Nonlinear Heat Transfer in Planar Solids: Direct and Inverse Applications

Abstract

For planar geometries, the present investigation develops a method for generating approximate solutions for heat conduction in solids with variable 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 nonlinear 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 nonlinear inverse problem. The concept of approximating the original material with a pseudolinear one is employed, and thermal diffusivity iteration is introduced. Numerical examples are presented to illustrate the computational procedures.