EFFICIENT TECHNIQUE FOR THE NUMERICAL SOLUTION OF THE ONE-DIMENSIONAL INVERSE PROBLEM OF HEAT CONDUCTION

Abstract

A very efficient numerical technique has been developed to solve the one-dimensional Inverse problem of heat conduction. The Gauss elimination algorithm for solving the tridiagonal system of linear algebraic equations associated with most implicit heat conduction codes is specialized to the inverse problem. When compared to the corresponding direct problem, the upper limit in additional computation time generally does not exceed 27-36%. The technique can be adapted to existing one-dimensional implicit heat conduction codes with minimal effort and applied to difference equations obtained from finite-difference, finite-element, finite control volume, or similar techniques, provided the difference equations are tridiagonal in form. It is also applicable to the nonlinear case in- which thermal properties are temperature-dependent and is valid for one-dimensional radial cylindrical and spherical geometries as well as composite bodies. The calculations reported here were done by modifying a one-dimensional implicit (direct) heat conduction code. Program changes consisted of 13 additional lines of FORTRAN coding.