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ISSN Online: 2377-424X

ISBN Print: 0-89116-130-9

International Heat Transfer Conference 6
August, 7-11, 1978, Toronto, Canada

NON-LINEAR HEAT TRANSFER IN SOLIDS: DIRECT AND INVERSE CONSIDERATIONS

Get access (open in a dialog) DOI: 10.1615/IHTC6.300
pages 221-226

Аннотация

The current study presents a method for generating approximate solutions for heat conduction in solids with varying thermal conductivity, for both the direct and inverse problems. In the first portion, the direct case, from theoretical considerations, an analytical solution is generated for the original non-linear differential system when it is replaced by a sequence of linear differential equations in some optimum fashion. The approach is unlike traditional methods appearing in the literature, since it does not require perturbation parameters, and penetration distances. It entails an iterative procedure for accuracy improvement.
For the second part of the study, an analytical procedure is developed for the non-linear inverse problem. When input data such as thermocouple responses are known at several interior locations in a solid with varying thermal properties, the transient behavior is established on the boundary. Numerical examples are presented to illustrate the computational procedures.