Tzou D.Y. Macro- to microscale heat transfer: the lagging behavior (Chichester, 2015). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаTzou D.Y. Macro- to microscale heat transfer: the lagging behavior. - 2nd ed. - Chichester: Wiley, 2015. - xxiii, 552 p.: ill. - Incl. bibl. ref. - Ind.: p.547-552. - ISBN 978-1-118-81822-0
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
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
2.1  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  Lame 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 Micro void ....................... 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 Г Waves .......................... 426
     12.1.1 Thermal Relaxation of Electrons ................... 427
     12.1.2 Relaxation of Internal Energy ..................... 431
     12.1.3 Propagation of Г Waves ............................ 436
     12.1.4 Effect of τr2 ..................................... 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


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