4.3: Insulation materials and their thermal properties Insulation Material Thickness, t (mm) Thermal Conductivity, k (W/(m.k)) Omegabond Fast Set Epoxy 1 0.09 Medium Dense Fiberboard (MDF) 3 0.10 Flexible Fiberglass Insulation 25.4 0.035 Acrylic Plastic Sheet 2 0.19 The thermal resistance at the back of the heat sink would be the combination of resistances for the insulation materials and surrounding air as shown in Figure 4.9.  hktktktktRppffwweeins1 (4.7) The back of the insulation material is flat surface. For different mounting orientation, the average heat transfer coefficient for this size of surface is assumed to be )(10 2kmWh  . This assumption is made on the basis of the previous flat plate simulation results and theoretical calculation using horizontal flat plate correlation. The calculated unit thermal resistance is found to be 0.88 Wkm )( 2 .  48   Figure 4.9: Thermal resistance of insulation materials  The total heat sink area (base area where there is no fins + fin surfaces) from where the convection heat transfer takes place is 0.0792 m2. This area is 7.92 times larger than the insulated area (heat sink back surface). Hence, the thermal resistance for the free convection from the heat sink surface can be calculated as  hRcon  92.71  (4.8) The calculated thermal resistance is found to be 0.0126 Wkm )( 2 , which is 69.8 times smaller than that of the thermal resistance of back insulation. Sinceinscon RR  , heat loss through the insulation layer is much smaller than the heat transfer from the heat sink by free convection. Therefore, the heat loss is negligible. 49  4.5.3 Thermal Distribution Infrared camera is used for the thermal analysis of the heat sink. Figure 4.10a shows a thermal image of the heat sink for an orientation of α=60° (Figure 4.10b). The base temperatures of the heat sink are noted by focusing the camera at each fin channels. Thermal distributions on the base along the channels are shown in Figure 4.10c. The distribution is also for the same orientation like Figure 4.10b. Figure 4.10c shows that the peripheral side of the heat sink base has lower temperature as it experiences contact with fresh cold fluid constantly. The highest temperature is found at around middle section. Abrupt changes in temperatures within very small distance along a channel are also evident, which is the effect of surface emissivity variation due to insufficient paint.  50   Figure 4.10: Thermal analysis of heat sink: (a) thermal image from IR camera for α=60° orientation; (b) heat sink orientation for α=60°(c) temperature distribution along the channel length for the orientation shown in figure (b)  The temperature distribution along the fin spacing varies with the mounting orientations. To observe the effect of the orientation angle on channel average temperature, the average temperatures of each channel for various orientations are plotted (Figure 4.11). For the simplicity of presentation, thermal results of only 10 different orientations are shown in the figure. The figure shows that horizontal orientation has the lowest and 90° rotation about side B has the 51  highest average channels temperatures. For the rotation about B, the lower the angle (β), the better the thermal performance it shows. Because higher angle interrupt the fluid flow as the fin lengths become perpendicular to the gravity vector. In case of rotation about side A, the higher the angle (α), the better the thermal performance is. The best heat transfer occurs for vertical position (α=90°) as hot fluid can easily pass through the fin spacing. For the diagonal rotation (change of θ) of the heat sink, the lower channels temperatures are observed for lower value of θ. With the increase of θ, the temperatures also increase and reach maximum at θ=60°, then decrease. This orientation analysis with temperature distribution is very helpful to gain the knowledge of heat sink mounting for desired thermal performance.  Figure 4.11: Channel average temperature plot at different orientation angle  0 2 4 6 8 10 12858687888990919293949596979899100101102103Channel avg. temperature (°C)Channel (fin spacing)52  4.5.4 Orientation Dependency Buoyancy flow from a heated surface is always opposite to the gravity direction. With the change of orientation angle of a surface, the g component along the surface is also changed which consequently change the buoyancy flow. As the convection heat transfer greatly depends on buoyancy flow, so change in flow conditions have great effect on thermal performance. For the easy understanding of the g component, consider Figure 4.12, which is also similar for the other orientations about other sides. The rotations of the heat sink about three different sides (A, B and C) form 90-α, 90-β and 90-θ angles with the vertical. As the gravity acceleration acts at Z direction, so the Y′ component of this acceleration is reduced to gsinα. For the rotation about B and C sides these are gsinβ and gsinθ respectively. To observe the trends of the thermal performance with the change of the gravity component, the average base plate temperatures for different orientations are plotted as shown in Figure 4.13. Each line of the plot represents orientation effect for the rotations about each side of the heat sink (A, B and C).  Figure 4.12: Gravity force component parallel to the heat sink base  53  For the heat sink rotation about side A, where fin lengths remain perpendicular to the g vector (Figure 4.12), shows increasing trend in base plate average temperature with the increase of angle α (or gsinα) as shown in Figure 4.13. Sudden increase in temperature is evident for higher rotational angles of 70° to 90°. That means for angles larger than 70° (α > 70°) have more detrimental effect on thermal performance that ultimately may cause device failure in many situations. With the increase of gravity component parallel to the surface (increase of gsinβ or increase of angle β), lower value of base plate temperature is observed for the rotation about side B. At higher orientation angle it shows the best thermal performance, though a very small increase in temperature is seen for complete vertical orientation. Rotation about diagonal side C shows that, for θ=10° and 20° the base plate temperature is lower than that of horizontal orientation. After that it increases with the increase of orientation angles and then decreases at later part for the higher angles of orientations. The highest temperature of 93°C is found for the orientation angle θ=60°.  Therefore, it can be said that, for straight fin the best orientation independent rotation for free convection is the rotation about side B (change of angle β). And the highest orientation dependency to thermal performance is seen for the rotation about side A (change of α). As straight fin heat sink’s thermal performance highly depends on the mounting orientation, so installation of this heat sink is inefficient for the portable and hand use devices. 54   Figure 4.13: Average base temperature for different mounting orientation  4.5.5 Heat Sink Performance Generally the fin surface temperature is lower than the base plate temperature. So it is expected that, the heat sink average temperature (considering the all heat transfer area) would also be lower than the base plate average temperature. But in this experiment due to measuring limitations only base plate average temperature is calculated. As, this base average temperature is higher than the actual heat sink average temperature, so a variation in calculating the heat sink performance can be observed.  Here, the base plate average temperature avgT  is calculated using infrared camera by observing the fin channels base. Using this avgT  which is higher than the actual heat sink average temperature, the calculated effective heat transfer coefficient would be lower than the actual. 0.0 0.2 0.4 0.6 0.8 1.08090100110Avg. base plate temperature (°C)sin, sin, sin Rotation about 'A' Rotation about 'B' Rotation about 'C'55  This effective heat transfer coefficient includes convection and radiation. For horizontal orientation the effective heat transfer coefficient can be calculated using    TTqhavge (4.9) here, q  is heat flux, which is given by  ftbt AAqq..  (4.10) For the specimen considered in this experiment, the total heat transfer area is 0.0792 m2 which is the combination of total base area where there is no fin )( .btA  and total fin surface area )( . ftA . For the calculated heat flux of 375 W/m2, the effective heat transfer coefficient, eh  is found to be 5.67 W/(m2.k). Here, for the horizontal orientation avgT  calculated by the IR Camera is 86.14°C. The radiation component of the effective heat transfer coefficient is  )()( 44surravgsurravgr TTTTh   (4.11) where   is the Stefan-Boltzmann constant,  is surface emissivity and   is view factor from the heat sink to ambient. For all the tests, surrounding temperature surrT = 20°C is considered. Considering the dimensions of Figure 4.2c, the view factor can be calculated using 56      tLstLsLs fbfffb  21221   (4.12) In the above equation there are two other view factors: view factor from base to fin (fb ) and view factor from fin to fin (ff  ). These can be calculated as    211 5.02sLsLfb   sLsLff11 5.02  (4.13)  (4.14) For the heat sink tested in this experiment, the overall view factor is found to be  = 0.14. Now, from equation (4.11) the calculated radiative heat transfer coefficient is rh = 1.07 W/(m2k). From this calculation it is realized that radiation component can not be neglected and has great contribution in overall heat transfer performance. For the adiabatic tip condition, the fin efficiency for rectangular cross section fin can be calculated as  ccf mLmLtanh  (4.15) where 2tLLc  is the corrected fin height, t is fin thickness and 21)2( kthm . From the above equation the calculated fin efficiency is found to be 0.996. Now, the corrected heat flux 57  for this fin efficiency can be calculated using the below equation (4.16) which is 376.38 W/m2. Using equation (4.17) the corrected effective heat transfer coefficient is calculated.  fftbtc AAqq ...   (4.16)   TTqhavgcce, (4.17) The corrected effective heat transfer coefficient is found to be ceh , = 5.69 W/(m2.k). It shows that there is 0.35% deviation from the effective heat transfer coefficient, eh . Hence, no iteration is needed. This suggests that the fin surface temperature is very close to the base plate temperature, which is also evident from the higher value of fin efficiency  996.0f . The assumed avgT  of base plate is very close to the actual heat sink average temperature and has negligible effect on heat transfer calculation. 4.6 NUMERICAL STUDY The experimental specimen of straight fin heat sink is also simulated numerically using ANSYS Fluent. The numerical methodologies are considered same as in chapter-3. To compare the results with experimental values, the heat load and ambient conditions are kept similar to the experimental tests. For the rotation about three different sides, experimental results are compared with the ANSYS Fluent simulation results for the same orientation angles as shown in Figure 4.14. In the figure, the solid lines are for simulation results, and the dash lines represent experimental results. For the lower orientation angles both the results (simulation and 58  experimental) match well for the rotation about any side. A very small temperature variation of 2 to 4°C is observed for larger angles of orientations. The probable cause of these deviations is the effect of variation in the room air circulation which changes with the outside weather conditions.  Figure 4.14: Comparison of experimental results with the numerical simulations.  To understand the relation between flow dynamics and heat transfer, velocity vectors of fluid flow from the experimental heat sink specimen are observed numerically. Figure 4.15 shows the flow dynamics for two different vertical orientations of the heat sink. Velocity vectors are presented at the observation plane (Figure 3.7), which is at 5mm above the fin base. For the 90° rotation of heat sink about diagonal side C (θ=90°), flow dynamics are shown at Figure 4.15a. The figure shows that, the fluid path is not straight. Initially, the vertically rising cold fluid enters into the 45° angled fin channels from bottom and travels along it, then discharges vertically with increased temperature. Figure 4.15b shows the free convection flow for another vertical 0 20 40 60 80859095100105110115Avg. base plate temperature (°C)degree Rotation about A Rotation about B Rotation about Csolid line: simulationdash line: experimental59  orientation by rotating the heat sink about side A (α=90°). Here, the buoyancy flow is blocked by the horizontally positioned fin surface. This flow dynamics and pattern are similar to the Figure 3.9.   Figure 4.15: Velocity vector at observation plane (Figure 3.7) for the experimental heat sink specimen: (a) for θ=90°, rotation about diagonal side C; (b) for α=90°, rotation about side A   From this chapter, the thermal behavior of the straight fin heat sink for different orientations are observed and realized experimentally. The results show the orientation dependency to cooling performance for the rotation about side A, which is similar to the simulation results of g-3 orientation. The experimental works are performed with lower heat loss and higher fin efficiency (0.996). Lower percentage of overall uncertainty is observed in the experimental measurements. The comparisons with simulation results also show similar thermal performances and flow dynamics.  60  CHAPTER 5: ANGLED-FIN HEAT SINK The results of straight-fin heat sink discussed earlier, show significant dependency of thermal performance on the mounting orientation. The heat sink might provide sufficient cooling for g-1 and g-2 orientations, but would cause device failure if it is mounted in g-3 orientation. To overcome this orientation dependency of free convection heat transfer, two other heat sink designs are considered for analysis. One is angled-fin heat sink, and the other one is pin-fin heat sink. Angled-fin heat sink is a new design introduced in this study which was not found in the previous studies. In this chapter, angled-fin heat sinks and their thermal performances are observed under various mounting conditions. For angled-fin heat sink the rectangular plate fins are placed at an angle of 45° with the base plate side (Figure 5.1a). The base plate dimensions, fin thickness, fin spacing and fin height are considered same as straight fin heat sink. The material properties, heat load, ambient and boundary conditions are also kept same. Orientation dependencies are discussed analysing both the thermal performance and fluid dynamics numerically. 5.1 NUMERICAL MODEL For the numerical analysis of angled-fin heat sink, ANSYS Fluent is used. As all the parameters are same except 45° angled fin position with base side, the numerical model is kept same as the numerical model of straight fin heat sink (Figure 3.1). The domain remains same and the gravity vectors are also varied in the same three directions. The thermal and flow pressure boundary conditions for the six sides of the domain are considered same as in the Figure 3.1b which are noted in detail in Table 3.1 and 3.2. For free convection boussinesq and for radiation 61  surface-to-surface models are also used here. Simulations are done for both horizontal and vertical orientations, and the thermal performance and flow dynamics are observed. 5.2 THERMAL PREFORMANCE After simulating the model of angled-fin heat sink for both horizontal and vertical orientations, the temperature distributions on the base plate are observed. Figure 5.1b shows the temperature contour of base plate bottom for the horizontal orientation. The maximum temperature is found at the center region which is 109˚C. The temperatures at the two corners where the fin length is minimum show lowest as the cold air can easily enter into the fin spacing and comes out travelling the shortest path. Comparing the Figure 3.4 and Figure 5.1b, with g-1 orientation, both the straight-fin heat sink and the angled-fin heat sink provide almost the same thermal performance, except the temperature distribution pattern. The heat transfer area of angled-fin heat sink (0.257m2) is slightly less than straight fin (0.259m2). 62   Figure 5.1: (a) Angled-heat sink placed horizontally (g-1 orientation); (b) Temperature contour on the bottom surface of the angled-fin heat sink in g-1 orientation.  The vertical orientation of the angled-fin heat sink is shown in Figure 5.2. In this case, there is no difference between the g-2 and g-3 orientations. For any vertical orientation, g-2 or g-3, the fin lengthwise is always at 45˚ angle with the ground, which avoids complete interruption of buoyancy flow. According to Figure 5.2, the hotspot is located at the upper-left corner, where air becomes hot after travelling a long distance through the fin spacing along the diagonal. The temperature ranges from 104˚C to 120˚C, and the average temperature is 116˚C. Comparing with Figure 3.5, there is a 10˚C increase of maximum temperature over the baseline (straight fin) heat sink with g-2 orientation. However, comparing with the baseline heat sink with g-3 orientation 63  (Figure 3.6), the angled-fin heat sink reduces the maximum temperature by 66˚C. Hence, this type of heat sink is much less dependent on mounting orientation.   Figure 5.2: Temperature contour on the bottom surface of the angled-fin heat sink placed vertically (g-2, g-3 orientations).  5.3 FREE CONVECTION FLOW The buoyancy flow for the vertically orientated angled-fin heat sink is observed. To present this velocity vector of fluid flow the same observation plane of Figure 3.7 is considered here. Figure 5.3 shows the buoyancy flow along the inclined fins for the vertical orientation, which corresponds to the thermal results shown in Figure 5.2. The 45˚ inclination not only determines the buoyancy flow inside the heat sink but also affect the air flow in the upper-left region of the domain. A maximum velocity of 0.51m/s is found at the fin edges from where hot air ascends to 64  ambient. Comparing with Figure 3.9, there is clear improvement of buoyancy flow due to the 45˚ inclination.  Figure 5.3: Velocity vectors of buoyancy flow on the observation plane of the angled-fin heat sink placed in g-2 or g-3 orientation shown in Figure 5.2.  5.4 PARAMETRIC STUDY As angled-fin heat sink is a new design and not many approaches were taken to study its thermal behavior, so further studies are needed. For that, a parametric study is done changing the fin configurations. Various angled-fin configurations are simulated and studied changing the fin thickness, fin spacing and number of fins. The effects of change of these parameters on heat sink performances are discussed.  For simplicity and to reduce simulation run time, angled-fin heat sinks with 100x100 mm base plate and 25 mm fin height are considered. The heat load and environmental conditions are 65  considered same as the pervious simulation of angled-fin heat sink. The objective of this parametric study is to understand the different fin parameters and be able to choose them carefully during effective heat sink design.  5.4.1 Change in Fin Thickness and Fin Spacing The effects of fin thickness and spacing on thermal performance of angled-fin heat sink are observed first. For a fixed number of angled-fin of 17, the fin thickness is changed from 1 mm to 4 mm with an increment of 1 mm. Fin thickness less than 1mm are not studied as it is impractical in most applications. Change in fin thickness also changes the fin spacing as the numbers of fins are constant.  Figure 5.4 shows a thermal behavior of angled-fin heat sink for varied fin thickness and spacing. Only the vertical orientation is shown, as the effects of parametric changes on thermal performances are prominent and easily understandable for this orientation due to the effective variation in the buoyancy flow. Both the average and maximum temperatures of heat sink base are plotted for varied fin thickness and spacing. Figure 5.4 shows that with the increase of fin thickness or the decrease of fin spacing, both the average and maximum temperatures show similar increasing trend. The thinner the fin the better is the thermal performance and best performance is found for 1mm thick fin. The performance of free convection heat transfer greatly depends on the buoyancy flow and heat transfer area. However, although the heat sink with thicker fin contributes to increasing the heat transfer area, with the loosing of fin spacing the buoyancy flow deteriorates, which cause temperature to increase. 66   Figure 5.4: Thermal performance of vertically orientated angled-fin heat sink versus fin thickness for the constant number of fins.  The effects of fin thickness and fin spacing on convective heat transfer coefficient are also studied. For the similar changes in fin thickness and spacing as stated above, the heat transfer coefficients are calculated and plotted. Figure 5.5 shows a bar chart of the average heat transfer coefficient calculated for free convection from vertically oriented heat sinks. It shows that with the increase of fin thickness or the decrease of fin spacing, the heat transfer coefficient decreases. It is known that for a given heat load and fixed environmental conditions the convection coefficient can only be increased by increasing the fluid velocity [5]. Here, reduction in fin spacing causes low buoyancy flow through fin spacing which in turn provides lower heat transfer coefficient. 1 2 3 41251301351401451501551607 6 5 4Heat sink base temperature (°C)Fin Thickness (mm) Avg. TempFin Spacing (mm) Max Temp67    Figure 5.5: Average heat transfer coefficient of vertically oriented angled-fin heat sink versus fin thickness  5.4.2 Change in Fin Numbers and Spacing From the Figure 5.4 and Figure 5.5, it is obvious that the heat sink with 1 mm fin thickness shows better thermal performance. For the given heat load and thermal conditions it shows lower base temperature with higher convection heat transfer coefficient. This 1 mm thick angled-fin heat sink is further studied by changing the other parameters. Keeping the fin thickness constant as 1 mm, the number of fins and fin spacing are changed. Numbers of fins on base plate are changed by varying the fin spacing from 5.5 mm to 8 mm with an increment of 0.5 mm. Thermal performances are studied by observing both the average and maximum temperatures on heat sink base for vertical orientation. A plot of these temperatures with the change of fin spacing and 7 6 5 40123456Avg. heat transfer coefficient (W/(m2.k))Fin Spacing (mm)1 2 3 40123456Avg. heat transfer coefficient (W/(m2.k))Fin Thickness (mm)68  number is shown in Figure 5.6. It shows that, initially the base temperature drops with the increase of spacing and minimum temperature is found for the heat sink with 6 mm fin spacing. After that, further increase of fin spacing shows increasing trend in base temperature. That means, for a certain fin thickness there is optimum fin spacing for which the thermal performance is the highest. For effective heat sink design this optimum point is important and should be evaluated for better cooling performance.   Figure 5.6: Variations of angled-fin base plate temperature with fin spacing for 1 mm thick fin  The convection heat transfer coefficients for this 1mm constant fin thickness with varied fin spacing and fin number are also evaluated. A bar chart of these calculated convection coefficients is shown in Figure 5.7. It shows that, with the increase in fin spacing, the heat transfer coefficient increases. The reason of this increase is the increase in base temperature with fin spacing that was shown in Figure 5.6 (exception for 5.5 mm fin spacing), which ultimately 5.5 6.0 6.5 7.0 7.5 8.0128130132134136138Heat sink base temperature (°C)Fin Spacing (mm) Max Temp. Avg. Temp69  increase the fluid velocity. For a given thermal condition, increase in fluid velocity also increases the heat transfer coefficient. At smaller fin spacing, the buoyancy flow deteriorates due to boundary layer formation which ultimately causes low convection coefficient. This is why 5.5 mm fin spacing shows higher base temperature with lower convection coefficient.   Figure 5.7: Variations in average heat transfer coefficient with fin spacing for vertically oriented 1mm thick angled-fin heat sink  5.5 ANGLED-FIN WITH INTERRUPTIONS The angled-fin heat sink is further studied with interruptions on it. One major problem with the continuous fin is the formation of boundary layer along the fin length. The interruptions within the fin length break this layer formation [52]. From that concept, the thermal performance of interrupted angle fin heat sink is studied for both vertical and horizontal orientations. Heat sinks with 3 and 5 interruptions are considered which are shown in Figure 5.8. The dimensions 5.5 6.0 6.5 7.0 7.5 8.00123456Avg. heat transfer coefficient (W/(m2.k))Fin Spacing (mm)70  of the heat sink are kept same as the angled-fin heat sink used for numerical simulation in Figure 5.1a. For the simulation of this interruptions effect, the thermal load and environmental conditions remain same. The interruptions are cut at perpendicular to the fin length with a cutting width of 5mm which is same as fin spacing. The thermal performance of these interrupted angled-fin heat sinks are studied and compared with the heat sink with no interruptions.  Figure 5.8: Angled-fin with interruptions: (a) 3 interruptions (b) 5 interruptions  The base plate average temperatures of the interrupted angled-fin heat sinks are observed for both horizontal and vertical orientations. Figure 5.9 shows a thermal plot of these interruptions effect. Here, 0 (zero) interruption means heat sink with no interruptions. For horizontal orientation the base temperature decreases with the increase of interruptions. That means, for this orientation, the addition of interruptions within the fin length increase the cooling performance. In case of vertical orientation the scenario is reverse. Here, the interruptions within fin lengths are not favourable to thermal performance. The base plate temperature increases with the increase of interruptions, although the rise in temperature is very small. However, heat sink with 71  interruptions make the heat sink lighter in weight and require less material to build, which is good for low cost and light weight heat sink design.   Figure 5.9: Variations in average base temperature with interruptions for angled-fin heat sink  The angled fin heat sink is a new design, discussed in this chapter numerically. For this heat sink, higher thermal performances are observed with lower orientation dependency. The buoyancy flow of vertical orientations also shows the advantages of fin placement at 45° angle with heat sink base. The parametric study and interrupted fin effects are also shown for different mounting orientations. 0 1 2 3 4 5100102104106108110112114Heat sink base avg. temperature (°C)Interruptions Vertical orientation Horizontal orientation72  CHAPTER 6: PIN FIN HEAT SINK Another very common heat sink design is pin fin heat sink. This type of heat sink is considered in this study to observe the orientation dependency under free convection heat transfer. Different from straight fins, pin fins do not cause continuous blockage of air flow. In this chapter, a series of pin fin heat sinks with varied fin diameter and fin numbers are simulated. Orientation dependencies are observed for both horizontal and vertical orientations.  6.1 NUMERICAL MODEL For the numerical simulation of pin fin heat sink ANSYS Fluent software is used. The pin fin heat sink used for the numerical model has dimensions comparable to the straight and angle fin heat sink. The heat sink material, base plate dimension, and fin height are chosen same as the other two types. A 12 × 12 fins with 5 mm in diameter pin-fin heat sink is shown in Figure 6.1a. For this configuration, the total heat transfer area is 0.154 m2 which is 40% smaller than the two previous heat sinks. The domain and boundary conditions applied for the numerical simulation are same as pervious which is shown in Figure 3.1b. The detailed boundary conditions for the 6 sides of the domain are considered same as Table 3.1 and 3.2. The Boussinesq approximation and surface-to-surface model for free convection and radiation heat transfer respectively are also considered in this case. The similar atmospheric conditions and meshing function are used here. The thermal performance and free convection flow are observed with varied mounting conditions. 73  6.2 THERMAL PERFORMANCE At first, the thermal performance of pin fin heat sink is observed by simulating the numerical model for horizontal orientation (g-1) as shown in Figure 6.1a. The temperature distribution on the bottom surface of the baseplate is presented in Figure 6.1b, which shows a symmetric distribution pattern. The hotspot is located in the center, which is around 10˚C higher than the edges. The maximum temperature is 106˚C, which is close to those of the horizontally oriented straight-fin and angled-fin heat sinks. Hence, this pin fin configuration is comparable to the other two types of fin for horizontal orientation.    Figure 6.1: (a) Pin-fin heat sink with 12×12 pin fins with 5 mm in diameter. (b) Temperature contour on the bottom surface of the pin-fin heat sink placed horizontally (g-1 orientation).  74  The pin-fin heat sink shown in Figure 6.1a is also simulated for vertical orientation. Temperature contour is presented in the Figure 6.2. Similar to the straight fin heat sink with g-2 orientation (see Figure 3.5), the hot spot moves to the upper edge of the heat sink. The temperature ranges from 101˚C to 117˚C with an average of 111˚C. Comparing with the vertical orientation of straight fin where fin lengths are perpendicular to g vector (see Figure 3.6) shows significant less dependence on orientation.   Figure 6.2: Temperature contour on the bottom surface of the pin-fin heat sink (12×12 pins, 5 mm in diameter) placed vertically (g-2, g-3 orientations).  6.3 FREE CONVECTION FLOW To observe the flow dynamics from the heated pin fin heat sink velocity vectors of the flow are presented at observation plane (Figure 3.7) which is 5 mm above the base plate. The 75  buoyancy flow for the vertically oriented pin-fin heat sink is shown in Figure 6.3. The velocity vector shows fluid flow in different direction as no restricted continuous path has to be followed by the flow. This dispersed flow direction reduces boundary layer formation and increase heat transfer performance. If the heat sink is rotated at 90˚, 180˚ or 270˚ angle in the direction of observation plane, the same fluid dynamics and thermal performance can be achieved because of the symmetric geometry.   Figure 6.3: Velocity vectors of buoyancy flow on the observation plane of the pin-fin heat sink (12×12 pins, 5 mm in diameter) placed in g-2 or g-3 orientation shown Figure 6.2.  6.4 PARAMETRIC STUDY The thermal performance and flow dynamics analysis indicates low orientation dependency design of pin fin heat sink. To investigate further on orientation dependency parametric studies are conducted. The purpose is to understand the relationship between heat sink design and 76  dependency of thermal performance on orientation. For the parametric study, pin fin design is varied by changing the pin diameter and number of fins on the heat sink base. Although a broad range of design parameters can be selected and simulated, for simplicity three pin fin diameters with varied number of fins are used here. The matrix is shown in Table 6.1, where 𝑑𝑑, 𝑑, and 𝐷 represent small, medium and large fin diameters. All the pin-fin heat sinks are simulated for horizontal and vertical orientations. Temperature on the free surface of the heat sink is averaged. The average surface temperature is used to assess the thermal performance and orientation dependency. Table 6.1: Designs of pin-fin heat sinks with varied pin diameters and number of pins. Symbol Fin Diameter (mm) Number of Pins dd 5 10×10 12×12 13×13 14×14 15×15 16×16 d 6.56 8×8 10×10 12×12 13×13 14×14 - D 8.57 7×7 8×8 9×9 10×10 11×11 -  Figure 6.4a shows the average temperature for vertical orientation, while Figure 6.4b shows the horizontal orientation.  Each line represents a specific fin diameter and shows a similar trend for both orientations. The average temperature first decreases with increasing the number of pins due to the increase of the heat transfer area. If the number of pins is further increased, the average temperature would increase, because the decrease of free convection due to the reduced fin spacing becomes dominant over the increase of the heat transfer area. Generally, for relatively small number of pins, it is better to have thicker pins. For relatively large number of pins, it is better to have thinner pins. 77  For each pin diameter, there is a turning point showing an optimum number of pins for which there is a minimum average temperature. However, the optimum point is different for different orientation. For the 𝑑𝑑-fin (5mm in diameter) this optimum number is ~14 × 14, maintaining the lowest average temperature of 93˚C for horizontal orientation. For vertical orientation, the lowest average temperature of 105°C can be found for the 12 rows of 𝑑𝑑-fins (5 mm in fin diameter). The optimum number of pins increases with decreasing the pin diameter. In other words, with thinner pins, it is allowed to go to larger number of pins to further lower the average surface temperature. To compare the orientation dependency, the difference of average temperature between the two orientations, the vertical orientation (Figure 6.4a) minus the horizontal orientation (Figure 6.4b) is calculated and plotted in Figure 6.4c. It shows that the difference is always positive, which means the average temperature for the horizontal orientation is lower than the vertical orientation for all pin fin configurations. For all the three pin diameters, a larger number of pins causes a higher temperature difference, and thus more orientation-dependent.  For the same temperature difference, a larger number of pins is allowed for thinner pins (𝑑𝑑-pin), but the number of pins needs to be reduced for thick pins (𝐷-pin). In other words, for the same number of pins, thick pins show higher temperature difference than thin pins. 78   Figure 6.4: Variations in average heat transfer coefficient of different heat sinks for vertical orientations. (S-g2: straight-fin heat sink with g-2 orientation; S-g3: straight-fin heat sink with g-3 orientation; A: angled-fin heat sink; P-D: pin-fin heat sinks with pin diameter 8.57 mm; P-d: pin-fin heat sinks with pin diameter 6.56 mm; P-dd: pin-fin heat sinks with pin diameter 5 mm). The x-axis values for pin-fin heat sinks are the number of pin rows.  Discussion above indicates the fin spacing has effect on orientation dependency. To verify, the data of temperature difference exhibited in Figure 6.4c are plotted versus fin spacing in Figure 6.4d. The spacing is the distance from edge to edge between neighbour pins as shown in Figure 6.4d. It shows a clear trend for all the three pin diameters that the temperature difference 79  decreases with the increase of fin spacing. The effect of changing spacing is significant when the spacing is small, and becomes less significant when the spacing is large. 80  CHAPTER 7: RESULT AND DISCUSSION This chapter aims to represent the summary of the findings from this study. A short discussion on the comparison of orientation dependencies and thermal performances for three different heat sinks are deliberated.  7.1 ORIENTATION DEPENDENCIES The thermal performances of the three types of heat sinks under varied mounting orientations are summarized in Figure 7.1, where the average base temperatures are shown for each case. The straight-fin heat sink works well for g-1 and g-2 orientations, but has significant temperature rise for g-3 orientation. The angled-fin and pin fin heat sinks show ~10oC rise from g-1 orientation to any vertical orientation. However, it avoids any steep temperature rise which could cause device failure. Additionally, the pin-fin heat sinks has the smallest heat transfer area but shows the lowest temperature, which is attributed to the well-mixing buoyancy flow shown in by Figure 6.3. Figure 7.1 clearly shows the low orientation-dependency of the angled-fin and pin-fin heat sinks. 81   Figure 7.1: Average temperature on the bottom surface of the heat sink (base average temperature) versus orientation for the three types of heat sinks.  7.2 THERMAL PERFORMANCES OF DIFFERENT HEAT SINKS The heat transfer capability of all the heat sinks considered in the present study for vertical orientations, g-2 and g-3 are also compared. To assess the heat transfer capability of heat sink, an average heat transfer coefficients is defined as  )(  TTAqhs (7.1) Here ?̅?𝑠 is average surface temperature of heat sink, 𝑇∞ is ambient temperature, q is the heat load applied on the bottom surface the heat sink. The area A is the total surface area of the heat sink, which includes the area of the base plate not occupied by fins and total area of fin surfaces. 82  Since both convection and radiation heat transfer modes are considered, the average heat transfer coefficient is an overall effective coefficient including the two heat transfer mechanisms. However, convection heat transfer is dominant in the present work. Figure 7.2 shows the variations in average heat transfer coefficient for different heat sinks for vertical orientation. The results include two vertical orientations g-2 and g-3 for the straight-fin heat sink, and the angled-fin heat sink, and a total of fifteen pin-fin heat sinks. The following can be observed from Figure 7.2:  1) The angled-fin heat sink shows a heat transfer coefficient close to that of g-2 orientation of straight fin heat sink, and is constant for both g-2 and g-3.  2) For the same pin diameter, the heat transfer coefficient of pin-fin heat sink decreases with increasing of the number of pins.  3) For the same number of pins, smaller diameter of pin shows higher heat transfer coefficient (e.g. comparing P-d-10 with P-dd-10). 83   Figure 7.2: Variations in average heat transfer coefficient of different heat sinks for vertical orientations. (S-g2: straight-fin heat sink with g-2 orientation; S-g3: straight-fin heat sink with g-3 orientation; A: angled-fin heat sink; P-D: pin-fin heat sinks with pin diameter 8.57 mm; P-d: pin-fin heat sinks with pin diameter 6.56 mm; P-dd: pin-fin heat sinks with pin diameter 5 mm). The x-axis values for pin-fin heat sinks are the number of pin rows.  84  CHAPTER 8: CONCLUSIONS AND RECOMMENDATIONS This chapter presents a precise conclusion of this study with some limitations and future recommendations. 8.1 CONCLUSIONS In summary, the straight-fin heat sink shows orientation dependency to thermal performance, which is not good for the thermal management of many electronic devices. The angled-fin heat sink shows less orientation-dependency in thermal performance. The thermal results of the pin-fin heat sink shows low temperature for small heat transfer area, which is due to its well-mixing fluid dynamics. Hence, for the same thermal performance, pin-fin heat sink requires less heat transfer area compared to the angled fin configuration, which is preferred for the thermal management of light devices. However, the difference of manufacturability between the angled-fin and pin-fin heat sinks also needs to be considered from the cost perspective. 8.2 LIMITATIONS OF THIS STUDY This study faces the following limitations due to the unavailability of proper equipment and time constraint.  The experimental study on straight fin heat sink is done in the room environment, which may not be an ideal condition for free convection due to room air circulation. The convection heat transfer would be more accurate if the tests were done in a thermal chamber with controlled environment. 85   Experiments on angled-fin and pin fin heat sinks with different configurations were not done due to the manufacturing constraints and time limitations.   Complete insulation of heat sink back was not possible due to the limitation of insulation materials. 8.3 FUTURE RECOMMENDATIONS This numerical and experimental study on orientation dependency of free convection heat sink has some potentials to improve further more. The following points should be noted for future improvements:  Free convection heat transfer has been becoming more popular due to its easy maintenance and low operation cost, which would be more popular if it becomes orientation independent. 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