Numerical Solution of One Case of Inverse Heat Conduction Problems

This paper is concerned with a method for solving one case of inverse heat conduction problems. The solution is presented in terms of a series containing the derivatives of the temperature with respect to time and shows no explicit dependence on the initial temperature distribution. In order to solve the problem some temperature histories at the interior points should be known. The derivatives are calculated with the aid of the regularization method. The results of some test cases are presented. Errors due to data accuracy, time steps, Biot numbers, etc. are investigated. The paper focuses on problems that are numerically formulated.