RESEARCH PAPERS: Conduction Heat Transfer

Solving an Inverse Heat Conduction Problem by a “Method of Lines”

[+] Author and Article Information
L. Eldén

Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden

J. Heat Transfer 119(3), 406-412 (Aug 01, 1997) (7 pages) doi:10.1115/1.2824112 History: Received February 19, 1996; Revised February 21, 1997; Online December 05, 2007


We consider a Cauchy problem for the heat equation in the quarter plane, where data are given at x = 1 and a solution is sought in the interval 0 < x < 1. This inverse heat conduction problem is a model of a situation where one wants to determine the surface temperature given measurements inside a heat-conducting body. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In an earlier paper we showed that replacement of the time derivative by a difference stabilizes the problem. In this paper we investigate the use of time differencing combined with a “method of lines” for solving numerically the initial value problem in the space variable. We discuss the numerical stability of this procedure, and we show that, in most cases, a usual explicit (e.g., Runge-Kutta) method can be used efficiently and stably. Numerical examples are given. The approach of this paper is proposed as an alternative way of implementing space-marching methods for the sideways heat equation.

Copyright © 1997 by The American Society of Mechanical Engineers
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