APPLICATION OF THE METHOD OF INTEGRAL RELATIONS TO TRANSIENT HEAT CONDUCTION

Abstract

This paper presents a general integral method of solving the one-dimensional transient heat conduction equation in a semi-infinite region with constant or variable thermal conductivity. The method is based upon the general framework of the orthonormal method of integral relations of Fletcher and Holt, with a modified procedure for obtaining the integral relations. In addition, a technique for obtaining the necessary initial conditions for the integral relations is proposed instead of the usual practice of using similarity solutions. The main advantages of the present method over most existing integral methods are its generality and controlled accuracy, as demonstrated by the numerical results obtained herein. Comparisons with available exact solutions are generally good.