Abstract

This paper concerns the determination of the effective thermal conductivity of heterogeneous media with randomly dispersed inclusions. Inclusions of arbitrary shape can be considered since the self-consistent problem is solved numerically with the finite element method. Results for many different cases of heterogeneous media with axially symmetrical inclusions are presented. Moreover, the influence of the inclusion’s shape on the pseudo-percolation threshold is investigated. [S0022-1481(00)00801-X]

Issue Section:
Technical Notes
Keywords:
finite element analysis, thermal conductivity, random media, mixtures, inclusions, heat transfer, composite materials, Composites, Conduction, Finite Element, Heat Transfer, Materials
Topics:
Finite element methods, Percolation theory, Thermal conductivity, Tensors, Shapes, Heat flux
1.
Lord
Rayleigh
,
1892
, “
On the Influence of the Obstacles in Rectangular Order Upon the Properties of a Medium
,”
Philos. Mag.
,
134
, pp.
481
–
502
.
2.
Wiener
,
O.
,
1912
,
Abh. Sa¨chs. Ges. (ahad) Wiss.
,
32
, p.
509
509
.
3.
Buyevich
,
Y. A.
,
1974
, “
On the Thermal Conductivity of Granular Material
,”
Chem. Eng. Sci.
,
29
, pp.
37
–
48
.
4.
Buyevich
,
Y. A.
,
1992
, “
Heat Mass Transfer in Disperse Media-I, II
,”
Int. J. Heat Mass Transf.
,
35
, pp.
2445
–
62
.
5.
Furman˜ski
,
P.
,
1997
, “
Heat Conduction in Composites: Homogenization and Macroscopic Behavior
,”
Appl. Mech. Rev.
,
50
, p.
327
327
.
6.
Bruggeman
,
D. A. G.
,
1935
, “
Berechnung Verschiedener Physikalischer Konstanten Von Heterogenen Substanzen
,”
Ann. Phys. (Paris)
,
24
, p.
636
636
.
7.
Landauer
,
R.
,
1952
, “
The Electrical Resistance of Binary Metallic Mixtures
,”
J. Appl. Phys.
,
23
, p.
779
779
.
8.
Kerner
,
E. H.
,
1956
, “
The Electrical Conductivity of Composite Media
,”
Proc. Phys. Soc. B
,
69
, p.
802
802
.
9.
Hashin
,
Z.
, and
Shtrikman
,
S.
,
1962
, “
A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials
,”
J. Appl. Phys.
,
33l
, p.
3125
3125
.
10.
Hashin
,
Z.
,
1968
, “
Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites
,”
J. Comp. Mat.
,
2
, pp.
284
–
300
.
11.
Yang
,
Q. S.
,
Tang
,
L.
, and
Chen
,
H.
,
1994
, “
Self-Consistent Finite Element Method: A New Method of Predicting Effective Properties of Inclusion Media
,”
Finite Elem. Anal. Design
,
17
, pp.
247
–
257
.
12.
Batchelor
,
G. K.
,
1974
, “
Transport Properties of Two-Phase Materials With Random Structure
,”
Annu. Rev. Fluid Mech.
,
6
, p.
227
227
.
13.
Miloh
,
T.
, and
Benveniste
,
Y.
,
1988
, “
A Generalized Self-Consistent Method for the Effective Conductivity of Composites With Ellipsoidal Inclusions and Cracked Body
,”
J. Appl. Phys.
,
63
, pp.
789
–
796
.
14.
Landauer, R., 1978, “Electrical Conductivity in Inhomogeneous Media,” Electrical, Transport and Optical Properties of Inhomogeneous Media, Garland & Tanner, eds., American Institute of Physics, New York, Vol. 99.
15.
Clerc
,
J. P.
, et al.,
1983
, “
La Percolation: Mode`les, Simulations Analogiques et Nume´riques
,”
Ann. Phys.
,
8
, pp.
1
–
108
.
16.
Banhegyi
,
G.
,
1986
, “
Comparison of Electrical Mixture Rules for Composites
,”
Colloid Polym. Sci.
,
264
, pp.
1030
–
1050
.
17.
Hatta
,
H.
, and
Taya
,
M.
,
1985
, “
Effective Thermal Conductivity of Misoriented Short Fiber Composite
,”
J. Appl. Phys.
,
58
, pp.
2478
–
2486
.
18.
Polder
,
D.
, and
Van Santen
,
J. H.
,
1946
, “
The Effective Permeability of Mixtures of Solids
,”
Physica XII
,
5
, p.
257
257
.
Copyright © 2000
 by ASME
You do not currently have access to this content.