Estimation of an unknown distributed heat source in the inverse heat conduction problem

Abstract

This article presents a hybrid numerical method to predict the unknown space and time dependent strength of heat source in one-dimensional inverse heat conduction problems. The hybrid numerical algorithm is based on the Borukhov-Vabishchevich (2000) and Newton's iterative method. The spatial distribution of the heat source strength is represented a priori as the series forms of the known function and. the unknown coefficient in the parameter estimation can be adjusted from the improperly initial distribution to the acceptable one automatically using the Newton's iterative method. To confirm the validity and efficiency of the present method, two comparative examples are presented. Comparisons are made between the present estimations and the exact solutions, and the agreement is found out to be generally good.