An Iterative Boundary Integral Numerical Solution for General Steady Heat Conduction Problems

[+] Author and Article Information
M. S. Khader

Calro University, Giza, Egypt

M. C. Hanna

Electrical & Computer Engineering, University of South Carolina, Columbia, S. C. 29208

J. Heat Transfer 103(1), 26-31 (Feb 01, 1981) (6 pages) doi:10.1115/1.3244423 History: Received May 16, 1980; Online October 20, 2009


An iterative boundary integral numerical method for solving the steady conduction of heat is developed. The method is general for two- and three-dimensional regions with arbitrary boundary shapes. The development is generalized to include the first, second, and third kind of boundary conditions and also radiative boundary and temperature-space dependent convective coefficient cases. With Kirchhoff’s transformation, cases of temperature-dependent thermal conductivity with general boundary conditions are also accounted for by the present method. A variety of problems are analyzed with this method and their solutions are compared to those obtained analytically. A comparison between the present method and the finite difference predictions is also investigated for a case of mixed temperature and convective boundary conditions. Moreover, two-dimensional regions with three kinds of boundary conditions and irregular-shaped boundaries are used to illustrate the versatility of the technique as a computational procedure.

Copyright © 1981 by ASME
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