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

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. 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.