Thermal Design
Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells
2. Edition June 2022
928 Pages, Hardcover
Professional Book
ISBN:
978-1-119-68597-5
John Wiley & Sons
Further versions
Thermal Design
Discover a new window to thermal engineering and thermodynamics through the study of thermal design
Thermal engineering is a specialized sub-discipline of mechanical engineering that focuses on the movement and transfer of heat energy between two mediums or altered into other forms of energy. Thermal engineers must have a strong knowledge of thermodynamics and the processes that convert generated energy from thermal sources into chemical, mechanical, or electrical energy -- as such, thermal engineers can be employed in many industries, particularly in automotive manufacturing, commercial construction, and the HVAC industry. As part of their job, thermal engineers often have to improve a current system to make it more efficient, and so must be aware of a wide array of variables and familiar with a broad sweep of systems to ensure the work they do is economically viable.
In this significantly updated new edition, Thermal Design details the physical mechanisms of standard thermal devices while integrating essential formulas and detailed derivations to give a practical understanding of the field to students. The textbook examines the design of thermal devices through mathematical modeling, graphical optimization, and occasionally computational-fluid-dynamic (CFD) simulation. Moreover, it presents information on significant thermal devices such as heat sinks, thermoelectric generators and coolers, heat pipes, and heat exchangers as design components in larger systems -- all of which are increasingly important and fundamental to numerous fields such as microelectronic cooling, green or thermal energy conversion, and thermal control and management in space.
Readers of the Second Edition of Thermal Design will also find:
* A new chapter on thermoelectrics that reflects the latest modern technology that has recently been developed
* More problems and examples to help clarify points throughout the book
* A range of appendices, including new additions, that include more specifics on topicscovered in the book, tutorials for applications, and computational work
* A solutions manual provided on a companion website
Thermal Design is a useful reference for engineers and researchers in me chanical engineering, as well as senior undergraduate and graduate students in mechanical engineering.
Preface to the Second Edition xix
Preface to the First Edition xxi
About the Companion Website xxv
1 Introduction 1
1.1 Introduction 1
1.2 Humans and Energy 1
1.3 Thermodynamics 2
1.3.1 Energy, Heat, and Work 2
1.3.2 The First Law of Thermodynamics 2
1.3.3 Heat Engines, Refrigerators, and Heat Pumps 5
1.3.4 The Second Law of Thermodynamics 7
1.3.5 Carnot Cycle 7
1.4 Heat Transfer 11
1.4.1 Introduction 11
1.4.2 Conduction 12
1.4.3 Convection 15
1.4.3.1 Parallel Flow on an Isothermal Plate 16
1.4.3.2 A Cylinder in Cross Flow 18
1.4.3.3 Flow in Ducts 20
1.4.3.4 Free Convection 25
1.4.4 Radiation 29
1.4.4.1 Thermal Radiation 29
1.4.4.2 View Factor 34
1.4.4.3 Radiation Exchange Between Diffuse-Gray Surfaces 34
Problems 38
References 42
2 Heat Sinks 45
2.1 Longitudinal Fin of Rectangular Profile 45
2.2 Heat Transfer from Fin 47
2.3 Fin Effectiveness 48
2.4 Fin Efficiency 48
2.5 Corrected Profile Length 49
2.6 Optimizations 49
2.6.1 Constant Profile Area A p 49
2.6.2 Constant Heat Transfer from a Fin 52
2.6.3 Constant Fin Volume or Mass 53
2.6.4 Optimum Dimensions of Rectangular Fin 55
2.6.5 Radial Fins 60
2.6.6 Optimization of Radial Fins 63
2.7 Plate Fin Heat Sinks 68
2.7.1 Free (Natural) Convection Cooling 68
2.7.1.1 Small Spacing Channel 68
2.7.1.2 Large Spacing Channel 71
2.7.1.3 Optimum Fin Spacing 71
2.7.2 Forced Convection Cooling 72
2.7.2.1 Small Spacing Channel 73
2.7.2.2 Large Spacing Channel 74
2.8 Multiple Fin Array Ii 75
2.8.1 Natural (Free) Convection Cooling 77
2.9 Thermal Resistance and Overall Surface Efficiency 78
2.10 Fin Design with Thermal Radiation 97
2.10.1 Single Longitudinal Fin with Radiation 97
Problems 109
Computer Assignments 116
Project 116
References 117
3 Heat Pipes 119
3.1 Operation of Heat Pipe 119
3.2 Surface Tension 120
3.3 Heat Transfer Limitations 122
3.3.1 Capillary Limitation 123
3.3.1.1 Maximum Capillary Pressure Difference 123
3.3.1.2 Vapor Pressure Drop 125
3.3.1.3 Liquid Pressure Drop 127
3.3.1.4 Normal Hydrostatic Pressure Drop 127
3.3.1.5 Axial Hydrostatic Pressure Drop 128
3.3.2 Approximation for Capillary Pressure Difference 128
3.3.3 Sonic Limitation 128
3.3.4 Entrainment Limitation 129
3.3.5 Boiling Limitation 129
3.3.6 Viscous Limitation 130
3.3.6.1 Summary of Heat Transport Limits 134
3.3.6.2 Effective Thermal Conductivity 135
3.4 Heat Pipe Thermal Resistance 136
3.4.1 Contact Resistance 138
3.5 Variable Conductance Heat Pipes (VCHP) 141
3.5.1 Gas-Loaded Heat Pipes 141
3.5.2 Clayepyron-Clausius Equation 143
3.5.3 Applications 144
3.6 Loop Heat Pipes 146
3.7 Micro Heat Pipes 148
3.7.1 Steady-State Models 148
3.7.1.1 Conventional Model 148
3.7.1.2 Cotter's Model 150
3.8 Working Fluid 154
3.8.1 Figure of Merit 154
3.8.2 Compatibility 156
3.9 Wick Structures 157
3.10 Design Example 158
3.10.1 Selection of Material and Working Fluid 158
3.10.2 Working Fluid Properties 159
3.10.2.1 Estimation of Vapor Space Radius 159
3.10.3 Estimation of Operating Limits 159
3.10.3.1 Capillary Limits 159
3.10.3.2 Sonic Limits 160
3.10.3.3 Entrainment Limits 160
3.10.3.4 Boiling Limits 161
3.10.4 Wall Thickness 162
3.10.5 Wick Selection 163
3.10.6 Maximum Arterial Depth 164
3.10.7 Design of Arterial Wick 165
3.10.8 Capillary Limitation 166
3.10.8.1 Liquid Pressure Drop in the Arteries 167
3.10.8.2 Liquid Pressure Drop in the Circumferential Wick 167
3.10.8.3 Vapor Pressure Drop in the Vapor Space 168
3.10.9 Performance Map 169
3.10.10 Check the Temperature Drop 170
Problems 170
Design Problem 173
References 174
4 Compact Heat Exchangers 177
4.1 Introduction 177
4.2 Fundamentals of Heat Exchangers 180
4.2.1 Counterflow and Parallel Flows 180
4.2.2 Overall Heat Transfer Coefficient 182
4.2.3 Log Mean Temperature Difference (LMTD) 184
4.2.4 Flow Properties 186
4.2.5 Nusselt Numbers 186
4.2.6 Effectiveness-NTU (epsilon-NTU) Method 189
4.2.6.1 Parallel Flow 191
4.2.6.2 Counterflow 192
4.2.6.3 Crossflow 192
4.2.7 Heat Exchanger Pressure Drop 199
4.2.8 Fouling Resistances (Fouling Factors) 201
4.2.9 Overall Surface (Fin) Efficiency 202
4.2.10 Reasonable Velocities of Various Fluids in Pipe Flow 203
4.3 Double-Pipe Heat Exchangers 204
4.4 Shell-and-Tube Heat Exchangers 213
4.4.1 Baffles 214
4.4.2 Multiple Passes 214
4.4.3 Dimensions of Shell-and-Tube Heat Exchanger 215
4.4.4 Shell-Side Tube Layout 215
4.5 Plate Heat Exchangers (PHEs) 224
4.5.1 Flow Pass Arrangements 224
4.5.2 Geometric Properties 226
4.5.3 Friction Factor 231
4.5.4 Nusselt Number 231
4.5.5 Pressure Drops 231
4.6 Pressure Drops in Compact Heat Exchangers 245
4.6.1 Fundamentals of Core Pressure Drop 246
4.6.2 Core Entrance and Exit Pressure Drops 248
4.6.3 Contraction and Expansion Loss Coefficients 249
4.6.3.1 Circular-Tube Core 250
4.6.3.2 Square-Tube Core 251
4.6.3.3 Flat-Tube Core 252
4.6.3.4 Triangular-Tube Core 252
4.7 Finned-Tube Heat Exchangers 257
4.7.1 Geometrical Characteristics 258
4.7.2 Flow Properties 259
4.7.3 Thermal Properties 260
4.7.4 Correlations for Circular Finned-Tube Geometry 260
4.7.5 Pressure Drop 261
4.7.6 Correlations for Louvered Plate-Fin Flat-Tube Geometry 263
4.8 Plate-Fin Heat Exchangers 275
4.8.1 Geometric Characteristics 275
4.8.2 Correlations for Offset Strip Fin (OSF) Geometry 277
4.9 Louver-Fin-Type Flat-Tube Plate-Fin Heat Exchangers 297
4.9.1 Geometric Characteristics 298
4.9.2 Correlations for Louver Fin Geometry 300
4.10 Plate-Finned Heat Pipe Heat Exchanger 314
4.10.1 Geometric Characteristics 314
4.10.2 Correlations for Plate-Finned Circular Tube Heat Exchanger 315
4.10.3 Fin Efficiency 317
4.10.4 Heat Pipes 318
4.10.5 Analytical Model for Plate-Finned Heat Pipe Heat Exchanger 319
Problems 320
References 332
5 Thermoelectric Design 335
5.1 Introduction 335
5.1.1 Thermoelectric Effect 337
5.1.2 Seebeck Effect 337
5.1.3 Peltier Effect 338
5.1.4 Thomson Effect 338
5.1.5 Thomson (or Kelvin) Relationships 339
5.1.6 The Figure of Merit 339
5.1.7 New Generation Thermoelectrics 339
5.2 Thermoelectric Generators 341
5.2.1 Ideal Equations 341
5.2.2 Performance Parameters of a Thermoelectric Module 344
5.2.3 Maximum Parameters for a Thermoelectric Module 345
5.2.4 Normalized Parameters 345
5.2.5 Effective Material Properties 351
5.2.6 Comparison of Calculations with a Commercial Product 352
5.2.7 Figure of Merit and Optimum Geometry 353
5.3 Thermoelectric Coolers and Heat Pumps 354
5.3.1 Ideal Equations 355
5.3.2 Maximum Parameters 358
5.3.3 Normalized Parameters for Thermoelectric Coolers 359
5.3.4 Normalized Parameters for Thermoelectric Heat Pumps 363
5.3.5 Effective Material Properties 371
5.3.5.1 Comparison of Calculations with a Commercial Product 373
5.4 Optimal Design 373
5.4.1 Introduction 373
5.4.2 Optimal Design for Thermoelectric Generators 374
5.4.3 Optimal Design of Thermoelectric Coolers and Heat Pumps 383
5.4.3.1 Thermoelectric Heat Pumps 387
5.4.3.2 Heat Sinks Without Thermoelectric Cooler Module 388
5.5 Thomson Effect, Exact Solution, and Compatibility Factor 398
5.5.1 Thermodynamics of Thomson Effect 398
5.5.1.1 Seebeck Effect 398
5.5.1.2 Peltier Effect 399
5.5.1.3 Thomson Effect 399
5.5.1.4 Thomson (or Kelvin) Relationships 400
5.5.2 Exact Solutions 402
5.5.2.1 Equations for the Exact Solutions and the Ideal Equation 402
5.5.2.2 Thermoelectric Generator 404
5.5.2.3 Thermoelectric Coolers 405
5.5.3 Compatibility Factor 407
5.5.3.1 Reduced Current Density 407
5.5.3.2 Heat Balance Equation 408
5.5.3.3 Numerical Solution 408
5.5.3.4 Infinitesimal Efficiency 409
5.5.3.5 Reduced Efficiency 409
5.5.3.6 Reduced Efficiency 409
5.5.3.7 Compatibility Factor 409
5.5.3.8 Segmented Thermoelements 410
5.5.3.9 Thermoelectric Potential 410
5.5.4 Thomson Effects 413
5.5.4.1 Formulation of Basic Equations 413
5.5.4.2 Numeric Solutions of Thomson Effect 416
5.5.4.3 Comparison Between Thomson Effect and Ideal Equation 418
5.6 Thermal and Electrical Contact Resistances for Micro and Macro Devices 421
5.6.1 Modeling and Validation 421
5.6.1.1 Cancelation of Spreading Resistance with Thermal Contact Resistance 422
5.6.1.2 Thermoelectric Coolers 423
5.6.1.3 Thermoelectric Generators 423
5.6.1.4 Validation of Model 423
5.6.2 Micro and Macro Thermoelectric Coolers 425
5.6.2.1 Effect of Leg Length 426
5.6.2.2 Effect of Material on Ceramic Plate 426
5.6.3 Micro and Macro Thermoelectric Generators 427
5.6.3.1 Model and Verification for Macro TE Generators 427
5.6.3.2 Effect of Load Resistance 428
5.6.3.3 Effect of Leg Length and Ceramic Material 429
5.7 Modeling of Thermoelectric Generators and Coolers with Heat Sinks 430
5.7.1 Modeling of Thermoelectric Generators with Heat Sinks 430
5.7.1.1 Modeling 430
5.7.1.2 Heat Sink Area and Cross Flow Area for Heat Sinks 433
5.7.1.3 Mass Flow Rates 433
5.7.1.4 Convection Heat Transfer Coefficients 434
5.7.1.5 Single-Fin Efficiencies 434
5.7.1.6 Overall Fin Efficiencies 435
5.7.1.7 Thermal Resistances of Heat Sink and Aluminum Block 435
5.7.1.8 Effective Material Properties 436
5.7.1.9 Comparison of Model and Measurements 437
5.7.1.10 Optimal Design of Heat Sink 437
5.7.1.11 Optimal Design of Thermoelectric Module 438
5.7.2 Plate-Fin Heat Sinks 438
5.7.2.1 Nusselt Number for Air 439
5.7.2.2 Turbulent Flow for Gases and Liquids 440
5.7.2.3 Optimal Design of Heat Sink 441
5.7.2.4 Single-Fin Efficiency 441
5.7.2.5 Overall Fin Efficiency 442
5.7.3 Modeling of Thermoelectric Coolers with Heat Sinks 442
5.7.3.1 Modeling 442
5.7.3.2 Heat Sink Area and Cross Flow Area for Heat Sinks 445
5.7.3.3 Mass Flow Rates 445
5.7.3.4 Convection Heat Transfer Coefficients 446
5.7.3.5 Single-Fin Efficiencies 446
5.7.3.6 Overall Fin Efficiencies 446
5.7.3.7 Thermal Resistances of Heat Sink and Aluminum Block 447
5.7.3.8 Effective Material Properties 447
5.7.3.9 Comparison of Model and Measurements 448
5.7.3.10 Conclusions 449
5.8 Applications 449
5.8.1 Exhaust Waste Heat Recovery 449
5.8.1.1 Recent Studies 449
5.8.1.2 Modeling of Module Tests 452
5.8.1.3 Modeling of TEG 455
5.8.1.4 New Design of TEG 462
5.8.2 Solar Thermoelectric Generators (STEGs) 466
5.8.2.1 Recent Studies 466
5.8.2.2 Modeling of a STEG 467
5.8.2.3 Optimal Design of STEG (Dimensional Analysis) 473
5.8.2.4 New Design of STEG 475
5.8.3 Automotive Thermoelectric Air Conditioner (TEAC) 479
5.8.3.1 Recent Studies 479
5.8.3.2 Modeling of Air-to-Air TEAC 480
5.8.3.3 Optimal Design of TEAC 487
5.8.3.4 New Design of TEAC 490
Problems 493
Computer Assignment 496
Projects 504
Computer Assignments 504
Computer Projects 504
References 505
6 Thermoelectric Materials 509
6.1 Crystal Structure 509
6.1.1 Atomic Mass 509
6.1.1.1 Avogadro's Number 509
6.1.2 Unit Cells of a Crystal 510
6.1.2.1 Bravais Lattices 511
6.1.3 Crystal Planes 515
6.2 Physics of Electrons 517
6.2.1 Quantum Mechanics 517
6.2.1.1 Electromagnetic Wave 517
6.2.1.2 Atomic Structure 519
6.2.1.3 Bohr's Model 520
6.2.1.4 Line Spectra 521
6.2.1.5 De Broglie Wave 522
6.2.1.6 Heisenberg Uncertainty Principle 523
6.2.1.7 Schrödinger Equation 524
6.2.1.8 A Particle in a One-Dimensional Box 524
6.2.1.9 Quantum Numbers 527
6.2.1.10 Electron Configurations 528
6.2.2 Band Theory and Doping 530
6.2.2.1 Covalent Bonding 530
6.2.2.2 Energy Band 531
6.2.2.3 Pseudo-Potential Well 532
6.2.2.4 Doping, Donors, and Acceptors 532
6.3 Density of States, Fermi Energy, and Energy Bands 534
6.3.1 Current and Energy Transport 534
6.3.2 Electron Density of States 535
6.3.2.1 Dispersion Relation 535
6.3.2.2 Effective Mass 535
6.3.2.3 Density of States 536
6.3.3 Fermi-Dirac Distribution 538
6.3.4 Electron Concentration 538
6.3.5 Fermi Energy in Metals 539
6.3.6 Fermi Energy in Semiconductors 541
6.3.7 Energy Bands 543
6.3.7.1 Multiple Bands 544
6.3.7.2 Direct and Indirect Semiconductors 545
6.3.7.3 Periodic Potential (Kronig-Penney Model) 545
6.4 Thermoelectric Transport Properties for Electrons 549
6.4.1 Boltzmann Transport Equation 549
6.4.2 Simple Model of Metals 552
6.4.2.1 Electric Current Density 552
6.4.2.2 Electrical Conductivity 552
6.4.2.3 Seebeck Coefficient 553
6.4.2.4 Electronic Thermal Conductivity 555
6.4.3 Power-Law Model for Metals and Semiconductors 556
6.4.3.1 Equipartition Principle 556
6.4.3.2 Parabolic Single-Band Model 557
6.4.4 Electron Relaxation Time 563
6.4.4.1 Acoustic-Phonon Scattering 563
6.4.4.2 Polar Optical Phonon Scattering 564
6.4.4.3 Ionized Impurity Scattering 564
6.4.4.4 Total Electron Relaxation Time 565
6.4.5 Multiband Effects 566
6.4.6 Nonparabolicity 567
6.4.6.1 Nonparabolic Density of States 567
6.5 Phonons 569
6.5.1 Crystal Vibration 569
6.5.1.1 One Atom in a Primitive Cell 569
6.5.1.2 Two Atoms in a Unit Cell 571
6.5.2 Specific Heat 573
6.5.2.1 Internal Energy 573
6.5.2.2 Debye Model 575
6.5.3 Lattice Thermal Conductivity 580
6.5.3.1 Klemens-Callaway Model 580
6.5.3.2 Umklapp Processes 582
6.5.3.3 Callaway Model 583
6.5.3.4 Phonon Relaxation Times 584
6.6 Low-Dimensional Nanostructures 587
6.6.1 Low-Dimensional Systems 588
6.6.1.1 Quantum Well (2D) 588
6.6.1.2 Quantum Wires (1D) 592
6.6.1.3 Quantum Dots (0D) 595
6.6.1.4 Thermoelectric Transport Properties of Quantum Wells 595
6.6.1.5 Thermoelectric Transport Properties of Quantum Wires 597
6.6.1.6 Proof-of-Principle Studies 598
6.6.1.7 Size Effects of Quantum Well on Lattice Thermal Conductivity 600
6.7 Generic Model of Bulk Silicon and Nanowires 602
6.7.1 Electron Density of States for Bulk and Nanowires 603
6.7.1.1 Density of States 603
6.7.2 Carrier Concentrations for Two-Band Model 603
6.7.2.1 Bulk 603
6.7.2.2 Nanowires 604
6.7.2.3 Bipolar Effect and Fermi Energy 604
6.7.3 Electron Transport Properties for Bulk and Nanowires 604
6.7.3.1 Electrical Conductivity 604
6.7.3.2 Seebeck Coefficient 605
6.7.3.3 Electronic Thermal Conductivity 605
6.7.4 Electron Scattering Mechanisms 605
6.7.4.1 Acoustic-Phonon Scattering 605
6.7.4.2 Ionized Impurity Scattering 606
6.7.4.3 Screening Effect 606
6.7.4.4 Polar Optical Phonon Scattering 606
6.7.4.5 Total Electron Relaxation Time 607
6.7.5 Lattice Thermal Conductivity 607
6.7.6 Phonon Relaxation Time 607
6.7.7 Input Data for Bulk Si and Nanowires 608
6.7.8 Bulk Si 608
6.7.8.1 Fermi Energy 609
6.7.8.2 Electron Mobility 610
6.7.8.3 Thermoelectric Transport Properties 610
6.7.8.4 Dimensionless Figure of Merit 610
6.7.9 Si Nanowires 611
6.7.9.1 Fermi Energy and Carrier Concentration 611
6.7.9.2 Electron Mobility 612
6.7.9.3 Thermoelectric Transport Properties for Si Nanowires 612
6.7.9.4 Dimensionless Figure of Merit 614
6.7.9.5 Effect of Size for Nanowires 614
6.7.9.6 Critical Nanowire Diameter 615
6.7.9.7 Phonon Properties for Si Nanowires 616
6.8 Theoretical Model of Thermoelectric Transport Properties 617
6.8.1 Introduction 618
6.8.2 Theoretical Equations 619
6.8.2.1 Carrier Transport Properties 619
6.8.2.2 Scattering Mechanisms for Electron Relaxation Times 621
6.8.2.3 Lattice Thermal Conductivity 624
6.8.2.4 Phonon Relaxation Times 625
6.8.2.5 Phonon Density of States and Specific Heat 626
6.8.2.6 Dimensionless Figure of Merit 627
6.8.3 Results and Discussion 627
6.8.3.1 Electron or Hole Scattering Mechanisms 627
6.8.4 Summary 647
Problems 649
References 657
7 Solar Cells 667
7.1 Introduction 667
7.1.1 Operation of Solar Cells 669
7.1.2 Solar Cells and Technology 671
7.1.3 Solar Irradiance 672
7.1.4 Air Mass 672
7.1.5 Nature of Light 674
7.2 Quantum Mechanics 675
7.2.1 Atomic Structure 677
7.2.2 Bohr's Model 677
7.2.3 Line Spectra 679
7.2.4 De Broglie Wave 680
7.2.5 Heisenberg Uncertainty Principle 681
7.2.6 Schrödinger Equation 682
7.2.7 A Free Particle in a 1D Box 682
7.2.8 Quantum Numbers 685
7.2.9 Electron Configurations 686
7.2.10 Van der Waals Forces 688
7.2.11 Covalent Bonding 689
7.2.12 Energy Band 690
7.2.13 Pseudo-Potential Well 691
7.3 Density of States 691
7.3.1 Number of States 691
7.3.2 Effective Mass 692
7.4 Equilibrium Intrinsic Carrier Concentration 693
7.4.1 Fermi Function 693
7.4.2 Nondegenerate Semiconductor 693
7.4.3 Equilibrium Electron and Hole Concentrations 694
7.4.4 Intrinsic Semiconductors 696
7.4.5 Intrinsic Carrier Concentration, N I 696
7.4.6 Intrinsic Fermi Energy 698
7.4.7 Alternative Expression for n 0 and p 0 698
7.5 Extrinsic Semiconductors in Thermal Equilibrium 699
7.5.1 Doping, Donors, and Acceptors 699
7.5.2 Extrinsic Carrier Concentration in Equilibrium 700
7.5.3 Built-in Voltage 702
7.5.4 Principle of Detailed Balance 703
7.5.5 Majority and Minority Carriers in Equilibrium 703
7.6 Generation and Recombination 704
7.6.1 Direct and Indirect Band Gap Semiconductors 704
7.6.2 Absorption Coefficient 705
7.6.3 Photogeneration 707
7.7 Recombination 707
7.7.1 Recombination Mechanisms 707
7.7.2 Band Energy Diagram Under Nonequilibrium Conditions 709
7.7.2.1 Back Surface Field (BSF) 710
7.7.3 Low-Level Injection 710
7.7.3.1 Low-Level Injection 711
7.7.4 Band-to-Band Recombination 712
7.7.5 Trap-Assisted (SRH) Recombination 713
7.7.6 Simplified Expression of the SRH Recombination Rate 714
7.7.7 Auger Recombination 715
7.7.8 Total Recombination Rate 716
7.8 Carrier Transport 716
7.8.1 Drift 717
7.8.2 Carrier Mobility 717
7.8.3 Diffusion 718
7.8.4 Total Current Densities 719
7.8.5 Einstein Relationship 719
7.8.6 Semiconductor Equations 720
7.8.7 Minority-Carrier Diffusion Equations 720
7.8.8 p-n Junction 721
7.8.9 Calculation of Depletion Width 723
7.8.10 Energy Band Diagram with a Reference Point 725
7.8.11 Quasi-Fermi Energy Levels 725
7.9 Minority Carrier Transport 726
7.9.1 Boundary Conditions 726
7.9.2 Minority Carrier Lifetimes 728
7.9.3 Minority Carrier Diffusion Lengths 728
7.9.4 Minority Carrier Diffusion Equation for Holes 729
7.9.5 Minority Carrier Diffusion Equation for Electrons 732
7.10 Characteristics of Solar Cells 735
7.10.1 Current Density 735
7.10.2 Current-Voltage Characteristics 740
7.10.3 Figures of Merit 742
7.10.4 Effect of Minority Electron Lifetime on Efficiency 744
7.10.5 Effect of Minority Hole Lifetime on Efficiency 746
7.10.6 Effect of Back Surface Recombination Velocity on Efficiency 746
7.10.7 Effect of Base Width on Efficiency 747
7.10.8 Effect of Emitter Width W N on Efficiency 748
7.10.9 Effect of Acceptor Concentration on Efficiency 750
7.10.10 Effect of Donor Concentration on Efficiency 752
7.10.11 Band Gap Energy with Temperature 752
7.10.12 Effect of Temperature on Efficiency 753
7.11 Additional Topics 754
7.11.1 Parasitic Resistance Effects (Ohmic Losses) 754
7.11.2 Quantum Efficiency 757
7.11.3 Ideal Solar Cell Efficiency 758
7.12 Modeling 763
7.12.1 Modeling for a Silicon Solar Cell 763
7.12.2 Comparison of the Solar Cell Model with a Commercial Product 776
7.13 Design of a Solar Cell 779
7.13.1 Solar Cell Geometry with Surface Recombination Velocities 779
7.13.2 Donor and Acceptor Concentrations 780
7.13.3 Minority Carrier Diffusion Lifetimes 780
7.13.4 Grid Spacing 781
7.13.5 Antireflection, Light Trapping, and Passivation 784
Problems 785
References 789
Appendix A Thermophysical Properties 791
References 834
Appendix B 837
B.1 Optimal Dimensionless Parameters for TEGs with ZT infinity 2 = 1 (See Figure B.1 at the end of tables) 837
B.2 Optimal Dimensionless Parameters for TECS With ZT infinity 2 = 1 (See Figure B.2 at the end of tables) 837
Appendix C Pipe Dimensions 847
Appendix D Periodic Table 849
Appendix E Thermoelectric Properties 857
E.1 Bismuth Telluride P-Type 858
E.2 Bismuth Telluride N-Type 859
E.3 Lead Telluride P-Type 859
E.4 Silicon Germanium N-Type 860
E.5 Skutterudites N-Type 861
E.6 Zintl Compound N-Type 861
References 862
Appendix F Fermi Integral 863
Appendix G Hall Factor 867
References 869
Appendix H Curve Fitting of Working Fluids 871
H.1 Curve Fit for Working Fluids Chosen 871
H.2 Curve Fitting for Working Fluid Properties Chosen 872
H.2.1 MathCad Format 872
Appendix L Tutorial for MathCAD 875
L.1 Tutorial Problem for MathCAD 875
Appendix M Conversion Factors 879
Index 881
Preface to the First Edition xxi
About the Companion Website xxv
1 Introduction 1
1.1 Introduction 1
1.2 Humans and Energy 1
1.3 Thermodynamics 2
1.3.1 Energy, Heat, and Work 2
1.3.2 The First Law of Thermodynamics 2
1.3.3 Heat Engines, Refrigerators, and Heat Pumps 5
1.3.4 The Second Law of Thermodynamics 7
1.3.5 Carnot Cycle 7
1.4 Heat Transfer 11
1.4.1 Introduction 11
1.4.2 Conduction 12
1.4.3 Convection 15
1.4.3.1 Parallel Flow on an Isothermal Plate 16
1.4.3.2 A Cylinder in Cross Flow 18
1.4.3.3 Flow in Ducts 20
1.4.3.4 Free Convection 25
1.4.4 Radiation 29
1.4.4.1 Thermal Radiation 29
1.4.4.2 View Factor 34
1.4.4.3 Radiation Exchange Between Diffuse-Gray Surfaces 34
Problems 38
References 42
2 Heat Sinks 45
2.1 Longitudinal Fin of Rectangular Profile 45
2.2 Heat Transfer from Fin 47
2.3 Fin Effectiveness 48
2.4 Fin Efficiency 48
2.5 Corrected Profile Length 49
2.6 Optimizations 49
2.6.1 Constant Profile Area A p 49
2.6.2 Constant Heat Transfer from a Fin 52
2.6.3 Constant Fin Volume or Mass 53
2.6.4 Optimum Dimensions of Rectangular Fin 55
2.6.5 Radial Fins 60
2.6.6 Optimization of Radial Fins 63
2.7 Plate Fin Heat Sinks 68
2.7.1 Free (Natural) Convection Cooling 68
2.7.1.1 Small Spacing Channel 68
2.7.1.2 Large Spacing Channel 71
2.7.1.3 Optimum Fin Spacing 71
2.7.2 Forced Convection Cooling 72
2.7.2.1 Small Spacing Channel 73
2.7.2.2 Large Spacing Channel 74
2.8 Multiple Fin Array Ii 75
2.8.1 Natural (Free) Convection Cooling 77
2.9 Thermal Resistance and Overall Surface Efficiency 78
2.10 Fin Design with Thermal Radiation 97
2.10.1 Single Longitudinal Fin with Radiation 97
Problems 109
Computer Assignments 116
Project 116
References 117
3 Heat Pipes 119
3.1 Operation of Heat Pipe 119
3.2 Surface Tension 120
3.3 Heat Transfer Limitations 122
3.3.1 Capillary Limitation 123
3.3.1.1 Maximum Capillary Pressure Difference 123
3.3.1.2 Vapor Pressure Drop 125
3.3.1.3 Liquid Pressure Drop 127
3.3.1.4 Normal Hydrostatic Pressure Drop 127
3.3.1.5 Axial Hydrostatic Pressure Drop 128
3.3.2 Approximation for Capillary Pressure Difference 128
3.3.3 Sonic Limitation 128
3.3.4 Entrainment Limitation 129
3.3.5 Boiling Limitation 129
3.3.6 Viscous Limitation 130
3.3.6.1 Summary of Heat Transport Limits 134
3.3.6.2 Effective Thermal Conductivity 135
3.4 Heat Pipe Thermal Resistance 136
3.4.1 Contact Resistance 138
3.5 Variable Conductance Heat Pipes (VCHP) 141
3.5.1 Gas-Loaded Heat Pipes 141
3.5.2 Clayepyron-Clausius Equation 143
3.5.3 Applications 144
3.6 Loop Heat Pipes 146
3.7 Micro Heat Pipes 148
3.7.1 Steady-State Models 148
3.7.1.1 Conventional Model 148
3.7.1.2 Cotter's Model 150
3.8 Working Fluid 154
3.8.1 Figure of Merit 154
3.8.2 Compatibility 156
3.9 Wick Structures 157
3.10 Design Example 158
3.10.1 Selection of Material and Working Fluid 158
3.10.2 Working Fluid Properties 159
3.10.2.1 Estimation of Vapor Space Radius 159
3.10.3 Estimation of Operating Limits 159
3.10.3.1 Capillary Limits 159
3.10.3.2 Sonic Limits 160
3.10.3.3 Entrainment Limits 160
3.10.3.4 Boiling Limits 161
3.10.4 Wall Thickness 162
3.10.5 Wick Selection 163
3.10.6 Maximum Arterial Depth 164
3.10.7 Design of Arterial Wick 165
3.10.8 Capillary Limitation 166
3.10.8.1 Liquid Pressure Drop in the Arteries 167
3.10.8.2 Liquid Pressure Drop in the Circumferential Wick 167
3.10.8.3 Vapor Pressure Drop in the Vapor Space 168
3.10.9 Performance Map 169
3.10.10 Check the Temperature Drop 170
Problems 170
Design Problem 173
References 174
4 Compact Heat Exchangers 177
4.1 Introduction 177
4.2 Fundamentals of Heat Exchangers 180
4.2.1 Counterflow and Parallel Flows 180
4.2.2 Overall Heat Transfer Coefficient 182
4.2.3 Log Mean Temperature Difference (LMTD) 184
4.2.4 Flow Properties 186
4.2.5 Nusselt Numbers 186
4.2.6 Effectiveness-NTU (epsilon-NTU) Method 189
4.2.6.1 Parallel Flow 191
4.2.6.2 Counterflow 192
4.2.6.3 Crossflow 192
4.2.7 Heat Exchanger Pressure Drop 199
4.2.8 Fouling Resistances (Fouling Factors) 201
4.2.9 Overall Surface (Fin) Efficiency 202
4.2.10 Reasonable Velocities of Various Fluids in Pipe Flow 203
4.3 Double-Pipe Heat Exchangers 204
4.4 Shell-and-Tube Heat Exchangers 213
4.4.1 Baffles 214
4.4.2 Multiple Passes 214
4.4.3 Dimensions of Shell-and-Tube Heat Exchanger 215
4.4.4 Shell-Side Tube Layout 215
4.5 Plate Heat Exchangers (PHEs) 224
4.5.1 Flow Pass Arrangements 224
4.5.2 Geometric Properties 226
4.5.3 Friction Factor 231
4.5.4 Nusselt Number 231
4.5.5 Pressure Drops 231
4.6 Pressure Drops in Compact Heat Exchangers 245
4.6.1 Fundamentals of Core Pressure Drop 246
4.6.2 Core Entrance and Exit Pressure Drops 248
4.6.3 Contraction and Expansion Loss Coefficients 249
4.6.3.1 Circular-Tube Core 250
4.6.3.2 Square-Tube Core 251
4.6.3.3 Flat-Tube Core 252
4.6.3.4 Triangular-Tube Core 252
4.7 Finned-Tube Heat Exchangers 257
4.7.1 Geometrical Characteristics 258
4.7.2 Flow Properties 259
4.7.3 Thermal Properties 260
4.7.4 Correlations for Circular Finned-Tube Geometry 260
4.7.5 Pressure Drop 261
4.7.6 Correlations for Louvered Plate-Fin Flat-Tube Geometry 263
4.8 Plate-Fin Heat Exchangers 275
4.8.1 Geometric Characteristics 275
4.8.2 Correlations for Offset Strip Fin (OSF) Geometry 277
4.9 Louver-Fin-Type Flat-Tube Plate-Fin Heat Exchangers 297
4.9.1 Geometric Characteristics 298
4.9.2 Correlations for Louver Fin Geometry 300
4.10 Plate-Finned Heat Pipe Heat Exchanger 314
4.10.1 Geometric Characteristics 314
4.10.2 Correlations for Plate-Finned Circular Tube Heat Exchanger 315
4.10.3 Fin Efficiency 317
4.10.4 Heat Pipes 318
4.10.5 Analytical Model for Plate-Finned Heat Pipe Heat Exchanger 319
Problems 320
References 332
5 Thermoelectric Design 335
5.1 Introduction 335
5.1.1 Thermoelectric Effect 337
5.1.2 Seebeck Effect 337
5.1.3 Peltier Effect 338
5.1.4 Thomson Effect 338
5.1.5 Thomson (or Kelvin) Relationships 339
5.1.6 The Figure of Merit 339
5.1.7 New Generation Thermoelectrics 339
5.2 Thermoelectric Generators 341
5.2.1 Ideal Equations 341
5.2.2 Performance Parameters of a Thermoelectric Module 344
5.2.3 Maximum Parameters for a Thermoelectric Module 345
5.2.4 Normalized Parameters 345
5.2.5 Effective Material Properties 351
5.2.6 Comparison of Calculations with a Commercial Product 352
5.2.7 Figure of Merit and Optimum Geometry 353
5.3 Thermoelectric Coolers and Heat Pumps 354
5.3.1 Ideal Equations 355
5.3.2 Maximum Parameters 358
5.3.3 Normalized Parameters for Thermoelectric Coolers 359
5.3.4 Normalized Parameters for Thermoelectric Heat Pumps 363
5.3.5 Effective Material Properties 371
5.3.5.1 Comparison of Calculations with a Commercial Product 373
5.4 Optimal Design 373
5.4.1 Introduction 373
5.4.2 Optimal Design for Thermoelectric Generators 374
5.4.3 Optimal Design of Thermoelectric Coolers and Heat Pumps 383
5.4.3.1 Thermoelectric Heat Pumps 387
5.4.3.2 Heat Sinks Without Thermoelectric Cooler Module 388
5.5 Thomson Effect, Exact Solution, and Compatibility Factor 398
5.5.1 Thermodynamics of Thomson Effect 398
5.5.1.1 Seebeck Effect 398
5.5.1.2 Peltier Effect 399
5.5.1.3 Thomson Effect 399
5.5.1.4 Thomson (or Kelvin) Relationships 400
5.5.2 Exact Solutions 402
5.5.2.1 Equations for the Exact Solutions and the Ideal Equation 402
5.5.2.2 Thermoelectric Generator 404
5.5.2.3 Thermoelectric Coolers 405
5.5.3 Compatibility Factor 407
5.5.3.1 Reduced Current Density 407
5.5.3.2 Heat Balance Equation 408
5.5.3.3 Numerical Solution 408
5.5.3.4 Infinitesimal Efficiency 409
5.5.3.5 Reduced Efficiency 409
5.5.3.6 Reduced Efficiency 409
5.5.3.7 Compatibility Factor 409
5.5.3.8 Segmented Thermoelements 410
5.5.3.9 Thermoelectric Potential 410
5.5.4 Thomson Effects 413
5.5.4.1 Formulation of Basic Equations 413
5.5.4.2 Numeric Solutions of Thomson Effect 416
5.5.4.3 Comparison Between Thomson Effect and Ideal Equation 418
5.6 Thermal and Electrical Contact Resistances for Micro and Macro Devices 421
5.6.1 Modeling and Validation 421
5.6.1.1 Cancelation of Spreading Resistance with Thermal Contact Resistance 422
5.6.1.2 Thermoelectric Coolers 423
5.6.1.3 Thermoelectric Generators 423
5.6.1.4 Validation of Model 423
5.6.2 Micro and Macro Thermoelectric Coolers 425
5.6.2.1 Effect of Leg Length 426
5.6.2.2 Effect of Material on Ceramic Plate 426
5.6.3 Micro and Macro Thermoelectric Generators 427
5.6.3.1 Model and Verification for Macro TE Generators 427
5.6.3.2 Effect of Load Resistance 428
5.6.3.3 Effect of Leg Length and Ceramic Material 429
5.7 Modeling of Thermoelectric Generators and Coolers with Heat Sinks 430
5.7.1 Modeling of Thermoelectric Generators with Heat Sinks 430
5.7.1.1 Modeling 430
5.7.1.2 Heat Sink Area and Cross Flow Area for Heat Sinks 433
5.7.1.3 Mass Flow Rates 433
5.7.1.4 Convection Heat Transfer Coefficients 434
5.7.1.5 Single-Fin Efficiencies 434
5.7.1.6 Overall Fin Efficiencies 435
5.7.1.7 Thermal Resistances of Heat Sink and Aluminum Block 435
5.7.1.8 Effective Material Properties 436
5.7.1.9 Comparison of Model and Measurements 437
5.7.1.10 Optimal Design of Heat Sink 437
5.7.1.11 Optimal Design of Thermoelectric Module 438
5.7.2 Plate-Fin Heat Sinks 438
5.7.2.1 Nusselt Number for Air 439
5.7.2.2 Turbulent Flow for Gases and Liquids 440
5.7.2.3 Optimal Design of Heat Sink 441
5.7.2.4 Single-Fin Efficiency 441
5.7.2.5 Overall Fin Efficiency 442
5.7.3 Modeling of Thermoelectric Coolers with Heat Sinks 442
5.7.3.1 Modeling 442
5.7.3.2 Heat Sink Area and Cross Flow Area for Heat Sinks 445
5.7.3.3 Mass Flow Rates 445
5.7.3.4 Convection Heat Transfer Coefficients 446
5.7.3.5 Single-Fin Efficiencies 446
5.7.3.6 Overall Fin Efficiencies 446
5.7.3.7 Thermal Resistances of Heat Sink and Aluminum Block 447
5.7.3.8 Effective Material Properties 447
5.7.3.9 Comparison of Model and Measurements 448
5.7.3.10 Conclusions 449
5.8 Applications 449
5.8.1 Exhaust Waste Heat Recovery 449
5.8.1.1 Recent Studies 449
5.8.1.2 Modeling of Module Tests 452
5.8.1.3 Modeling of TEG 455
5.8.1.4 New Design of TEG 462
5.8.2 Solar Thermoelectric Generators (STEGs) 466
5.8.2.1 Recent Studies 466
5.8.2.2 Modeling of a STEG 467
5.8.2.3 Optimal Design of STEG (Dimensional Analysis) 473
5.8.2.4 New Design of STEG 475
5.8.3 Automotive Thermoelectric Air Conditioner (TEAC) 479
5.8.3.1 Recent Studies 479
5.8.3.2 Modeling of Air-to-Air TEAC 480
5.8.3.3 Optimal Design of TEAC 487
5.8.3.4 New Design of TEAC 490
Problems 493
Computer Assignment 496
Projects 504
Computer Assignments 504
Computer Projects 504
References 505
6 Thermoelectric Materials 509
6.1 Crystal Structure 509
6.1.1 Atomic Mass 509
6.1.1.1 Avogadro's Number 509
6.1.2 Unit Cells of a Crystal 510
6.1.2.1 Bravais Lattices 511
6.1.3 Crystal Planes 515
6.2 Physics of Electrons 517
6.2.1 Quantum Mechanics 517
6.2.1.1 Electromagnetic Wave 517
6.2.1.2 Atomic Structure 519
6.2.1.3 Bohr's Model 520
6.2.1.4 Line Spectra 521
6.2.1.5 De Broglie Wave 522
6.2.1.6 Heisenberg Uncertainty Principle 523
6.2.1.7 Schrödinger Equation 524
6.2.1.8 A Particle in a One-Dimensional Box 524
6.2.1.9 Quantum Numbers 527
6.2.1.10 Electron Configurations 528
6.2.2 Band Theory and Doping 530
6.2.2.1 Covalent Bonding 530
6.2.2.2 Energy Band 531
6.2.2.3 Pseudo-Potential Well 532
6.2.2.4 Doping, Donors, and Acceptors 532
6.3 Density of States, Fermi Energy, and Energy Bands 534
6.3.1 Current and Energy Transport 534
6.3.2 Electron Density of States 535
6.3.2.1 Dispersion Relation 535
6.3.2.2 Effective Mass 535
6.3.2.3 Density of States 536
6.3.3 Fermi-Dirac Distribution 538
6.3.4 Electron Concentration 538
6.3.5 Fermi Energy in Metals 539
6.3.6 Fermi Energy in Semiconductors 541
6.3.7 Energy Bands 543
6.3.7.1 Multiple Bands 544
6.3.7.2 Direct and Indirect Semiconductors 545
6.3.7.3 Periodic Potential (Kronig-Penney Model) 545
6.4 Thermoelectric Transport Properties for Electrons 549
6.4.1 Boltzmann Transport Equation 549
6.4.2 Simple Model of Metals 552
6.4.2.1 Electric Current Density 552
6.4.2.2 Electrical Conductivity 552
6.4.2.3 Seebeck Coefficient 553
6.4.2.4 Electronic Thermal Conductivity 555
6.4.3 Power-Law Model for Metals and Semiconductors 556
6.4.3.1 Equipartition Principle 556
6.4.3.2 Parabolic Single-Band Model 557
6.4.4 Electron Relaxation Time 563
6.4.4.1 Acoustic-Phonon Scattering 563
6.4.4.2 Polar Optical Phonon Scattering 564
6.4.4.3 Ionized Impurity Scattering 564
6.4.4.4 Total Electron Relaxation Time 565
6.4.5 Multiband Effects 566
6.4.6 Nonparabolicity 567
6.4.6.1 Nonparabolic Density of States 567
6.5 Phonons 569
6.5.1 Crystal Vibration 569
6.5.1.1 One Atom in a Primitive Cell 569
6.5.1.2 Two Atoms in a Unit Cell 571
6.5.2 Specific Heat 573
6.5.2.1 Internal Energy 573
6.5.2.2 Debye Model 575
6.5.3 Lattice Thermal Conductivity 580
6.5.3.1 Klemens-Callaway Model 580
6.5.3.2 Umklapp Processes 582
6.5.3.3 Callaway Model 583
6.5.3.4 Phonon Relaxation Times 584
6.6 Low-Dimensional Nanostructures 587
6.6.1 Low-Dimensional Systems 588
6.6.1.1 Quantum Well (2D) 588
6.6.1.2 Quantum Wires (1D) 592
6.6.1.3 Quantum Dots (0D) 595
6.6.1.4 Thermoelectric Transport Properties of Quantum Wells 595
6.6.1.5 Thermoelectric Transport Properties of Quantum Wires 597
6.6.1.6 Proof-of-Principle Studies 598
6.6.1.7 Size Effects of Quantum Well on Lattice Thermal Conductivity 600
6.7 Generic Model of Bulk Silicon and Nanowires 602
6.7.1 Electron Density of States for Bulk and Nanowires 603
6.7.1.1 Density of States 603
6.7.2 Carrier Concentrations for Two-Band Model 603
6.7.2.1 Bulk 603
6.7.2.2 Nanowires 604
6.7.2.3 Bipolar Effect and Fermi Energy 604
6.7.3 Electron Transport Properties for Bulk and Nanowires 604
6.7.3.1 Electrical Conductivity 604
6.7.3.2 Seebeck Coefficient 605
6.7.3.3 Electronic Thermal Conductivity 605
6.7.4 Electron Scattering Mechanisms 605
6.7.4.1 Acoustic-Phonon Scattering 605
6.7.4.2 Ionized Impurity Scattering 606
6.7.4.3 Screening Effect 606
6.7.4.4 Polar Optical Phonon Scattering 606
6.7.4.5 Total Electron Relaxation Time 607
6.7.5 Lattice Thermal Conductivity 607
6.7.6 Phonon Relaxation Time 607
6.7.7 Input Data for Bulk Si and Nanowires 608
6.7.8 Bulk Si 608
6.7.8.1 Fermi Energy 609
6.7.8.2 Electron Mobility 610
6.7.8.3 Thermoelectric Transport Properties 610
6.7.8.4 Dimensionless Figure of Merit 610
6.7.9 Si Nanowires 611
6.7.9.1 Fermi Energy and Carrier Concentration 611
6.7.9.2 Electron Mobility 612
6.7.9.3 Thermoelectric Transport Properties for Si Nanowires 612
6.7.9.4 Dimensionless Figure of Merit 614
6.7.9.5 Effect of Size for Nanowires 614
6.7.9.6 Critical Nanowire Diameter 615
6.7.9.7 Phonon Properties for Si Nanowires 616
6.8 Theoretical Model of Thermoelectric Transport Properties 617
6.8.1 Introduction 618
6.8.2 Theoretical Equations 619
6.8.2.1 Carrier Transport Properties 619
6.8.2.2 Scattering Mechanisms for Electron Relaxation Times 621
6.8.2.3 Lattice Thermal Conductivity 624
6.8.2.4 Phonon Relaxation Times 625
6.8.2.5 Phonon Density of States and Specific Heat 626
6.8.2.6 Dimensionless Figure of Merit 627
6.8.3 Results and Discussion 627
6.8.3.1 Electron or Hole Scattering Mechanisms 627
6.8.4 Summary 647
Problems 649
References 657
7 Solar Cells 667
7.1 Introduction 667
7.1.1 Operation of Solar Cells 669
7.1.2 Solar Cells and Technology 671
7.1.3 Solar Irradiance 672
7.1.4 Air Mass 672
7.1.5 Nature of Light 674
7.2 Quantum Mechanics 675
7.2.1 Atomic Structure 677
7.2.2 Bohr's Model 677
7.2.3 Line Spectra 679
7.2.4 De Broglie Wave 680
7.2.5 Heisenberg Uncertainty Principle 681
7.2.6 Schrödinger Equation 682
7.2.7 A Free Particle in a 1D Box 682
7.2.8 Quantum Numbers 685
7.2.9 Electron Configurations 686
7.2.10 Van der Waals Forces 688
7.2.11 Covalent Bonding 689
7.2.12 Energy Band 690
7.2.13 Pseudo-Potential Well 691
7.3 Density of States 691
7.3.1 Number of States 691
7.3.2 Effective Mass 692
7.4 Equilibrium Intrinsic Carrier Concentration 693
7.4.1 Fermi Function 693
7.4.2 Nondegenerate Semiconductor 693
7.4.3 Equilibrium Electron and Hole Concentrations 694
7.4.4 Intrinsic Semiconductors 696
7.4.5 Intrinsic Carrier Concentration, N I 696
7.4.6 Intrinsic Fermi Energy 698
7.4.7 Alternative Expression for n 0 and p 0 698
7.5 Extrinsic Semiconductors in Thermal Equilibrium 699
7.5.1 Doping, Donors, and Acceptors 699
7.5.2 Extrinsic Carrier Concentration in Equilibrium 700
7.5.3 Built-in Voltage 702
7.5.4 Principle of Detailed Balance 703
7.5.5 Majority and Minority Carriers in Equilibrium 703
7.6 Generation and Recombination 704
7.6.1 Direct and Indirect Band Gap Semiconductors 704
7.6.2 Absorption Coefficient 705
7.6.3 Photogeneration 707
7.7 Recombination 707
7.7.1 Recombination Mechanisms 707
7.7.2 Band Energy Diagram Under Nonequilibrium Conditions 709
7.7.2.1 Back Surface Field (BSF) 710
7.7.3 Low-Level Injection 710
7.7.3.1 Low-Level Injection 711
7.7.4 Band-to-Band Recombination 712
7.7.5 Trap-Assisted (SRH) Recombination 713
7.7.6 Simplified Expression of the SRH Recombination Rate 714
7.7.7 Auger Recombination 715
7.7.8 Total Recombination Rate 716
7.8 Carrier Transport 716
7.8.1 Drift 717
7.8.2 Carrier Mobility 717
7.8.3 Diffusion 718
7.8.4 Total Current Densities 719
7.8.5 Einstein Relationship 719
7.8.6 Semiconductor Equations 720
7.8.7 Minority-Carrier Diffusion Equations 720
7.8.8 p-n Junction 721
7.8.9 Calculation of Depletion Width 723
7.8.10 Energy Band Diagram with a Reference Point 725
7.8.11 Quasi-Fermi Energy Levels 725
7.9 Minority Carrier Transport 726
7.9.1 Boundary Conditions 726
7.9.2 Minority Carrier Lifetimes 728
7.9.3 Minority Carrier Diffusion Lengths 728
7.9.4 Minority Carrier Diffusion Equation for Holes 729
7.9.5 Minority Carrier Diffusion Equation for Electrons 732
7.10 Characteristics of Solar Cells 735
7.10.1 Current Density 735
7.10.2 Current-Voltage Characteristics 740
7.10.3 Figures of Merit 742
7.10.4 Effect of Minority Electron Lifetime on Efficiency 744
7.10.5 Effect of Minority Hole Lifetime on Efficiency 746
7.10.6 Effect of Back Surface Recombination Velocity on Efficiency 746
7.10.7 Effect of Base Width on Efficiency 747
7.10.8 Effect of Emitter Width W N on Efficiency 748
7.10.9 Effect of Acceptor Concentration on Efficiency 750
7.10.10 Effect of Donor Concentration on Efficiency 752
7.10.11 Band Gap Energy with Temperature 752
7.10.12 Effect of Temperature on Efficiency 753
7.11 Additional Topics 754
7.11.1 Parasitic Resistance Effects (Ohmic Losses) 754
7.11.2 Quantum Efficiency 757
7.11.3 Ideal Solar Cell Efficiency 758
7.12 Modeling 763
7.12.1 Modeling for a Silicon Solar Cell 763
7.12.2 Comparison of the Solar Cell Model with a Commercial Product 776
7.13 Design of a Solar Cell 779
7.13.1 Solar Cell Geometry with Surface Recombination Velocities 779
7.13.2 Donor and Acceptor Concentrations 780
7.13.3 Minority Carrier Diffusion Lifetimes 780
7.13.4 Grid Spacing 781
7.13.5 Antireflection, Light Trapping, and Passivation 784
Problems 785
References 789
Appendix A Thermophysical Properties 791
References 834
Appendix B 837
B.1 Optimal Dimensionless Parameters for TEGs with ZT infinity 2 = 1 (See Figure B.1 at the end of tables) 837
B.2 Optimal Dimensionless Parameters for TECS With ZT infinity 2 = 1 (See Figure B.2 at the end of tables) 837
Appendix C Pipe Dimensions 847
Appendix D Periodic Table 849
Appendix E Thermoelectric Properties 857
E.1 Bismuth Telluride P-Type 858
E.2 Bismuth Telluride N-Type 859
E.3 Lead Telluride P-Type 859
E.4 Silicon Germanium N-Type 860
E.5 Skutterudites N-Type 861
E.6 Zintl Compound N-Type 861
References 862
Appendix F Fermi Integral 863
Appendix G Hall Factor 867
References 869
Appendix H Curve Fitting of Working Fluids 871
H.1 Curve Fit for Working Fluids Chosen 871
H.2 Curve Fitting for Working Fluid Properties Chosen 872
H.2.1 MathCad Format 872
Appendix L Tutorial for MathCAD 875
L.1 Tutorial Problem for MathCAD 875
Appendix M Conversion Factors 879
Index 881
HoSung Lee, PhD, is a Professor in the department of Mechanical and Aerospace Engineering at Western Michigan University, USA. His other areas of research include optimal design of thermoelectric generators and coolers and thermoelectric materials.
