A modification to the finite difference equations is proposed in modeling multidimensional flows in an anisotropic material. The method is compared to the control volume version of the Taylor expansion and the finite element formulation derived from the Galerkin weak statement. For the same number of nodes, the proposed finite difference formulation approaches the accuracy of the finite element method. For the two-dimensional case, the effect on accuracy and solution stability is approximately the same as quadrupling the number of nodes for the Taylor expansion with only a proportionately small increase in the number of computations. Excellent comparisons are made with a new limiting case exact solution modeling anisotropic heat conduction and a transient, anisotropic conduction experiment from the literature.

1.
Baker, A. J., 1983, Finite Element Computational Mechanics, 1st ed., Hemisphere Publishing, New York.
2.
Banaszek
J.
,
1984
, “
A Conservative Finite Element Method for Heat Conduction Problems
,”
International Journal for Numerical Methods in Engineering
, Vol.
20
, pp.
2033
2050
.
3.
Blackwell
B. F.
, and
Hogan
R. E.
,
1993
, “
Numerical Solution of Axisymmetric Heat Conduction Problems Using Finite Control Volume Technique
,”
Journal of Thermophysics and Heat Transfer
, Vol.
7
, No.
3
, pp.
462
471
.
4.
Chang
Y. P.
,
Kang
C. S.
, and
Chen
D. J.
,
1973
, “
The Use of Fundamental Green’s Functions for the Solution of Problems of Heat Conduction in Anisotropic Media
,”
International Journal of Heat and Mass Transfer
, Vol.
16
, pp.
1905
1918
.
5.
Fillo, J. A., Powell, J., and Benenati, R., 1975, “A Nonsteady Heat Conduction Code With Radiation Boundary Conditions,” ASME Paper No. 75-WA-HT-91.
6.
Forsythe, G. E., and Wasow, W. R., 1960, Finite Difference Methods for Partial Differential Equations, 1st ed., Wiley, New York.
7.
Friedman
H. A.
, and
McFarland
B. L.
,
1968
, “
Two-Dimensional Ablation and Heat Conduction Analysis for Multimaterial Thrust Chamber Walls
,”
Journal of Spacecraft and Rockets
, Vol.
5
, No.
7
, pp.
753
761
.
8.
Gray
G. G.
, and
O’Neill
K.
,
1976
, “
On the General Equations for Flow in Porous Media and Their Reduction to Darcy’s Law
,”
Water Resources Research
, Vol.
12
, No.
2
, pp.
148
154
.
9.
Katayama, K., Saito, A., and Kobayashi, N., 1974, “Transient Heat Conduction in Anisotropic Solids,” 1974 International Heat Transfer Conference, Vol. I, pp. 137–141.
10.
Ozisik, M. N., 1980, Heat Conduction, 1st ed., Wiley, New York.
11.
Padovan
J.
,
1974
, “
Steady Conduction of Heat in Linear and Nonlinear Fully Anisotropic Media by Finite Elements
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
96
, pp.
313
317
.
12.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, 1st ed., Hemisphere Publishing, New York.
13.
Polehn, R. A., 1994, “Thermal Response of an Axisymmetric, Charring-Decomposing Polymer,” Ph.D. Dissertation, University of Tennessee at Knoxville, TN.
14.
Scheideggar
A. E.
,
1954
, “
Directional Permeability of Porous Media to Homogenous Fluids
,”
Geofisica pura e Applicata
, Vol.
28
, pp.
75
90
.
15.
Sinha
S. K.
,
Sundararajan
T.
, and
Garg
V. K.
,
1992
, “
Anisotropic Porous Medium Model for Alloy Solidification
,”
Transport Phenomena in Materials Processing and Manufacturing
, ASME HTD-Vol.
196
, pp.
193
200
.
16.
Stokes, E. H., and Koenig, J. R., 1991, “Gas Permeability of FM 5055 (Pre-Avtex Shutdown) Carbon Phenolic Composite in the Fill Direction as a Function of Across-Ply Compressive Load and Temperature,” SRI-MME-91-056-6672-003, Southern Research Institute, Birmingham, AL.
17.
Weaver
J. A.
, and
Viskanta
R.
,
1989
, “
Effects of Anisotropic Heat Conduction on Solidification
,”
Numerical Heat Transfer
, Part A, Vol.
15
, pp.
181
195
.
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