Preface xi
Nomenclature xiii
1 Heat Transport by Phonons and Electrons 1
1.1 Challenges in Microscale Heat Conduction 2
1.2 Phonon–Electron Interaction Model 5
1.2.1 Single Energy Equation 10
1.3 Phonon-Scattering Model 11
1.3.1 Operator Method 13
1.3.2 Phonon Hydrodynamics 15
1.4 Phonon Radiative Transfer Model 18
1.5 Relaxation Behavior in Thermal Waves 24
1.5.1 Engineering Assessment of the Relaxation Time 26
1.5.2 Admissibility with Phonon Radiative Transport Phenomena 27
1.6 Micro/Nanoscale Thermal Properties 28
1.6.1 Heat Capacity 29
1.6.2 Thermal Conductivity 30
1.6.3 Normal and Umklapp Relaxation Times 34
1.7 Size Effect 37
1.8 Phase Lags 51
References 56
2 Lagging Behavior 61
2.1 Phase-Lag Concept 62
2.2 Internal Mechanisms 64
2.3 Temperature Formulation 66
2.4 Heat Flux Formulation 69
2.5 Methods of Solutions 70
2.5.1 Method of Laplace Transform 73
2.5.2 Separation of Variables 82
2.5.3 Method of Fourier Transform 87
2.6 Precedence Switching in Fast-Transient Processes 90
2.7 Rate Effect 91
2.8 Problems Involving Heat Fluxes and Finite Boundaries 92
2.9 Characteristic Times 99
2.10 Alternating Sequence 103
2.11 Determination of Phase Lags 104
2.12 Depth of Thermal Penetration 108
Appendix 2.1 FORTRAN Code for the Riemann-Sum Approximation of Laplace Inversion 117
Appendix 2.2 Mathematica Code for Calculating the Depth of Thermal Penetration 122
References 122
3 Thermodynamic and Kinetic Foundation 125
3.1 Classical Thermodynamics 126
3.2 Extended Irreversible Thermodynamics 131
3.3 Lagging Behavior 135
3.4 Thermomechanical Coupling 137
3.4.1 Rigid Conductors 141
3.4.2 Isothermal Deformation 142
3.5 Dynamic and Nonequilibrium Temperatures 143
3.6 Conductive and Thermodynamic Temperatures 146
3.7 Kinetic Theory 149
References 156
4 Temperature Pulses in Superfluid Liquid Helium 159
4.1 Second Sound in Liquid Helium 160
4.2 Experimental Observations 163
4.3 Lagging Behavior 164
4.4 Heating Pulse in Terms of Fluxes 167
4.5 Overshooting Phenomenon of Temperature 172
4.6 Longitudinal and Transverse Pulses 181
4.6.1 Lamé Potential 182
4.6.2 Helmholtz Potential 183
References 190
5 Ultrafast Pulse-Laser Heating on Metal Films 193
5.1 Experimental Observations 194
5.2 Laser Light Intensity 196
5.2.1 Gaussian Distribution 196
5.2.2 Alternate Form of Light Intensity 197
5.3 Microscopic Phonon–Electron Interaction Model 200
5.4 Characteristic Times – The Lagging Behavior 202
5.5 Phase Lags in Metal Films 204
5.6 Effect of Temperature-Dependent Thermal Properties 210
5.7 Cumulative Phase Lags 211
5.8 Conduction in the Metal Lattice 213
5.9 Multiple-Layered Films 219
5.9.1 Mixed Formulation 220
5.9.2 Initial Conditions for Heat Flux 221
5.9.3 Laplace Transform Solution 222
5.9.4 Surface Reflectivity 224
References 228
6 Nonhomogeneous Lagging Response in Porous Media 231
6.1 Experimental Observations 232
6.2 Mathematical Formulation 234
6.3 Short-Time Responses in the Near Field 236
6.4 Two-Step Process of Energy Exchange 240
6.5 Lagging Behavior 241
6.6 Nonhomogeneous Phase Lags 243
6.7 Precedence Switching in the Fast-Transient Process 249
References 253
7 Thermal Lagging in Amorphous Media 255
7.1 Experimental Observations 256
7.2 Fourier Diffusion: The t–1/2 Behavior 258
7.3 Fractal Behavior in Space 259
7.4 Lagging Behavior in Time 262
7.4.1 Classical Diffusion, Z = 1 264
7.4.2 Partial Expansions 265
7.4.3 Riemann-Sum Approximation 265
7.4.4 Real-Time Responses 269
7.5 Thermal Control 271
References 279
8 Material Defects in Thermal Processing 281
8.1 Localization of Heat Flux 282
8.1.1 Microcracks 284
8.2 Energy Transport around a Suddenly Formed Crack 288
8.3 Thermal Shock Formation – Fast-Transient Effect 290
8.3.1 Asymptotic Analysis 291
8.3.2 Subsonic Regime with M< 1 294
8.3.3 Supersonic Regime with M> 1 298
8.3.4 Transonic Stage with M= 1 301
8.4 Diminution of Damage – Microscale Interaction Effect 304
8.4.1 Eigenvalues 308
8.4.2 Eigenfunctions 308
8.5 High Heat Flux around a Microvoid 311
8.5.1 Mathematical Formulation 312
8.5.2 Linear Decomposition 314
8.5.3 Steady-State Solution 315
8.5.4 Fast-Transient Component 317
8.5.5 Flux Intensification 319
References 324
9 Lagging Behavior in other Transport Processes 327
9.1 Film Growth 328
9.1.1 Lagging Behavior 330
9.1.2 Thermal Oxidation of Silicon 336
9.1.3 Intermetallics 340
9.2 Thermoelectricity 343
9.2.1 Thermoelectric Coupling 344
9.2.2 Lagging Behavior 346
9.2.3 Dominating Parameters 348
9.3 Visco/Thermoelastic Response 351
9.4 Nanofluids 352
References 355
10 Lagging Behavior in Biological Systems 359
10.1 Bioheat Equations 360
10.1.1 Two-Equation Model 360
10.1.2 Three-Equation Model 363
10.2 Mass Interdiffusion 370
10.3 Lagging Behavior 376
10.3.1 Rapidly Stretched Springs 376
10.3.2 One-Dimensional Fins 378
References 379
11 Thermomechanical Coupling 381
11.1 Thermal Expansion 382
11.1.1 Mechanically Driven Cooling Phenomenon 385
11.1.2 Thermomechanical Coupling Factor 386
11.1.3 Apparent Thermal Conductivity 388
11.2 Thermoelastic Deformation 388
11.3 Mechanically Driven Cooling Waves 391
11.3.1 Heat Transport by Diffusion 396
11.3.2 Heat Transport by Thermal Waves 398
11.3.3 Lagging Behavior in Heat Transport 406
11.4 Thermal Stresses in Rapid Heating 408
11.4.1 Diffusion 413
11.4.2 CV Waves 414
11.4.3 Lagging Behavior 417
11.5 Hot-Electron Blast 419
References 422
12 High-Order Effect and Nonlocal Behavior 425
12.1 Intrinsic Structures of T Waves 426
12.1.1 Thermal Relaxation of Electrons 427
12.1.2 Relaxation of Internal Energy 431
12.1.3 Propagation of T Waves 436
12.1.4 Effect of τT 2 439
12.1.5 Effect of Microvoids on the Amplification of T Waves 443
12.2 Multiple Carriers 447
12.2.1 Two-Carrier System 448
12.2.2 Three-Carrier System 449
12.2.3 N-Carrier System 452
12.3 Thermal Resonance 453
12.4 Heat Transport in Deformable Conductors 458
12.4.1 Energy Equation 459
12.4.2 Momentum Equation 472
12.5 Nonlocal Behavior 473
12.5.1 Nonlocal Lengths 475
12.5.2 Thermomass Model 478
12.5.3 Deformable Conductors 486
12.5.4 Effect of Dual Conduction 488
References 490
13 Numerical Methods 491
13.1 Neumann Stability 492
13.1.1 Interfacial Resistance 495
13.2 Finite-Difference Differential Formulation 501
13.2.1 Mixed Formulation 503
13.3 Hot-Electron Blast 507
13.3.1 Full Coupling 520
13.4 Thermoelectric Coupling 531
13.4.1 The Case of Constant J 531
13.4.2 The Case of Constant E 533
Appendix 13.1 Mathematica Code for the Finite-Difference Differential Method: Equations (13.23)–(13.26) 535
Appendix 13.2 Mathematica Code for the Finite-Difference Differential Method: Equations (13.35), (13.37), and (13.38) 537
Appendix 13.3 Mathematica Code (V5.0) for the Finite-Difference
Differential Method: Equations (13.51) and (13.52) 539
Appendix 13.4 Mathematica Code (V5.0) for the Finite-Difference
Differential Method: Equations (13.62), (13.63) and (13.52) 541
Appendix 13.5 Mathematica Code (V5.0) for the Finite-Difference
Differential Method: Equations (13.68) and (13.66) 543
Appendix 13.6 Mathematica Code (V5.0) for the Finite-Difference
Differential Method: Equations (13.69) and (13.66) 544
References 545
Index 547
D. Y. Robert Tzou is a James C. DowellProfessor of Engineering in the Mechanical and AerospaceEngineering Department at the University of Missouri. Heserved as the Department Chairman in 1997-2012, and has become theAssociate Dean for Academic Programs in the College of Engineeringsince 2012. Tzou is a Fellow of American Society of MechanicalEngineers. His research is in the general area of ultrafastthermomechanics, in which he delivered keynote speeches at a numberof national and international professional society conferences andpublished more than 150 journal/conference articles. Hisresearch has been financed by the National Science Foundation, theAir Force Office of Scientific Research, the Army Research Office,Sandia National Laboratories, Los Alamos National Laboratory andthe Air Force Research Laboratory. Tzou has pioneered on thelagging behavior during ultrafast heat/mass transport inmicro/nanoscale since 1997. He is the founding chair for theASME International Conference on Micro/Nanoscale Heat Transfer,http://www.asmeconferences.org/MNHMT2013/Organizers.cfm. Tzouworked at the University of New Mexico and Lehigh University beforejoining the Missouri faculty.
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