Transient heat conduction with temperature-dependent thermal conductivity by the orthogonal collocation method

Abstract

The orthogonal collocation method is employed in this work for solving the nonlinear transient heat conduction in a finite slab with variable thermal conductivity. Linear and nonlinear temperature dependences of thermal conductivity are considered. The orthogonal collocation method involves the approximation of the spatial derivative terms in the governing energy equation by an orthogonal polynomial and thus the nonlinear partial differential equation is transformed into a set of ordinary differential equation, which in turn can be integrated by any numerical integration scheme. Because of the accuracy and stability of the numerical integration method, very satisfactory results can be obtained with low order of orthogonal collocation approximation. The examples given in this work show that a wide variety of temperature-dependent heat conduction problems can be tackled by this method without much difficulty.