In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown space and time dependent convection heat transfer coefficient of an annular fin. While knowing the temperature or strain history at the measuring positions of the fin, the convection heat transfer coefficient between the fin and the ambient fluid can be successfully computed. No prior information is needed on the functional form of the unknown convection heat transfer coefficient; and thus, the present study is classified as the function estimation inverse calculation. A particular feature in this study is that the thermal and strain fields are coupled, which makes solving the inverse problem a highly challenging task. The accuracy of the inverse analysis is examined by using the simulated temperature or strain measurements. Results show that excellent estimations of the convection heat transfer coefficient, temperature distributions and thermal stress distributions can be obtained for all the cases considered in this study. (c) 2006 Elsevier Ltd. All rights reserved.