We analyze the effects of boundary conditions on the evolution of ballistic heat transport in four theoretical models and propose that a Fourier equation with an effective size-dependent thermal conductivity is a good candidate for the description of ballistic transport when boundary conditions are suitably imposed.
Issue Section:
Micro/Nanoscale Heat Transfer
1.
Zhang
, Z.
, 2007, Nano/Microscale Heat Transfer
, McGraw-Hill
, New York
.2.
Cahill
, D. C.
, Ford
, W. K.
, Goodson
, K. E.
, Mahan
, G. D.
, Majumdar
, A.
, Maris
, H. J.
, Merlin
, R.
, and Phillpot
, S. R.
, 2003, “Nanoscale Thermal Transport
,” J. Appl. Phys.
0021-8979, 93
(2
), pp. 793
–818
.3.
Joshi
, A. A.
, and Majumdar
, A.
, 1993, “Transient Ballistic and Diffusive Phonon Heat Transport in Thin Films
,” J. Appl. Phys.
0021-8979, 74
(1
), pp. 31
–39
.4.
Chen
, G.
, 2001, “Ballistic-Diffusive Heat-Conduction Equations
,” Phys. Rev. Lett.
0031-9007, 86
(11
), pp. 2297
–2300
.5.
Chen
, G.
, 2002, “Ballistic-Diffusive Equations for Transient Heat-Conduction From Nano to Macroscales
,” ASME J. Heat Transfer
0022-1481, 124
, pp. 320
–328
.6.
Naqvi
, K. R.
, and Waldenstrøm
, S.
, 2005, “Brownian Motion Description of Heat Conduction by Phonons
,” Phys. Rev. Lett.
0031-9007, 95
, p. 065901
.7.
Alvarez
, F. X.
, and Jou
, D.
, 2007, “Memory and Nonlocal Effects in Heat Transport: From Diffusive to Ballistic Regimes
,” Appl. Phys. Lett.
0003-6951, 90
, p. 083109
.8.
Alvarez
, F. X.
, and Jou
, D.
, 2008, “Size and Frequency Dependence of Effective Thermal Conductivity in Nanosystems
,” J. Appl. Phys.
0021-8979, 103
(9
), p. 094321
.9.
Jou
, D.
, Casas-Vázquez
, J.
, and Lebon
, G.
, 2001, Extended Irreversible Thermodynamics
, 3rd ed., Springer-Verlag
, Berlin
.10.
Jou
, D.
, and Casas-Vazquez
, J.
, 1990, “Nonequilibrium Absolute Temperature, Thermal Waves and Phonon Hydrodynamics
,” Physica A
0378-4371, 163
(1
), pp. 47
–58
.11.
Li
, D.
, Wu
, Y.
, Fan
, R.
, Yang
, P.
, and Majumdar
, A.
, 2003, “Thermal Conductivity of Si/SiGe Superlattice Nanowires
,” Appl. Phys. Lett.
0003-6951, 83
(15
), pp. 3186
–3188
.12.
Casas-Vázquez
, J.
, and Jou
, D.
, 2003, “Temperature in Non-Equilibrium States: A Review of Open Problems and Current Proposals
,” Rep. Prog. Phys.
0034-4885, 66
(11
), pp. 1937
–2023
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.