International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1633-1641

A two-dimensional inverse heat conduction problem for estimating heat source

A. Shidfar,1 A. Zakeri,1 and A. Neisi2

1Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
2Department of Statistics, Faculty of Economics, Allameh Tabatabaie University,, Dr. Beheshti Avenue, Tehran 15136-15411, Iran

Received 28 May 2002; Revised 9 May 2005

Copyright © 2005 A. Shidfar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This note considers the problem of estimating unknown time-varying strength of the temporal-dependent heat source, from measurements of the temperature inside the square domain, when the prior knowledge of the source functions is not available. This problem is an inverse heat conduction problem. In this process, the direct problem will be solved by using the heat fundamental solution. Then a sequential algorithm is developed to solve a Volterra integral equation, which has been produced by using unknown source term and overposed data conditions. This algorithm is based on the piecewise linear continuous functions. The performance of the present technique of inverse analysis is evaluated, by means of several numerical experiments, and is found to be very accurate as well as efficient.