Macro- to Microscale Heat Transfer: The Lagging Behavior, 2nd Edition

Content: 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 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 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   T 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