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Thermoelectrics: Design and Materials

ISBN: 978-1-118-84893-7
440 pages
September 2016
Thermoelectrics: Design and Materials (1118848934) cover image

Description

Thermoelectrics: Design and Materials

HoSung Lee, Western Michigan University, USA

 

A comprehensive guide to the basic principles of thermoelectrics

 

Thermoelectrics plays an important role in energy conversion and electronic temperature control. The book comprehensively covers the basic physical principles of thermoelectrics as well as recent developments and design strategies of materials and devices.

The book is divided into two sections: the first section is concerned with design and begins with an introduction to the fast developing and multidisciplinary field of thermoelectrics. This section also covers thermoelectric generators and coolers (refrigerators) before examining optimal design with dimensional analysis. A number of applications are considered, including solar thermoelectric generators, thermoelectric air conditioners and refrigerators, thermoelectric coolers for electronic devices, thermoelectric compact heat exchangers, and biomedical thermoelectric energy harvesting systems. The second section focuses on materials, and covers the physics of electrons and phonons, theoretical modeling of thermoelectric transport properties, thermoelectric materials, and nanostructures.

 

Key features:

  • Provides an introduction to a fast developing and interdisciplinary field.
  • Includes detailed, fundamental theories.
  • Offers a platform for advanced study.

 

Thermoelectrics: Design and Materials is a comprehensive reference ideal for engineering students, as well as researchers and practitioners working in thermodynamics.

 

Cover designed by Yujin Lee

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Table of Contents

Preface xiii

1 Introduction 1

1.1 Introduction 1

1.2 Thermoelectric Effect 3

1.2.1 Seebeck Effect 3

1.2.2 Peltier Effect 3

1.2.3 Thomson Effect 4

1.2.4 Thomson (or Kelvin) Relationships 4

1.3 The Figure of Merit 4

1.3.1 New-Generation Thermoelectrics 5

Problems 7

References 7

2 Thermoelectric Generators 8

2.1 Ideal Equations 8

2.2 Performance Parameters of a Thermoelectric Module 11

2.3 Maximum Parameters for a Thermoelectric Module 12

2.4 Normalized Parameters 13

Example 2.1 Exhaust Waste Heat Recovery 15

2.5 Effective Material Properties 17

2.6 Comparison of Calculations with a Commercial Product 18

Problems 19

Computer Assignment 21

References 22

3 Thermoelectric Coolers 23

3.1 Ideal Equations 23

3.2 Maximum Parameters 26

3.3 Normalized Parameters 27

Example 3.1 Thermoelectric Air Conditioner 29

3.4 Effective Material Properties 33

3.4.1 Comparison of Calculations with a Commercial Product 34

Problems 36

Reference 37

4 Optimal Design 38

4.1 Introduction 38

4.2 Optimal Design for Thermoelectric Generators 38

Example 4.1 Exhaust Thermoelectric Generators 46

4.3 Optimal Design of Thermoelectric Coolers 49

Example 4.2 Automotive Thermoelectric Air Conditioner 57

Problems 61

References 63

5 Thomson Effect, Exact Solution, and Compatibility Factor 64

5.1 Thermodynamics of Thomson Effect 64

5.2 Exact Solutions 68

5.2.1 Equations for the Exact Solutions and the Ideal Equation 68

5.2.2 Thermoelectric Generator 70

5.2.3 Thermoelectric Coolers 71

5.3 Compatibility Factor 71

5.4 Thomson Effects 79

5.4.1 Formulation of Basic Equations 79

5.4.2 Numeric Solutions of Thomson Effect 83

5.4.3 Comparison between Thomson Effect and Ideal Equation 85

Problems 87

Projects 88

References 88

6 Thermal and Electrical Contact Resistances for Micro and Macro Devices 89

6.1 Modeling and Validation 89

6.2 Micro and Macro Thermoelectric Coolers 92

6.3 Micro and Macro Thermoelectric Generators 94

Problems 97

Computer Assignment 97

References 98

7 Modeling of Thermoelectric Generators and Coolers With Heat Sinks 99

7.1 Modeling of Thermoelectric Generators With Heat Sinks 99

7.2 Plate Fin Heat Sinks 108

7.3 Modeling of Thermoelectric Coolers With Heat Sinks 111

Problems 119

References 119

8 Applications 120

8.1 Exhaust Waste Heat Recovery 120

8.1.1 Recent Studies 120

8.1.2 Modeling of Module Tests 122

8.1.3 Modeling of a TEG 126

8.1.4 New Design of a TEG 133

8.2 Solar Thermoelectric Generators 138

8.2.1 Recent Studies 138

8.2.2 Modeling of a STEG 138

8.2.3 Optimal Design of a STEG (Dimensional Analysis) 144

8.2.4 New Design of a STEG 146

8.3 Automotive Thermoelectric Air Conditioner 149

8.3.1 Recent Studies 149

8.3.2 Modeling of an Air-to-Air TEAC 150

8.3.3 Optimal Design of a TEAC 157

8.3.4 New Design of a TEAC 160

Problems 162

References 163

9 Crystal Structure 164

9.1 Atomic Mass 164

9.1.1 Avogadro’s Number 164

Example 9.1 Mass of One Atom 164

9.2 Unit Cells of a Crystal 165

9.2.1 Bravais Lattices 166

Example 9.2 Lattice Constant of Gold 169

9.3 Crystal Planes 170

Example 9.3 Indices of a Plane 171

Problems 171

10 Physics of Electrons 172

10.1 Quantum Mechanics 172

10.1.1 Electromagnetic Wave 172

10.1.2 Atomic Structure 174

10.1.3 Bohr’s Model 174

10.1.4 Line Spectra 176

10.1.5 De Broglie Wave 177

10.1.6 Heisenberg Uncertainty Principle 178

10.1.7 Schrödinger Equation 178

10.1.8 A Particle in a One-Dimensional Box 179

10.1.9 Quantum Numbers 181

10.1.10 Electron Configurations 183

Example 10.1 Electronic Configuration of a Silicon Atom 184

10.2 Band Theory and Doping 185

10.2.1 Covalent Bonding 185

10.2.2 Energy Band 186

10.2.3 Pseudo-Potential Well 186

10.2.4 Doping, Donors, and Acceptors 187

Problems 188

References 188

11 Density of States, Fermi Energy, and Energy Bands 189

11.1 Current and Energy Transport 189

11.2 Electron Density of States 190

11.2.1 Dispersion Relation 190

11.2.2 Effective Mass 190

11.2.3 Density of States 191

11.3 Fermi-Dirac Distribution 193

11.4 Electron Concentration 194

11.5 Fermi Energy in Metals 195

Example 11.1 Fermi Energy in Gold 196

11.6 Fermi Energy in Semiconductors 197

Example 11.2 Fermi Energy in Doped Semiconductors 198

11.7 Energy Bands 199

11.7.1 Multiple Bands 200

11.7.2 Direct and Indirect Semiconductors 200

11.7.3 Periodic Potential (Kronig-Penney Model) 201

Problems 205

References 205

12 Thermoelectric Transport Properties for Electrons 206

12.1 Boltzmann Transport Equation 206

12.2 Simple Model of Metals 208

12.2.1 Electric Current Density 208

12.2.2 Electrical Conductivity 208

Example 12.1 Electron Relaxation Time of Gold 210

12.2.3 Seebeck Coefficient 210

Example 12.2 Seebeck Coefficient of Gold 212

12.2.4 Electronic Thermal Conductivity 212

Example 12.3 Electronic Thermal Conductivity of Gold 213

12.3 Power-Law Model for Metals and Semiconductors 213

12.3.1 Equipartition Principle 214

12.3.2 Parabolic Single-Band Model 215

Example 12.4 Seebeck Coefficient of PbTe 217

Example 12.5 Material Parameter 221

12.4 Electron Relaxation Time 222

12.4.1 Acoustic Phonon Scattering 222

12.4.2 Polar Optical Phonon Scattering 222

12.4.3 Ionized Impurity Scattering 223

Example 12.6 Electron Mobility 223

12.5 Multiband Effects 224

12.6 Nonparabolicity 225

Problems 228

References 229

13 Phonons 230

13.1 Crystal Vibration 230

13.1.1 One Atom in a Primitive Cell 230

13.1.2 Two Atoms in a Unit Cell 232

13.2 Specific Heat 234

13.2.1 Internal Energy 234

13.2.2 Debye Model 235

Example 13.1 Atomic Size and Specific Heat 239

13.3 Lattice Thermal Conductivity 241

13.3.1 Klemens-Callaway Model 241

13.3.2 Umklapp Processes 244

13.3.3 Callaway Model 244

13.3.4 Phonon Relaxation Times 245

Example 13.2 Lattice Thermal Conductivity 247

Problems 249

References 250

14 Low-Dimensional Nanostructures 251

14.1 Low-Dimensional Systems 251

14.1.1 Quantum Well (2D) 251

Example 14.1 Energy Levels of a Quantum Well 255

14.1.2 Quantum Wires (1D) 256

14.1.3 Quantum Dots (0D) 258

14.1.4 Thermoelectric Transport Properties of Quantum Wells 260

14.1.5 Thermoelectric Transport Properties of Quantum Wires 261

14.1.6 Proof-of-Principle Studies 263

14.1.7 Size Effects of Quantum Well on Lattice Thermal Conductivity 264

Problems 267

References 267

15 Generic Model of Bulk Silicon and Nanowires 268

15.1 Electron Density of States for Bulk and Nanowires 268

15.1.1 Density of States 268

15.2 Carrier Concentrations for Two-band Model 269

15.2.1 Bulk 269

15.2.2 Nanowires 269

15.2.3 Bipolar Effect and Fermi Energy 269

15.3 Electron Transport Properties for Bulk and Nanowires 270

15.3.1 Electrical Conductivity 270

15.3.2 Seebeck Coefficient 270

15.3.3 Electronic Thermal Conductivity 270

15.4 Electron Scattering Mechanisms 271

15.4.1 Acoustic-Phonon Scattering 271

15.4.2 Ionized Impurity Scattering 272

15.4.3 Polar Optical Phonon Scattering 272

15.5 Lattice Thermal Conductivity 273

15.6 Phonon Relaxation Time 273

15.7 Input Data for Bulk Si and Nanowires 275

15.8 Bulk Si 275

15.8.1 Fermi Energy 275

15.8.2 Electron Mobility 275

15.8.3 Thermoelectric Transport Properties 275

15.8.4 Dimensionless Figure of Merit 276

15.9 Si Nanowires 276

15.9.1 Electron Properties 276

15.9.2 Phonon Properties for Si Nanowires 280

Problems 282

References 284

16 Theoretical Model of Thermoelectric Transport Properties 286

16.1 Introduction 286

16.2 Theoretical Equatons 287

16.2.1 Carrier Transport Properties 287

16.2.2 Scattering Mechanisms for Electron Relaxation Times 290

16.2.3 Lattice Thermal Conductivity 293

16.2.4 Phonon Relaxation Times 293

16.2.5 Phonon Density of States and Specific Heat 295

16.2.6 Dimensionless Figure of Merit 295

16.3 Results and Discussion 295

16.3.1 Electron or Hole Scattering Mechanisms 295

16.3.2 Transport Properties 299

16.4 Summary 315

Problems 316

References 316

Appendix A Physical Properties 323

Appendix B Optimal Dimensionless Parameters for TEGs with ZT12=1 353

Appendix C ANSYS TEG Tutorial 365

Appendix D Periodic Table 376

Appendix E Thermoelectric Properties 391

Appendix F Fermi Integral 399

Appendix G Hall Factor 402

Appendix H Conversion Factors 405

Index 409

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Author Information

HoSung Lee is a Professor in the Department of Mechanical and Aerospace Engineering at Western Michigan University. His main areas of research include energy conversion, and thermoelectrics with particular focus on optimal design and applications, thermal design and automotive engine cooling and fuel efficiency. He also teaches numerous courses in the area of thermodynamics and heat transfer.

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