The Transient Temperature Distribution in One-Dimensional Heat-Conduction Problems With Nonlinear Boundary Conditions

[+] Author and Article Information
W. Żyszkowski

Institute of Nuclear Research, Swierk near Warsaw, Poland

J. Heat Transfer 91(1), 77-82 (Feb 01, 1969) (6 pages) doi:10.1115/1.3580123 History: Received April 03, 1968; Online August 25, 2011


The transient, one-dimensional temperature distribution is determined for bodies with internal heat generation and nonlinear boundary condition in the form:

k·e·grad θ + ε(θn − T0n)
   + ε1(θ − T0) = 0
Approximate analytical solutions are derived with the aid of Biot’s variational method. The additional boundary condition introduced by Lardner is modified, and this modification makes it possible to solve the problem. The solution has been obtained assuming a parabolic profile of temperature distribution. Formulas are given for plates, cylinders, and spheres. Some results are illustrated with the graphs, and compared with the exact solution for the case of convective heat transfer.

Copyright © 1969 by ASME
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