Research Papers

Numerical Solution of Unsteady Conduction Heat Transfer in Anisotropic Cylinders

[+] Author and Article Information
Aslib Imane, Hamza Hamid, Lahjomri Jawad, Zniber Khalid, Oubarra Abdelaziz

Laboratory of Mechanics,
Faculty of Science Aïn Chock,
University Hassan II,
Casablanca 20100, Morocco

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received January 29, 2016; final manuscript received April 19, 2016; published online May 17, 2016. Assoc. Editor: John C. Chai.

J. Thermal Sci. Eng. Appl 8(3), 031013 (May 17, 2016) (9 pages) Paper No: TSEA-16-1026; doi: 10.1115/1.4033467 History: Received January 29, 2016; Revised April 19, 2016

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.
Ozisik, M. N. , 1993, Heat Conduction, 2nd ed., Wiley, New York.
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.


Grahic Jump Location
Fig. 4

Integration domain of Eq. (7)

Grahic Jump Location
Fig. 3

Isotropic geometry studied of the solid cylinder after a linear coordinate transformation

Grahic Jump Location
Fig. 2

Geometry studied of the solid cylinder in the plane (r,z)

Grahic Jump Location
Fig. 1

Geometry and boundary conditions of the solid cylinder

Grahic Jump Location
Fig. 10

History for center dimensionless temperature for Bir = 0.1 and 10

Grahic Jump Location
Fig. 5

History of temperature profile in an isotropic cylinder for θR=θL=θF=0, and θi=1

Grahic Jump Location
Fig. 6

Steady-state temperature profiles in orthotropic cylinder for θR=θF=0 and θL=1

Grahic Jump Location
Fig. 7

Full-fields temperature distribution for symmetric configuration (θL=θR=1 and θF=θi=0), for kz/kr=1

Grahic Jump Location
Fig. 8

Full-fields temperature distribution for symmetric configuration (θL=θR=1 and θF=θi=0), for kz/kr=2

Grahic Jump Location
Fig. 9

Full-fields temperature distribution for symmetric configuration (θL=θR=1 and θF=θi=0), for kz/kr=0.5



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In