This paper investigates a numerical solution of 2D transient heat conduction in an anisotropic cylinder, subjected to a prescribed temperature over the two end sections and a convective boundary condition over the whole lateral surface. The analysis of this anisotropic heat conduction problem is tedious because the corresponding partial differential equation contains a mixed-derivative. In order to overcome this difficulty, a linear coordinate transformation is used to reduce the anisotropic cylinder heat conduction problem to an equivalent isotropic one, without complicating the boundary conditions but with a more complicated geometry. The alternating-direction implicit finite-difference method (ADI) is used to integrate the isotropic equation combined with boundary conditions. Inverse transformation provides profile temperature in the anisotropic cylinder for full-field configuration. The numerical code is validated by the analytical heat conduction solutions available in the literature such as transient isotropic solution and steady-state orthotropic solution. The aim of this paper is to study the effect of cross-conductivity on the temperature profile inside an axisymmetrical anisotropic cylinder versus time, radial Biot number (Bir), and principal conductivities. The results show that cross-conductivity promotes the effect of Bir according to the principal conductivities. Furthermore, the anisotropy increases the time required to achieve the steady-state heat conduction.

References

References
1.
Minkowycz
,
W. J.
, and
Haji-Sheikh
,
A.
,
2009
, “
Asymptotic Behaviors of Heat Transfer in Porous Passages With Axial Conduction
,”
Int. J. Heat Mass Transfer
,
52
(
13–14
), pp.
3101
3108
.
2.
Nagayama
,
G.
, and
Cheng
,
P.
,
2004
, “
Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation
,”
Int. J. Heat Mass Transfer
,
47
(
3
), pp.
501
513
.
3.
Mera
,
N. S.
,
Elliot
,
L.
,
Ingham
,
D. B.
, and
Lesnic
,
D.
,
2002
, “
An Iterative Algorithm for Singular Cauchy Problems for the Steady State Anisotropic Heat Conduction Equation
,”
Eng. Anal. Boundary Elem.
,
26
(
2
), pp.
157
168
.
4.
Ma
,
C. C.
, and
Chang
,
S. W.
,
2004
, “
Analytical Exact Solutions of Heat Conduction Problems for Anisotropic Multi-Layered Media
,”
Int. J. Heat Mass Transfer
,
47
(
8–9
), pp.
1643
1655
.
5.
Hsieh
,
M. H.
, and
Ma
,
C. C.
,
2002
, “
Analytical Investigations for Heat Conduction Problems in Anisotropic Thin-Layer Media With Embedded Heat Sources
,”
Int. J. Heat Mass Transfer
,
45
(
20
), pp.
4117
4132
.
6.
Bouzid
,
S.
,
Boumaaza
,
A. C.
, and
Afrid
,
M.
,
2008
, “
Calcul du champ de température dans un solide anisotrope par la méthode des éléments finis. Cas bidimensionnel
,”
Revue des Energies Renouvelables CISM'08 Oum El Bouaghi Conference
, pp.
103
111
.
7.
Marczak
,
R. J.
, and
Denda
,
M.
,
2011
, “
New Derivations of the Fundamental Solution for Heat Conduction Problems in Three-Dimensional General Anisotropic Media
,”
Int. J. Heat Mass Transfer
,
54
(
15–16
), pp.
3605
3612
.
8.
Gu
,
Y.
,
Chen
,
W.
, and
He
,
X.-Q.
,
2012
, “
Singular Boundary Method for Steady-State Heat Conduction in Three Dimensional General Anisotropic Media
,”
Int. J. Heat Mass Transfer
,
55
(
17–18
), pp.
4837
4848
.
9.
Wang
,
H. M.
, and
Liu
,
C. B.
,
2013
, “
Analytical Solution of Two-Dimensional Transient Heat Conduction in Fiber-Reinforced Cylindrical Composites
,”
Int. J. Therm. Sci.
,
69
, pp.
43
52
.
10.
Amiri Delouei
,
A.
,
Kayhani
,
M. H.
, and
Norouzi
,
M.
,
2012
, “
Exact Analytical Solution of Unsteady Axi-Symmetric Conductive Heat Transfer in Cylindrical Orthotropic Composite Laminates
,”
Int. J. Heat Mass Transfer
,
55
(
15–16
), pp.
4427
4436
.
11.
Ozisik
,
M. N.
, and
Shouman
,
S. M.
,
1980
, “
Transient Heat Conduction in an Anisotropic Medium in Cylindrical Coordinates
,”
J. Franklin Inst.
,
309
(
6
), pp.
457
472
.
12.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
McGraw-Hill
,
New York
.
13.
Ozisik
,
M. N.
,
1993
,
Heat Conduction
,
2nd ed.
,
Wiley
,
New York
.
14.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
1997
,
Numerical Recipes in Fortran 77: The Art of Scientific Computing
,
2nd ed.
, Vol.
1
,
Cambridge University Press
, New York.
You do not currently have access to this content.