A general expression has been obtained to estimate thermal conductivities of both stochastic and periodic structures with high-solid thermal conductivity. An air layer partially occupied by slanted circular rods of high-thermal conductivity was considered to derive the general expression. The thermal conductivity based on this general expression was compared against that obtained from detailed three-dimensional numerical calculations. A good agreement between two sets of results substantiates the validity of the general expression for evaluating the stagnant thermal conductivity of the periodic structures. Subsequently, this expression was averaged over a hemispherical solid angle to estimate the stagnant thermal conductivity for stochastic structures such as a metal foam. The resulting expression was found identical to the one obtained by Hsu et al., Krishnan et al., and Yang and Nakayama. Thus, the general expression can be used for both stochastic and periodic structures.

References

1.
Hestroni
,
G.
,
Gurevich
,
M.
, and
Rozenblit
,
R.
,
2006
, “
Sintered Porous Medium Heat Sink for Cooling of High-Power Mini-Devices
,”
Int. J. Heat Fluid Flow
,
27
(2), pp.
259
266
.
2.
Lu
,
T. J.
,
Stone
,
H. A.
, and
Ashby
,
M. F.
,
1998
, “
Heat Transfer in Open-Cell Metal Foams
,”
Acta Mater.
,
46
(10), pp.
3619
3635
.
3.
Boomsman
,
K.
,
Poulikakos
,
D.
, and
Ventikos
,
Y.
,
2003
, “
Simulation of Flow Through Open Cell Foams Using an Idealized Periodic Cell Structure
,”
Int. J. Heat Fluid Flow
,
24
(6), pp.
825
834
.
4.
Krishnan
,
S.
,
Garimella
,
S. V.
, and
Murthy
,
J. Y.
,
2008
, “
Simulation of Thermal Transport in Open-Cell Metal Foams: Effect of Periodic Unit-Cell Structure
,”
ASME J. Heat Transfer
,
130
(2), p.
024503
.
5.
Tian
,
J.
,
Kim
,
T.
,
Lu
,
T. J.
,
Hodson
,
H. P.
, and
Queheillalt
,
D. T.
,
2004
, “
The Effects of Topology Upon Fluid-Flow and Heat-Transfer Within Cellular Copper Structures
,”
Int. J. Heat Mass Transfer
,
47
(14–16), pp.
3171
3186
.
6.
Yan
,
H. B.
,
Zhang
,
Q. C.
,
Lu
,
T. J.
, and
Kim
,
T.
,
2015
, “
A Lightweight X-Type Metallic Lattice in Single-Phase Forced Convection
,”
Int. J. Heat Mass Transfer
,
83
, pp.
273
283
.
7.
Haydn
,
N.
,
Wadley
,
G.
, and
Queheillalt
,
D. T.
,
2007
, “
Thermal Applications of Cellular Lattice Structures
,”
Mater. Sci. Forum
,
539–543
, pp.
242
247
.
8.
Nan
,
C. W.
,
Birringer
,
R.
,
Clarke
,
D. R.
, and
Gleiter
,
H.
,
1997
, “
Effective Thermal Conductivity of Particulate Composites With Interfacial Thermal Resistance
,”
J. Appl. Phys.
,
81
(
10
), pp.
6692
6699
.
9.
Hsu
,
C. T.
,
Cheng
,
P.
, and
Wong
,
K. W.
,
1995
, “
A Lumped Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media
,”
ASME J. Heat Transfer
,
117
(2), pp.
264
269
.
10.
Paek
,
J. W.
,
Kang
,
B. H.
,
Kim
,
S. Y.
, and
Hyun
,
J. M.
,
2000
, “
Effective Thermal Conductivity and Permeability of Aluminium Foam Materials
,”
Int. J. Thermophys.
,
21
(2), pp.
453
464
.
11.
Dul'nev
,
G. N.
,
1965
, “
Heat Transfer Through Solid Disperse Systems
,”
J. Eng. Phys.
,
9
(3), pp.
275
279
.
12.
Yang
,
C.
, and
Nakayama
,
A.
,
2010
, “
A Synthesis of Tortuosity and Dispersion in Effective Thermal Conductivity of Porous Media
,”
Int. J. Heat Mass Transfer
,
53
(15–16), pp.
3222
3230
.
13.
Krishnan
,
S.
,
Murthy
,
J. Y.
, and
Garimella
,
S. V.
,
2006
, “
Direct Simulation of Transport in Open-Cell Metal Foam
,”
ASME J. Heat Transfer
,
128
(8), pp.
793
799
.
14.
Lemlich
,
R.
,
1987
, “
A Theory for the Limiting Conductivity of Polyhedral Foam at Low Density
,”
J. Colloid Interface Sci.
,
64
(1), pp.
107
110
.
You do not currently have access to this content.