HYBRID PERTURBATI0IM-GALERK1N TECHNIQUE FOR NONLINEAR HEAT CONDUCTION PROBLEMS I: STEADY PROBLEMS

Abstract

A two-step hybrid analysis technique is applied to steady, nonlinear heat conduction problems involving a parameter. In the first step, a few coordinate functions in a perturbation expansion of the solution are generated. In the second step, an approximate solution consisting of the sum of a subset of these perturbation coordinate functions, each multiplied by an unknown amplitude, is constructed, and then these amplitudes are determined using the Bubnov-Galerkin method. The technique is applied to conduction in a rod with a temperature-dependent conductivity, a problem with a fourth-order radiation term, and Joule heating of an insulated cable with temperature-dependent electrical and thermal conductivities.