Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

[+] Author and Article Information
D. M. France

Argonne National Laboratory, Argonne, Ill.

J. Heat Transfer 93(4), 449-454 (Nov 01, 1971) (6 pages) doi:10.1115/1.3449844 History: Received November 24, 1970; Online August 11, 2010


A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

Copyright © 1971 by ASME
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