Preface ........................................................ xv
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 ... 15
1.4.3.2 A Cylinder in Cross Flow ............... 18
1.4.3.3 Flow in Ducts .......................... 18
1.4.3.4 Free Convection ........................ 22
1.4.4 Radiation ....................................... 25
1.4.4.1 Thermal Radiation ...................... 25
1.4.4.2 View Factor ............................ 29
1.4.4.3 Radiation Exchange between Diffuse-
Gray Surfaces .......................... 31
References ................................................. 32
2 Heat Sinks ................................................. 34
2.1 Longitudinal Fin of Rectangular Profile ................ 34
2.2 Heat Transfer from Fin ................................. 36
2.3 Fin Effectiveness ...................................... 37
2.4 Fin Efficiency ......................................... 38
2.5 Corrected Profile Length ............................... 38
2.6 Optimizations .......................................... 39
2.6.1 Constant Profile Area Ap ........................ 39
2.6.2 Constant Heat Transfer from a Fin ............... 41
2.6.3 Constant Fin Volume or Mass ..................... 42
2.7 Multiple Fin Array I ................................... 45
2.7.1 Free (Natural) Convection Cooling ............... 45
2.7.1.1 Small Spacing Channel .................. 45
2.7.1.2 Large Spacing Channel .................. 48
2.7.1.3 Optimum Fin Spacing .................... 49
2.7.2 Forced Convection Cooling ....................... 49
2.7.2.1 Small Spacing Channel .................. 49
2.7.2.2 Large Spacing Channel .................. 51
2.8 Multiple Fin Array II .................................. 53
2.8.1 Natural (Free) Convection Cooling ............... 55
2.9 Thermal Resistance and Overall Surface Efficiency ...... 56
2.10 Fin Design with Thermal Radiation ...................... 80
2.10.1 Single Longitudinal Fin with Radiation .......... 81
References .................................................. 94
Problems .................................................... 94
3 Thermoelectrics ............................................ 100
3.1 Introduction .......................................... 100
3.2 Thermoelectric Effect ................................. 102
3.2.1 Seebeck Effect ................................. 102
3.2.2 Peltier Effect ................................. 103
3.2.3 Thomson Effect ................................. 103
3.2.4 Thomson (or Kelvin) Relationships .............. 103
3.3 Thermoelement Couple (Thermocouple) ................... 104
3.4 The Figure of Merit ................................... 104
3.5 Similar and Dissimilar Materials ...................... 105
3.5.1 Similar Materials .............................. 105
3.5.2 Dissimilar Materials ........................... 106
3.6 Thermoelectric Generator (TEG) ........................ 107
3.6.1 Similar and Dissimilar Materials ............... 107
3.6.1.1 Similar Materials ..................... 107
3.6.1.2 Dissimilar Materials .................. 108
3.6.2 Conversion Efficiency and Current .............. 109
3.6.3 Maximum Conversion Efficiency .................. 109
3.6.4 Maximum Power Efficiency ....................... 111
3.6.5 Maximum Performance Parameters ................. 112
3.6.6 Multicouple Modules ............................ 115
3.7 Thermoelectric Coolers (TEC) .......................... 126
3.7.1 Similar and Dissimilar Materials ............... 127
3.7.1.1 Similar Materials ..................... 127
3.7.1.2 Dissimilar Materials .................. 128
3.7.2 The Coefficient of Performance ................. 128
3.7.3 Optimum Current for the Maximum Cooling Rate ... 129
3.7.4 Maximum Performance Parameters ................. 129
3.7.5 Optimum Current for the Maximum COP ............ 130
3.7.6 Generalized Charts ............................. 131
3.7.2 Optimum Geometry for the Maximum Cooling in
Similar Materials .............................. 132
3.7.8 Thermoelectric Modules ......................... 133
3.7.9 Commercial TEC ................................. 135
3.7.10 Multistage Modules ............................. 135
3.7.10.1 Commercial Multistage Peltier
Modules ............................... 137
3.7.11 Design Options ................................. 137
3.8 Applications .......................................... 142
3.8.1 Thermoelectric Generators ...................... 142
3.8.2 Thermoelectric Coolers ......................... 143
3.9 Design Example ........................................ 143
3.9.1 Design Concept ................................. 144
3.9.2 Design of Internal and External Heat Sinks ..... 145
3.9.3 Design of Thermoelectric Cooler (TEC) .......... 149
3.9.4 Finding the Exact Solution for Tc and Th ....... 150
3.9.5 Performance Curves for Thermoelectric Air
Cooler ......................................... 152
3.10 Thermoelectric Module Design .......................... 153
3.10.1 Thermal and Electrical Contact Resistances
for TEG ........................................ 153
3.10.2 Thermal and Electrical Contact Resistances
for TEC ........................................ 158
3.11 Design Example of TEC Module .......................... 166
3.11.1 Design Concept ................................. 166
3.11.2 Summary of Design of a TEC Module .............. 173
References ................................................. 174
Problems ................................................... 175
4 Heat Pipes ................................................. 180
4.1 Operation of Heat Pipe ................................ 180
4.2 Surface Tension ....................................... 181
4.3 Heat Transfer Limitations ............................. 183
4.3.1 Capillary Limitation ........................... 184
4.3.1.1 Maximum Capillary Pressure
Difference ............................ 185
4.3.1.2 Vapor Pressure Drop ................... 187
4.3.1.3 Liquid Pressure Drop .................. 189
4.3.1.4 Normal Hydrostatic Pressure Drop ...... 189
4.3.1.5 Axial Hydrostatic Pressure Drop ....... 191
4.3.2 Approximation for Capillary Pressure
Difference ..................................... 191
4.3.3 Sonic Limitation ............................... 192
4.3.4 Entrainment Limitation ......................... 192
4.3.5 Boiling Limitation ............................. 193
4.3.6 Viscous Limitation ............................. 193
4.4 Heat Pipe Thermal Resistance .......................... 197
4.4.1 Contact Resistance ............................. 200
4.5 Variable Conductance Heat Pipes (VCHP) ................ 202
4.5.1 Gas-Loaded Heat Pipes .......................... 203
4.5.2 Clayepyron-Clausius Equation ................... 205
4.5.3 Applications ................................... 206
4.6 Loop Heat Pipes ....................................... 208
4.7 Micro Heat Pipes ...................................... 210
4.7.1 Steady-State Models ............................ 211
4.7.1.1 Conventional Model .................... 211
4.7.1.2 Cotter's Model ........................ 212
4.8 Working Fluid ......................................... 217
4.8.1 Figure of Merit ................................ 217
4.8.2 Compatibility .................................. 219
4.9 Wick Structures ....................................... 219
4.10 Design Example ........................................ 221
4.10.1 Selection of Material and Working Fluid ........ 221
4.10.2 Working Fluid Properties ....................... 221
4.10.3 Estimation of Vapor Space Radius ............... 223
4.10.4 Estimation of Operating Limits ................. 223
4.10.4.1 Capillary Limits ...................... 223
4.10.4.2 Sonic Limits .......................... 223
4.10.4.3 Entrainment Limits .................... 224
4.10.4.4 Boiling Limits ........................ 225
4.10.5 Wall Thickness ................................. 226
4.10.6 Wick Selection ................................. 227
4.10.7 Maximum Arterial Depth ......................... 229
4.10.8 Design of Arterial Wick ........................ 230
4.10.9 Capillary Limitation ........................... 230
4.10.9.1 Liquid Pressure Drop in the
Arteries .............................. 231
4.10.9.2 Liquid Pressure Drop in the
Circumferential Wick .................. 232
4.10.9.3 Vapor Pressure Drop in the Vapor
Space ................................. 232
4.10.10 Performance Map ............................... 234
4.10.11 Check the Temperature Drop .................... 235
References ................................................. 236
Problems ................................................... 237
5 Compact Heat Exchangers .................................... 240
5.1 Introduction .......................................... 240
5.2 Fundamentals of Heat Exchangers ....................... 243
5.2.1 Counterflow and Parallel Flows ................. 243
5.2.2 Overall Heat Transfer Coefficient .............. 245
5.2.3 Log Mean Temperature Difference (LMTD) ......... 247
5.2.4 Flow Properties ................................ 249
5.2.5 Nusselt Numbers ................................ 250
5.2.6 Effectiveness-NTU (e-NTU) Method ............... 250
5.2.6.1 Parallel Flow ......................... 252
5.2.6.2 Counterflow ........................... 253
5.2.6.3 Crossflow ............................. 253
5.2.7 Heat Exchanger Pressure Drop ................... 257
5.2.8 Fouling Resistances (Fouling Factors) .......... 261
5.2.9 Overall Surface (Fin) Efficiency ............... 262
5.2.10 Reasonable Velocities of Various Fluids in
Pipe Flow ...................................... 264
5.3 Double-Pipe Heat Exchangers ........................... 265
5.4 Shell-and-Tube Heat Exchangers ........................ 272
5.4.1 Baffles ........................................ 273
5.4.2 Multiple Passes ................................ 273
5.4.3 Dimensions of Shell-and-Tube Heat Exchanger .... 274
5.4.4 Shell-side Tube Layout ......................... 274
5.5 Plate Heat Exchangers (PHE) ........................... 285
5.5.1 Flow Pass Arrangements ......................... 285
5.5.2 Geometric Properties ........................... 286
5.5.3 Friction Factor ................................ 290
5.5.4 Nusselt Number ................................. 290
5.5.5 Pressure Drops ................................. 290
5.6 Pressure Drops in Compact Heat Exchangers ............. 303
5.6.1 Fundamentals of Core Pressure Drop ............. 304
5.6.2 Core Entrance and Exit Pressure Drops .......... 306
5.6.3 Contraction and Expansion Loss Coefficients .... 307
5.6.3.1 Circular-Tube Core .................... 308
5.6.3.2 Square-Tube Core ...................... 309
5.6.3.3 Flat-Tube Core ........................ 310
5.6.3.4 Triangular-Tube Core .................. 311
5.7 Finned-Tube Heat Exchangers ........................... 312
5.7.1 Geometrical Characteristics .................... 313
5.7.2 Flow Properties ................................ 315
5.7.3 Thermal Properties ............................. 315
5.7.4 Correlations for Circular Finned-Tube
Geometry ....................................... 316
5.7.5 Pressure Drop .................................. 317
5.7.6 Correlations for Louvered Plate-Fin Flat-Tube
Geometry ....................................... 3
5.8 Plate-Fin Heat Exchangers ............................. 332
5.8.1 Geometric Characteristics ...................... 333
5.8.2 Correlations for Offset Strip Fin (OSF)
Geometry ....................................... 335
5.9 Louver-Fin-Type Flat-Tube Plate-Fin Heat Exchangers ... 352
5.9.1 Geometric Characteristics ...................... 352
5.9.2 Correlations for Louver Fin Geometry ........... 355
References ................................................. 372
Problems ................................................... 373
6 Solar Cells ................................................ 382
6.1 Introduction .......................................... 382
6.1.1 Operation of Solar Cells ....................... 384
6.1.2 Solar Cells and Technology ..................... 386
6.1.3 Solar Irradiance ............................... 387
6.1.4 Air Mass ....................................... 388
6.1.5 Nature of Light ................................ 389
6.2 Quantum Mechanics ..................................... 390
6.2.1 Atomic Structure ............................... 392
6.2.2 Bohr's Model ................................... 393
6.2.3 Line Spectra ................................... 394
6.2.4 De Brogue Wave ................................. 396
6.2.5 Heisenberg Uncertainty Principle ............... 397
6.2.6 Schrцdinger Equation ........................... 397
6.2.7 A Particle in a 1-D Box ........................ 398
6.2.8 Quantum Numbers ................................ 401
6.2.9 Electron Configurations ........................ 403
6.2.10 Van der Waals Forces ........................... 405
6.2.11 Covalent Bonding ............................... 405
6.2.12 Energy Band .................................... 406
6.2.13 Pseudo-Potential Well .......................... 407
6.3 Density of States ..................................... 408
6.3.1 Number of States ............................... 408
6.3.2 Effective Mass ................................. 409
6.4 Equilibrium Intrinsic Carrier Concentration ........... 409
6.4.1 Fermi Function ................................. 410
6.4.2 Nondegenerate Semiconductor .................... 411
6.4.3 Equilibrium Electron and Hole Concentrations ... 411
6.4.4 Intrinsic Semiconductors ....................... 413
6.4.5 Intrinsic Carrier Concentration, n ............. 414
6.4.6 Intrinsic Fermi Energy ......................... 415
6.4.7 Alternative Expression for no and po ........... 416
6.5 Extrinsic Semiconductors in Thermal Equilibrium ....... 416
6.5.1 Doping, Donors, and Acceptors .................. 417
6.5.2 Extrinsic Carrier Concentration in
Equilibrium .................................... 418
6.5.3 Built-in Voltage ............................... 420
6.5.4 Principle of Detailed Balance .................. 421
6.5.5 Majority and Minority Carriers in
Equilibrium .................................... 421
6.6 Generation and Recombination .......................... 422
6.6.1 Direct and Indirect Band Gap Semiconductors .... 422
6.6.2 Absorption Coefficient ......................... 424
6.6.3 Photogeneration ................................ 424
6.7 Recombination ......................................... 425
6.7.1 Recombination Mechanisms ....................... 425
6.7.2 Band Energy Diagram under Nonequilibrium
Conditions ..................................... 427
6.7.2.1 Back Surface Field (BSF) .............. 427
6.7.3 Low-Level Injection ............................ 429
6.7.3.1 Low-Level Injection ................... 429
6.7.4 Band-to-Band Recombination ..................... 430
6.7.5 Trap-Assisted (SRH) Recombination .............. 431
6.7.6 Simplified Expression of the SRH
Recombination Rate ............................. 433
6.7.7 Auger Recombination ............................ 434
6.7.8 Total Recombination Rate ....................... 435
6.8 Carrier Transport ..................................... 436
6.8.1 Drift .......................................... 436
6.8.2 Carrier Mobility ............................... 436
6.8.3 Diffusion ...................................... 437
6.8.4 Total Current Densities ........................ 438
6.8.5 Einstein Relationship .......................... 439
6.8.6 Semiconductor Equations ........................ 440
6.8.7 Minority-Carrier Diffusion Equations ........... 440
6.8.8 P-n Junction ................................... 441
6.8.9 Calculation of Depletion Width ................. 444
6.8.10 Energy Band Diagram with a Reference Point ..... 445
6.8.11 Quasi-Fermi Energy Levels ...................... 446
6.9 Minority Carrier Transport ............................ 447
6.9.1 Boundary Conditions ............................ 448
6.9.2 Minority Carrier Lifetimes ..................... 449
6.9.3 Minority Carrier Diffusion Lengths ............. 450
6.9.4 Minority Carrier Diffusion Equation for
Holes .......................................... 450
6.9.5 Minority Carrier Diffusion Equation for
Electrons ...................................... 454
6.10 Characteristics of Solar Cells ........................ 457
6.10.1 Current Density ................................ 457
6.10.2 Current-Voltage Characteristics ................ 463
6.10.3 Figures of Merit ............................... 466
6.10.4 Effect of Minority Electron Lifetime on
Efficiency ..................................... 468
6.10.5 Effect of Minority Hole Lifetime on
Efficiency ..................................... 470
6.10.6 Effect of Back Surface Recombination Velocity
on Efficiency .................................. 470
6.10.7 Effect of Base Width on Efficiency ............. 471
6.10.8 Effect of Emitter Width WN on Efficiency ....... 472
6.10.9 Effect of Acceptor Concentration on
Efficiency ..................................... 474
6.10.10 Effect of Donor Concentration on Efficiency ... 475
6.10.11 Band Gap Energy with Temperature .............. 476
6.10.12 Effect of Temperature on Efficiency ........... 477
6.11 Additional Topics ..................................... 478
6.11.1 Parasitic Resistance Effects (Ohmic Losses) .... 478
6.11.2 Quantum Efficiency ............................. 481
6.11.3 Ideal Solar Cell Efficiency .................... 483
6.12 Modeling .............................................. 488
6.12.1 Modeling for a Silicon Solar Cell .............. 488
6.12.2 Comparison of the Solar Cell Model with
a Commercial Product ........................... 503
6.13 Design of a Solar Cell ................................ 506
6.13.1 Solar Cell Geometry with Surface
Recombination Velocities ....................... 506
6.13.2 Donor and Acceptor Concentrations .............. 507
6.13.3 Minority Carrier Diffusion Lifetimes ........... 507
6.13.4 Grid Spacing ................................... 508
6.13.5 Anti-Reflection, Light Trapping and
Passivation ................................................. 512
References .................................................. 512
Problems .................................................... 513
Appendix A Thermophysical Properties ......................... 518
Appendix В Thermoelectrics ................................... 561
B.l Thermoelectric Effects ................................ 561
Seebeck Effect ........................................ 561
Peltier Effect ........................................ 562
Thomson Effect ........................................ 562
B.2 Thomson (or Kelvin) Relationships ..................... 562
B.3 Heat Balance Equation ................................. 566
B.4 Figure of Merit and Optimum Geometry .................. 568
References ................................................. 573
Appendix С Pipe Dimensions ................................... 574
Appendix D Curve Fitting of Working Fluids ................... 576
Curve Fit for Working Fluids Chosen ........................ 576
D.l Curve Fitting for Working Fluid Properties Chosen ..... 576
D.l.l MathCad Format ................................. 576
Appendix E Tutorial I for 2-D ............................... 580
Problem Description for Tutorial I ......................... 580
E.l Tutorial I: Using Gambit and Fluent for Thermal
Behavior of an Electrical Wire ........................ 581
E.l.l Creating Geometry in Gambit .................... 581
E.2 Calculations for Heat Generation ...................... 588
Appendix F Tutorial II for 3-D ............................... 590
Problem Description for Tutorial II ................... 590
F.l Tutorial II Double-Pipe Heat Exchanger: Using
SolidWorks, Gambit, and Fluent ........................ 591
F.l.l Double-Pipe Heat Exchanger ..................... 591
F.1.2 Construct Model in SolidWorks .................. 591
F.1.3 Meshing the Double Pipe Heat Exchanger in
Gambit ......................................... 595
F.1.4 Analysis of Heat Exchanger in Fluent ........... 600
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