On the Solution of the Diffusion Equation With a Heat Source

[+] Author and Article Information
S. A. Hovanessian

California Research Corporation, La Habra, Calif.

J. Heat Transfer 84(4), 312-316 (Nov 01, 1962) (5 pages) doi:10.1115/1.3684379 History: Received May 29, 1961


Analytical and finite difference solutions are developed for the temperature distribution in a medium of rectangular cross section having uniform properties and either constant temperature or insulated boundaries and with a line heat source of constant strength perpendicular to the section. The analytical solutions are infinite series which converge rapidly except at the source location where they diverge to infinity. The finite difference solutions are given in closed form. The temperature values obtained from the latter are compared to those of the former and the effect of time step and space increments on the finite difference solutions studied.

Copyright © 1962 by ASME
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