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

1298 Pages·2014·22.553 MB·English

by  Tzou, D. Y

CONTENTS
Cover
Title page
Copyright page
Preface
Nomenclature
1 Heat Transport by Phonons and Electrons
1.1 Challenges in Microscale Heat
Conduction
1.2 Phonon–Electron Interaction Model
1.3 Phonon-Scattering Model
1.4 Phonon Radiative Transfer Model
1.5 Relaxation Behavior in Thermal
Waves
1.6 Micro/Nanoscale Thermal Properties
1.7 Size Effect
1.8 Phase Lags
References
2 Lagging Behavior
2.1 Phase-Lag Concept
2.2 Internal Mechanisms
2.3 Temperature Formulation
2.4 Heat Flux Formulation
2.5 Methods of Solutions
2
2.6 Precedence Switching in
Fast-Transient Processes
2.7 Rate Effect
2.8 Problems Involving Heat Fluxes and
Finite Boundaries
2.9 Characteristic Times
2.10 Alternating Sequence
2.11 Determination of Phase Lags
2.12 Depth of Thermal Penetration
Appendix 2.1 FORTRAN Code for the
Riemann-Sum Approximation of Laplace
Inversion
Appendix 2.2 Mathematica Code for
Calculating the Depth of Thermal
Penetration
References
3 Thermodynamic and Kinetic Foundation
3.1 Classical Thermodynamics
3.2 Extended Irreversible
Thermodynamics
3.3 Lagging Behavior
3.4 Thermomechanical Coupling
3.5 Dynamic and Nonequilibrium
Temperatures
3.6 Conductive and Thermodynamic
Temperatures
3.7 Kinetic Theory
References
3
4 Temperature Pulses in Superfluid Liquid
Helium
4.1 Second Sound in Liquid Helium
4.2 Experimental Observations
4.3 Lagging Behavior
4.4 Heating Pulse in Terms of Fluxes
4.5 Overshooting Phenomenon of
Temperature
4.6 Longitudinal and Transverse Pulses
References
5 Ultrafast Pulse-Laser Heating on Metal
Films
5.1 Experimental Observations
5.2 Laser Light Intensity
5.3 Microscopic Phonon–Electron
Interaction Model
5.4 Characteristic Times – The Lagging
Behavior
5.5 Phase Lags in Metal Films
5.6 Effect of Temperature-Dependent
Thermal Properties
5.7 Cumulative Phase Lags
5.8 Conduction in the Metal Lattice
5.9 Multiple-Layered Films
References
6 Nonhomogeneous Lagging Response in
Porous Media
4
6.1 Experimental Observations
6.2 Mathematical Formulation
6.3 Short-Time Responses in the Near
Field
6.4 Two-Step Process of Energy
Exchange
6.5 Lagging Behavior
6.6 Nonhomogeneous Phase Lags
6.7 Precedence Switching in the
Fast-Transient Process
References
7 Thermal Lagging in Amorphous Media
7.1 Experimental Observations
–1/2
7.2 Fourier Diffusion: The t Behavior
7.3 Fractal Behavior in Space
7.4 Lagging Behavior in Time
7.5 Thermal Control
References
8 Material Defects in Thermal Processing
8.1 Localization of Heat Flux
8.2 Energy Transport around a Suddenly
Formed Crack
8.3 Thermal Shock Formation –
Fast-Transient Effect
8.4 Diminution of Damage – Microscale
Interaction Effect
8.5 High Heat Flux around a Microvoid
5
References
9 Lagging Behavior in other Transport
Processes
9.1 Film Growth
9.2 Thermoelectricity
9.3 Visco/Thermoelastic Response
9.4 Nanofluids
References
10 Lagging Behavior in Biological Systems
10.1 Bioheat Equations
10.2 Mass Interdiffusion
10.3 Lagging Behavior
References
11 Thermomechanical Coupling
11.1 Thermal Expansion
11.2 Thermoelastic Deformation
11.3 Mechanically Driven Cooling Waves
11.4 Thermal Stresses in Rapid Heating
11.5 Hot-Electron Blast
References
12 High-Order Effect and Nonlocal Behavior
12.1 Intrinsic Structures of TWaves
12.2 Multiple Carriers
12.3 Thermal Resonance
12.4 Heat Transport in Deformable
Conductors
6
12.5 Nonlocal Behavior
References
13 Numerical Methods
13.1 Neumann Stability
13.2 Finite-Difference Differential
Formulation
13.3 Hot-Electron Blast
13.4 Thermoelectric Coupling
Appendix 13.1 Mathematica Code for the
Finite-Difference Differential Method:
Equations (13.23)–(13.26)
Appendix 13.2 Mathematica Code for the
Finite-Difference Differential Method:
Equations (13.35), (13.37), and (13.38)
Appendix 13.3 Mathematica Code (V5.0)
for the Finite-Difference Differential
Method: Equations (13.51) and (13.52).
ListSurfacePlot3D needs to be modified
for newer versions of Mathematica than
V5.0
Appendix 13.4 Mathematica Code (V5.0)
for the Finite-Difference Differential
Method: Equations (13.62), (13.63) and
(13.52). ListSurfacePlot3D needs to be
modified for newer versions of
Mathematica than V5.0
Appendix 13.5 Mathematica Code (V5.0)
for the Finite-Difference Differential
Method: Equations (13.68) and (13.66).
ListSurfacePlot3D needs to be modified
7
for newer versions of Mathematica than
V5.0
Appendix 13.6 Mathematica Code (V5.0)
for the Finite-Difference Differential
Method: Equations (13.69) and (13.66).
ListSurfacePlot3D needs to be modified
for newer versions of Mathematica than
V5.0
References
Index
End User License Agreement
List of Tables
Chapter 01
Table 1.1 Phonon–electron coupling
factorGfor some noble and transition
metals (Qiu and Tien, 1992)
Table 1.2 Size effect of thermal
conductivity in thin films: Experimental
data by Nath and Chora (1974) and
Kelemen (1976).
Chapter 05
Table 5.1 The equivalent thermal
diffusivity (αE), the equivalent thermal
wave speed (CE), and the phase lags of
the temperature gradient and the heat
flux vector (τTand τq) for typical metals
8
4 3
(Ce=2.1×10 J/m K at room
temperature; ps≡picosecond)
Chapter 08
Table 8.1 Transition of the r
dependencies of temperature gradient
and heat flux vector in the vicinity of a
moving crack tip (r≡radial distance
measured from the crack tip)
Chapter 11
Table 11.1 Typical values of the
coefficients of thermal expansion in
strain (κε) and stress (κσ), where Pa=N
−2 −3 9 6
m =J m , Gpa=10 Pa, MJ=10 J
Table 11.2 Typical values of
thermomechanical coupling factors for
metals and ceramics, where
2
η=3KT0κε /Cp.
Chapter 12
Table 12.1 Correspondence of the
dual-phase-lag (DPL) model with
Fourier diffusion, thermal (CV) wave,
two-step (parabolic and hyperbolic),
phonon-scattering model, and
Gurtin–Pipkin’s model in terms of τT
and τq: τR≡the relaxation time in the
umklapp process, τN≡the relaxation
time in the normal process, τe≡time
constant in the memory function of
9
internal energy, τ≡effective relaxation
time (Jeffreys and thermal waves) and
time constant in the memory function of
heat flux vector (Gurtin–Pipkin),
Fe≡amplitude of the exponential kernel
of internal energy, Fq≡amplitude of the
exponential kernel of heat flux vector,
k1≡nondimensional parameter, ratio of
τT/τq(Jeffreys)
Table 12.2 Thermal diffusivity (α), phase
lags (τTand τq), and speed ofTwave
4 −3 −1
(CT) (Ce=2.1×10 Jm K at room
temperature, ps≡picosecond,
ns≡nanosecond)
List of Illustrations
Chapter 01
Figure 1.1 Energy transport through
phonon collision. The mean free path for
phonon 1 in successive collisions is
(d1+d2+d3)/3. The mean free “time”
for phonon 1 in successive collisions is (t
– t1)/3.
Figure 1.2 Phonon interaction and
scattering in a thin film of thickness of
the same order of magnitude as the
mean free path, illustrating the challenge
of the microscale effect in space to the
concept of the temperature gradient.
10