Transient Nonsimilarity Nonlinear Heat Diffusion Solutions

[+] Author and Article Information
F. B. Cheung

Reactor Analysis and Safety Division, Argonne National Laboratory, Argonne, Ill. 60439

J. Heat Transfer 105(2), 295-301 (May 01, 1983) (7 pages) doi:10.1115/1.3245577 History: Received September 21, 1982; Online October 20, 2009


An approximate analytical method for treating parabolic type nonlinear heat diffusion equations is descibed in this study. The method involves transformation of the partial differential equations along with their initial and boundary conditions in terms of several pseudo-similarity variables followed by numerical solution of a system of quasi-ordinary differential equations. One obvious advantage of the approach is that the solution at a particular time can be found independently of the previous history of the temperature field. The simplicity and directness of the method are illustrated by solving the problem of combined conduction and thermal radiation in a large, heat-generating, particulate bed in contact with a solid. Comparison of the present analytical results is made with available finite difference solutions and found to be good.

Copyright © 1983 by ASME
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