This article solves the two dimensional inverse problem of estimating the unknown heat flux at a pin fin base by the conjugate gradient method. In the estimating processes, no prior information on the functional form of the unknown quantity is required. The accuracy of the inverse analysis is examined by simulated exact and inexact measurements of temperature at interior locations of the pin fin. The numerical results show that good estimations on the heat flux can be obtained for all the test cases considered in this study. Furthermore such a technique can be applied to determine the heat flux acting on an internal surface, where a direct measurement is not feasible. (C) 2003 Elsevier Ltd. All rights reserved.