THERMODYNAMIC AND HEAT TRANSFER STUDIES ON THERMOELECTRIC POWER GENERATION AND COOLING OPTIONS S.MANIKANDAN

Transcription

1 THERMODYNAMIC AND HEAT TRANSFER STUDIES ON THERMOELECTRIC POWER GENERATION AND COOLING OPTIONS S.MANIKANDAN CENTRE FOR ENERGY STUDIES INDIAN INSTITUTE OF TECHNOLOGY DELHI HAUZ KHAS, NEW DELHI OCTOBER 2017

2 Indian Institute of Technology Delhi (IITD), New Delhi, 2017

3 THERMODYNAMIC AND HEAT TRANSFER STUDIES ON THERMOELECTRIC POWER GENERATION AND COOLING OPTIONS by S.MANIKANDAN Centre for Energy Studies Submitted in fulfillment of the requirements of the degree of Doctor of Philosophy to the INDIAN INSTITUTE OF TECHNOLOGY DELHI OCTOBER 2017

4 Certificate This is to certify that the thesis entitled Thermodynamic and Heat Transfer Studies on Thermoelectric Power Generation and Cooling Options being submitted by Mr. S.Manikandan to Indian Institute of Technology Delhi in fulfillment of the requirements for the award of the degree of Doctor of Philosophy is a record of bonafide research work carried out by him under my guidance and supervision at Centre for Energy Studies, Indian Institute of Technology Delhi. The results obtained herein have not been submitted in part or in full to any other University or Institute for the award of any degree to the best of our knowledge. Dr. S. C. Kaushik Professor Centre for Energy Studies Indian Institute of Technology Delhi Delhi Hauz Khas, New Delhi i

5 ACKNOWLEDGEMENTS It gives me immense pleasure to express my gratitude to all those who supported me during the course of my study. First and foremost, I would like to express my deep gratitude to my research supervisor, Prof. S. C. Kaushik, for providing me thorough guidance, motivation, encouragement and invaluable suggestions throughout my research work in spite of his busy academic and professional schedules. I am indebted to the Almighty for giving me such an intellectual and kind human being as guide or mentor. I thank the Indo US Science and Technology Forum (IUSSTF), Department of Science and Technology, Government of India for the Building Energy Efficiency Higher and Advanced Network (BHAVAN) fellowship, and express my gratitude to Prof. Ronggui Yang, Department of Mechanical Engineering, University of Colorado at Boulder, USA for his support and guidance during my BHAVAN internship. I would like to extend my sincere thanks to the chairman and all members of my SRC (Student Research Committee) for providing their valuable suggestions during the various evaluation stages of my research work. I am also grateful to Director, IIT Delhi and Head, Centre for Energy Studies for providing facilities and extending every possible support. Special thanks are due to Dr. S. K. Tyagi, Dr. Ranjana Hans, Mr. Rahul Rawat, Mr. Manoj Dixit, Ms. Ravita Lamba, Mr. O P Sharma, Mr. Rupinder Pal Singh, Mr. Saket Verma and all research colleagues for extending all kind of support from time to time during my period of study. Thanks are also due to other members of the solar thermal science laboratory, CES, IIT Delhi for their interactions with me during the research work. This thesis would be incomplete without an expression of my sincere and deep sense of gratitude to the reviewers, editors and production teams of the international journals in which my research papers are published for their careful reading, their valuable comments and suggestions which greatly improved the contents and quality of the research. I would also like to thank all the authors of the research papers and books which I have referred to and cited in the published papers and the present thesis. I wish to express my gratitude to my friends for providing their support that has helped me a lot in completing my research work. Their presence in my life inspires me to have positive thinking in times of distress and constantly striving for achieving new tough goals in life. ii

6 I would like to express my gratitude to my wife Anusuya Manikandan for her support, patience, cooperation and encouragement throughout the research span. I am obliged to my daughter Vishaka for sparing the valuable time I spent on this work which was actually her golden childhood time. Last but not least, I would like to thank my mother Smt. Krishna Bai, father Shri. Sundararaj, who always prayed for my success. I have strong belief that whatever I have achieved in my life is all because of their prayers and blessings. S.Manikandan iii

7 ABSTRACT The thermoelectric devices, which work on the principles of reversible Seebeck, Peltier and Thomson effects having advantages of simple in operation, reliable, noiseless and lightweight makes them suitable for power generation, cooling and heating applications. The performance of the thermoelectric devices are dependent on the dimensionless figure of merit (ZT) of the thermoelectric materials which have not improved significantly much since The commercially available Bismuth Telluride based thermoelectric devices have lower figure of merit. Moreover, most of reported research in the literature have investigated the thermoelectric devices based on the first law of thermodynamics. In this thesis, the thermoelectric generator and thermoelectric cooler devices have been studied based on the first and second law of thermodynamics to quantify the irreversibilities in the thermoelectric devices and it is found that the internal irreversibilities are higher than the external irreversibilities. The maximum power point tracking technique (MPPT) has been applied to the thermoelectric generator-cooler combined system to improve its performance and it was found that the MPPT technique will improve the system efficiency and cooling power of the combined system. The impact of Thomson effect on the performance and the optimum number of thermocouples in the first and second stage of the two stage thermoelectric generator and cooler have been studied. Thus obtained optimum number of thermocouples are different from the optimum number of thermocouples without considering the Thomson effect. The thermoelement geometry has been modified to improve the thermal performance of the thermoelectric devices and the transient heat transfer studies have proved that the annular shaped geometry of the thermoelement can perform better than the conventional flat geometry of the thermoelement. The modified current pulse operation of the thermoelectric cooler has been studied to improve the cooling power and coefficient of performance (COP) of the thermoelectric cooler simultaneously. The solar heat pipe based thermoelectric generator for power generation has been investigated. The solar photovoltaic cell operated thermoelectric cooler has also been experimentally studied and it is found that it can maintain 9 o C to 14 o C without and with loaded condition respectively inside the cold box and provided the COP of under loaded condition. A user friendly computer software has been developed using MATLAB graphical user interface for the thermodynamic design of thermoelectric devices. The results and conclusions of the present studies are useful for the design and development of actual thermoelectric systems for power generation and cooling applications. iv

8 स र थर म इल क ट र क (त प व द य त) ड इस (उपकरण), ज कक प रतत त स ब क, प क ट ट यर और थ र मसन ससद त पर क र म करत ह तथ ऑपर शन र म सरल, व श सन य, श र र म रत और जन र म हटक ह न क क रण बबजल उत प दन, क सल ग (श तलन) और ह ट ग अन प रय ग क सलए उपय रत ह थर म इल क ट र क उपकरण क परफ रर म स थर म इल क ट र क पद थ क ग ण त त क आय र म रटहत आ कड (आय र म रटहत कफगर ऑफ़ र म रर ) (ज..) पर तनर र करत ह, क ट जसर म कक 1950 क ब द स बह त ज य द स ध र नह ह आ ह व य स तयक र प स उपलब ध बबस र मथ टय र इ ( ल र इ ) आध ररत थर म इल क ट र क ड इस क कफगर ऑफ़ र म रर कर म ह इसक अल, स टहत य र म उपलब ध अधधक श अन स ध न र म थर म इल क ट र क ड इस (उपकरण ) क ऊष र म गततक क पहल ऊज ससद त क आध र पर ज च क गई ह इस थ ससस र म, थर म इल क ट र क जनर र और थर म इल क ट र क क लर उपकरण क अध ययन उनर म उपक ट स थत इरर सस बबसल ज़ (अपरर त न यत ) क अन र म न लग न क सलए, ऊष र म गततक क पहल और द सर ससद त क आध र पर ककय गय ह और यह प य गय ह कक आ तररक इरर सस बबसल ज़ (अपरर त न यत ए ) ब ह य इरर सस बबसल ज़ (अपरर त न यत ओ ) स अधधक ह थर म इल क ट र क जनर र-क लर स य रत ससस र म (प रण ल ) क परफ रर म स स ध रन (ब हतर बन न ) क सलए अधधकतर म प र प इ कक ग (एर म.प.प..) तकन क क उपय ग ककय गय (ल ग क गई) ह और यह प य गय कक एर म.प.प.. तकन क स य रत ससस र म (प रण ल ) क दक षत और क सल ग (श तलन) र म स ध र कर ग थ र मसन इफ़ र (प रर ) क परफ रर म स (प रदश न) पर असर (प रर ) और द व -चरण (द -चरण) थर म इल क ट र क जनर र और क लर क पहल और द सर स ज (चरण) र म थर म कपटस क अन क लतर म (इष तर म) स ख य क अध ययन ककय गय इस प रक र प र प त थर म कपटस क अन क लतर म स ख य, बबन थ र मसन प रर श सर मल ककय ह ए प र प त थर म कपटस क अन क लतर म (इष तर म) स ख य स अलग ह थर म इल क ट र क ड इस क थर म ल (त प य) प रदश न (परफ रर म स) क ब हतर बन न क सलए थर म एसलर म (तत त ) ज र म (ज य सर मतत) क स श धधत ककय गय ह और ससए (क षणणक) ह (गर म ) हस त तरण न यह स बबत ककय (कर टदय ) ह कक थर म एसलर म (तत त ) क क ल आक र क ज र म (ज य सर मतत), प र पररक फ ल (सर मतल) ज य सर मतत स ब हतर प रदश न कर सकत ह थर म इल क ट र क क लर क क सल ग प र (शक ट रत) और प रदश न ग ण क (क एकफससए ) (स.ओ.प.) र म एक स थ स ध र करन क सलए थर म इल क ट र क क लर क स श धधत व द य त ध र पटस ऑपर शन क अध ययन ककय गय बबजल उत प दन क सलए स र गर म (त प य) प इप आध ररत थर म इल क ट र क जनर र क ज च क गई ह स र (स लर) फ ट इक स ल स च सलत थर म इल क ट र क क लर क र प रय ग त र मक र प स अध ययन ककय गय और प य गय ह कक यह ससस र म (प रण ल ) ठ ब रस क अ दर क त पर म न ल (र र) क उपक ट स थतत र म 9 0 C (ड ग र स क ट टसयस) तथ ल (र र) क अन पक ट स थतत र म 14 0 C तक बन ए रख सकत ह और ल (र र) क उपक ट स थतत र म स.ओ.प. प रद न क थर म इल क ट र क उपकरण क थर म यन सर मक ड ज इन क सलए र म ल ब (MATLAB) ग र कफकल य जर इ रफ स क उपय ग करक एक य जर (उपय गकत ) क अन क ल क प य र स फ यर व कससत ककय गय ह त र म न अध ययन क पररण र म और तनष कर, बबजल उत प दन और क सल ग अन प रय ग क सलए स तव क थर म इल क ट र क ससस र म (प रण ल ) क ड ज इन और व क स क सलए उपय ग ह

9 CONTENTS Certificate Acknowledgements Abstract Contents List of Figures List of Tables Nomenclature i ii iv v xi xix xxi CHAPTER 1: GENERAL INTRODUCTION Background Thermal Modelling of Thermoelectric devices Choice of Thermoelectric materials Scope and Objectives of the Thesis Organization of the Thesis 13 CHAPTER 2 : THERMODYNAMIC ANALYSIS AND MAXIMUM POWER POINT TRACKING IN THERMOELECTRIC GENERATOR-COOLER COMBINED SYSTEM Introduction Thermodynamic basis of TEC and TEG Thermoelectric Cooler Thermoelectric Generator Thermoelectric generator-cooler combined 37 system 2.3 Results and discussion 42 v

10 2.3.1 Thermoelectric cooler Thermoelectric generator TEG TEC combined system Conclusions 60 CHAPTER 3 : STUDY OF THOMSON EFFECT IN SINGLE AND TWO STAGE THERMOELECTRIC GENERATOR AND THERMOELECTRIC COOLING SYSTEMS ON PERFORMANCE Introduction Thermodynamic studies of two stage TEG and TEC Thermodynamic modelling of two stage 65 thermoelectric generator Thermodynamic modelling of two stage 73 thermoelectric cooler Development of user friendly computer 78 software TESimulator for design and analysis of thermoelectric devices 3.3 Results and discussion Two stage irreversible thermoelectric 86 generator Two stage irreversible thermoelectric cooler Conclusions 95 CHAPTER 4 : EFFECT OF THERMOELEMENT GEOMETRY ON PERFORMANCE OF SINGLE STAGE 97 vi

11 THERMOELECTRIC GENERATOR AND THERMOELECTRIC COOLING SYSTEMS 4.1 Introduction Thermal modelling of annular TEG and TEC Heat Transfer modelling of annular 99 thermoelectric generator Heat Transfer modelling of annular 106 thermoelectric cooler 4.3 Results and discussion Annular thermoelectric generator Annular thermoelectric cooler Conclusions 125 CHAPTER 5 : TRANSIENT HEAT TRANSFER ANALYSIS AND THERMAL PERFORMANCE OF THE THERMOELECTRIC GENERATOR AND THERMOELECTRIC COOLING SYSTEMS Introduction Thermal modelling of annular TEG and TEC 129 systems Heat Transfer studies of annular 129 thermoelectric generator Heat transfer studies of annular 136 thermoelectric cooler 5.3 Results and Discussion Annular thermoelectric generator 142 vii

12 5.3.2 Annular thermoelectric cooler Conclusions 155 CHAPTER 6 : TRANSIENT PULSE OPERATION OF THE THERMOELECTRIC COOLER FOR BUILDING SPACE COOLING APPLICATION Introduction Thermal modelling of TEC Results and discussion Conclusions 176 CHAPTER 7 : SOLAR OPERATION OF THERMOELECTRIC 179 GENERATOR AND PV-THERMOELECTRIC COOLING SYSTEMS 7.1 Introduction Thermal modelling of Solar annular TEG Thermal modelling of Solar annular 182 thermoelectric generator 7.3 Solar Photovoltaic-Thermoelectric cooler system: 187 Experimental study 7.4 Results and discussion Solar annular thermoelectric generator Solar Photovoltaic Thermoelectric cooler Conclusions 203 CHAPTER 8 : OVERALL CONCLUSIONS AND RECOMMENDATIONS Conclusions Contributions 206 viii

13 8.3 Recommendations for further work 207 APPENDIX-A: APPENDIX-B: Thermodynamic modelling of ideal, endoreversible and exoreversible thermoelectric generator systems Parametric constants for calculating the junction temperatures and optimum currents of two stage TEG and TEC REFERENCES 221 ABOUT THE AUTHOR 235 ix

14 LIST OF FIGURES Fig. No. Title of the Figure Page No. 1.1 Schematic of thermoelectric cooler Cross section view of a thermo-element Power factor and thermal conductivity of materials Types of thermodynamic thermoelectric systems (a) Reversed heat engine (b) Thermoelectric cooler (a) Heat engine (b) Thermoelectric generator V-I characteristics of thermoelectric generator DC/DC converter configuration Temperature profile of TEG and TEC for exoreversible and 41 irreversible case 2.7(a) Cooling power of thermoelectric cooler for different ΔTc for 43 exoreversible case 2.7(b) Cooling power of thermoelectric cooler for different ΔTc for 43 irreversible case 2.8(a) COP of thermoelectric cooler for different ΔTc for exoreversible 43 case 2.8(b) COP of thermoelectric cooler for different ΔTc for irreversible 43 case 2.9(a) Exergy efficiency of thermoelectric cooler for different ΔTc for 45 exoreversible case 2.9(b) Exergy efficiency of thermoelectric cooler for different ΔTc for 45 irreversible case 2.10(a) Cooling power vs. COP of irreversible thermoelectric cooler for 45 different ΔTc 2.10(b) Cold exergy vs. exergy efficiency of irreversible thermoelectric 45 cooler for different ΔTc 2.11 Internal and external irreversibilities in different thermodynamic modes of thermoelectric cooler 47 xi

15 2.12(a) Cooling power vs exergy efficiency of thermoelectric cooler with variable total heat transfer area 2.12(b) Cooling power vs exergy efficiency of thermoelectric cooler with variable contact resistance 2.13(a) Power output of thermoelectric generator for different ΔTg for exoreversible case 2.13(b) Power output of thermoelectric generator for different ΔTg for irreversible case 2.14(a) Energy efficiency of thermoelectric generator for different ΔTg for exoreversible case 2.14(b) Energy efficiency of thermoelectric generator for different ΔTg for irreversible case 2.15(a) Exergy efficiency of thermoelectric generator for different ΔTg for exoreversible case 2.15(b) Exergy efficiency of thermoelectric generator for different ΔTg for irreversible case 2.16 Irreversibilities in different thermodynamic modes of thermoelectric generator 2.17(a) Power output and exergy efficiency of thermoelectric generator for variable heat transfer area 2.17(b) Power output and exergy efficiency of thermoelectric generator for variable contact resistance 2.18(a) Power output of TEG and Cooling Power of TEC with duty cycle of the DC/DC converter 2.18(b) COP of TEC and combined system efficiency with duty cycle of the DC/DC converter 2.19(a) Cooling power of TEC and System efficiency with duty cycle (b) 2.20(a) of converter with different ΔTg Cooling power of TEC and System efficiency with duty cycle of converter with different ΔTc Influence of heat source temperature of TEG on the cold exergy output and combined system exergy efficiency xii

16 2.20(b) Influence of heat source temperature of TEC on the cold exergy 58 output and combined system exergy efficiency 3.1 Two stage thermoelectric generator Two stage thermoelectric cooler TESimulator Installer Main window of the TESimulator TEGSimulator window Selection of operating conditions Flowchart for the thermodynamic design of thermoelectric 84 cooler using TESimulator 3.8 Screenshot on the operation of TECSimulator Export figure option in TESimulator Power output vs. current of a two stage exoreversible 87 thermoelectric converter 3.11(a) Power output vs. energy efficiency of a two stage exoreversible 87 thermoelectric generator 3.11(b) Power output vs. exergy efficiency of a two stage irreversible 87 thermoelectric generator 3.12(a) Power output vs. number of thermocouples in the first stage of 88 the irreversible TTEG 3.12(b) Exergy efficiency vs. number of thermocouples in the first 88 stage of the irreversible TTEG 3.13(a) Comparison of power output and exergy efficiency of the 89 TTEG with and without Thomson effect 3.13(b) Comparison of irreversibilities in a TTEG with and without 89 Thomson effect 3.14(a) Cooling power of a two stage exoreversible thermoelectric 91 cooler 3.14(b) COP of a two stage exoreversible thermoelectric cooler Cooling power vs. exergy efficiency of a two stage irreversible 92 thermoelectric cooler 3.16(a) Cooling power of an irreversible TTEC vs. number of thermocouples in the first stage 93 xiii

17 3.16(b) Exergy efficiency of an irreversible TTEC vs. number of 93 thermocouples in the first stage 3.17(a) Cooling power and energy efficiency in the TTEC with and 93 without Thomson effect 3.17(b) Irreversibilities in the TTEC with and without Thomson effect (a) Schematic of ATEG (b) Cross section view of ATEG (a) Schematic of ATEC (b) Cross section view of ATEC Effect of theta and Sr in the dimensionless power output of 114 ATEG 4.4 Effect of theta and Sr in the Energy efficiency of ATEG Effect of theta and Sr in exergy efficiency of ATEG Effect of theta and Sr in irreversibilities of ATEG Effect of RL/Ro and Sr in the power output of ATEG Effect of RL/Ro and Sr in the Energy efficiency of ATEG Effect of RL/Ro and Sr in dimensional irreversibilities of ATEG Effect of RL/Ro and Sr in exergy efficiency of ATEG Effect of theta and Sr on the dimensionless cooling power of 120 ATEC at maximum energy efficiency condition 4.12 Effect of theta and Sr on the Energy efficiency of ATEC at 120 maximum energy efficiency condition 4.13 Effect of theta and Sr on the exergy efficiency of ATEC at 122 maximum energy efficiency condition 4.14 Effect of theta and Sr on the irreversibilities of ATEC at 122 maximum energy efficiency condition 4.15 Effect of theta and Sr on the dimensionless cooling power 123 output of ATEC at maximum cooling power condition 4.16 Effect of theta and Sr on the Exergy efficiency of ATEC at 124 maximum cooling power condition 5.1(a) Annular thermoelectric generator (b) Cross section view of annular thermoelectric element Annular thermoelectric cooler system 136 xiv

18 5.3 Temperature difference between the hot and cold side of ATEG and FTEG for variable heat input 5.4 Power output and energy efficiency of ATEG and FTEG for variable heat input 5.5 Temperature difference between the hot and cold side of ATEG and FTEG for variable operating current 5.6 Time variation on energy efficiency of ATEG for variable current 5.7 Power output and energy efficiency of ATEG and FTEG for variable current 5.8 Variation in temperature difference between hot and cold junction of ATEG and FTEG for variable heat transfer coefficient 5.9 Power output and energy efficiency of ATEG and FTEG for different heat transfer coefficient 5.10 Cold and hot side temperature of annular and flat thermoelectric cooler 5.11 Cold side temperature of annular and flat thermoelectric cooler for different cooling power 5.12 Cold side temperature of annular and flat thermoelectric cooler for different current 5.13 Hot and cold side temperature of annular and flat thermoelectric cooler for different heat transfer coefficient 5.14 Cold side temperature of the annular and flat thermoelectric cooler for higher values of heat transfer coefficient 5.15 Cold side temperature of annular and flat thermoelectric cooler for different length of thermoelement 6.1 Schematic representation of the thermoelectric cooler for building space cooling application 6.2 Input variables and cold side temperature profile of normal pulse operation and modified pulse operation of TEC 6.3 Variation of cold side temperature and COP of TEC with hot side heat transfer coefficient at steady state xv

19 6.4 Variation on cooling power and COP of TEC as a function of 167 steady state current 6.5 Cold side temperature of TEC with modified pulse operation Average cooling power and COP as a function of pulse cooling 169 load. 6.7(a) Cold side temperature vs. the pulse current ratio with constant 170 average cooling power 6.7(b) Cold side temperature vs. the pulse current ratio with constant 170 average cold side temperature 6.8 Variation in COP and the average cold side temperature of the 171 thermoelectric cooler with pulse current ratio 6.9 Variation of average cooling power and COP of TEC with 172 current pulse ratio and pulse cooling power 6.10 Cold side temperature of TEC for different pulse width Variation of average cooling power, COP and average cold side 174 temperature with different pulse width 6.12 Schematic of rectangular, ramp up and exponential rise pulse Cold side temperature of TEC for different pulse shapes COP and average cooling power of TEC for different pulse 176 shapes 7.1(a) Solar heat pipe annular thermoelectric generator system (b) Cross section view of solar heat pipe flat thermoelectric 183 generator 7.2 Schematic of solar annular thermoelectric generator Thermal network of solar annular thermoelectric generator Block diagrammatic representation of Solar PV-TEC system Experimental setup of Solar-PV thermoelectric cooler system (a) Pyranometer (b) Solar Photovoltaic panel Power output of solar thermoelectric generator with solar radiation. Dashed line with square ticks for SATEG and the continuous line for SFTEG systems. 192 xvi

20 7.8 Electrical energy efficiency of solar thermoelectric generator with solar radiation. Dashed line with square ticks for SATEG and the continuous line for SFTEG systems 7.9 Electrical exergy efficiency of solar thermoelectric generator with solar radiation. Dashed line with square ticks for SATEG and the continuous line for SFTEG systems 7.10 Thermal exergy efficiency of solar thermoelectric generator with solar radiation 7.11 Variation in power output of solar thermoelectric generator with number of thermocouples 7.12 Variation in electrical energy efficiency of solar thermoelectric generator with number of thermocouples 7.13 Variation in electrical energy efficiency and thermal energy efficiency of solar thermoelectric generator with number of thermocouple 7.14 Variation in electrical energy efficiency and thermal energy efficiency of solar annular thermoelectric generator with water temperature 7.15 Temperature profile of solar thermoelectric cooler without load conditions 7.16 Temperature profile of the solar thermoelectric cooler with load condition for evening condition 7.17 Solar radiation and input power to the solar thermoelectric cooler 7.18 Temperature profile of the thermoelectric cooler with load under morning condition 7.19 Temperature difference between the hot, cold side and water temperature and cold side temperature of thermoelectric cooler xvii

21 LIST OF TABLES Table. No. Title of the Table Page No. 1.1 FOM of Skeutterudite thermoelectric materials FOM of Clathrate and alkali thermoelectric materials FOM of nano thermoelectric materials Impedance relations of DC/DC converter Comparison of performance parameters of exoreversible and 48 irreversible thermoelectric cooler for ΔTc of 10K 2.3 Comparison of irreversibilities in endoreversible, 48 exoreversible and irreversible thermoelectric cooler 2.4 Comparison of performance parameters of exoreversible and 53 irreversible thermoelectric generator for ΔTg of 150K 2.5 Impact of MPPT in exoreversible combined system for ΔTc 59 of 10K and ΔTg of 150K 2.6 Impact of MPPT in irreversible combined system for ΔTc of 59 10K and ΔTg of 150K 2.7 Comparison between the exoreversible and irreversible 59 combined system with MPPT 3.1 Plot markers for different operating conditions for the 86 thermoelectric devices 3.2 Optimum number of thermocouples for the maximum power 90 output, energy/exergy efficiency in an irreversible TTEG with ΔTg of 150 K and TH of 450 K 3.3 Optimum number of thermocouples for maximum cooling 94 power, maximum energy and exergy efficiency in an irreversible TTEC with ΔTc of 20K and TC of 280K 4.1 Expressions for IQc and Ienergy of ATEC Comparison of the results of this study with results of Shen 119 et al. (2015) when θ=1.5, RL/Ro=2 and ZTm= Results of the analysis when θ=1.034 and Z * Teff= for maximum energy efficiency condition 124 xix

22 4.4 Results of the analysis when θ=1.034 and Z * Teff = for 125 maximum cooling power condition 5.1 Material and physical properties of the thermoelectric 130 generator (Bi2Te3) 5.2 Material and physical properties of the thermoelectric cooler 136 (Bi2Te3). 5.3 Comparison of power output and energy efficiency of flat and 148 annular thermoelectric generator 5.4 Comparison of COP of flat and annular thermoelectric cooler 155 for different cooling load 6.1 Properties of the thermoelectric cooler Geometrical and physical properties of evacuated tube solar 185 collector. 7.2 Properties of thermoelectric material Specifications of solar thermoelectric cooler Comparison of maximum performance parameters of SATEG and SFTEG system at solar radiation of 1000 W/m 2 and Twater of 308 K. 198 xx

23 NOMENCLATURE h Heat transfer coefficient (W/m 2 K) i number of nodes m mass (kg) r Radius (m) t time (s) x ratio of number of thermocouples in first stage to second stage A Area (m 2 ) COP Coefficient of Performance D Density (kg/m 3 ) Ex Exergy (W) I Current (A) Irr Irreversibilities (W) K Thermal conductance (W/K) L length (m) M Total number of thermoelectric couples in two stage TEG and TEC N Total number of thermoelectric modules P Electrical Power (W) Q Heat transfer rate (W) R Electrical Resistance (Ω) S Entropy (W/K) T Temperature (K) U Overall heat transfer coefficient (W/m 2 K) V Voltage (V) Z Figure of merit (K -1 ) Greek Letters α Seebeck coefficient (V/K) k Thermal conductivity (W/mK) ρ Electrical resistivity (Ωm) σ Electrical conductivity (S/m) xxi

24 Δ Difference θ Dimensionless temperature ƞ Energy efficiency Ψ Exergy efficiency φ Angle τ Thomson coefficient (V/K) Subscripts o Environment state 1 hot junction of thermoelectric device 2 cold junction of thermoelectric device c Cooler dl Infinitesimal length dr Infinitesimal radial length dt Infinitesimal time en Endoreversible ex Exoreversible gen Generation g Generator in Input ir Irreversible m Interstage/ mean n n-type material out Output p p-type material r Cooler C Cold side of thermoelectric device H Hot side of thermoelectric device I Ideal Superscripts n Incremental time xxii