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.

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
.
You do not currently have access to this content.