Inverse estimation of location of internal heat source in conduction

Abstract

In this study, an inverse method is proposed for estimating the boundary conditions in a heat conduction problem using a regression analysis, neural network trained by a local optimizer and lastly, that trained by the local and global optimizers simultaneously. The test problem consists of a square slab with an internal heat source of circular shape. Once the boundary conditions of the square slab and periphery of the heat source are specified, the temperature can be estimated for two-dimensional heat conduction problems. This constitutes the forward heat transfer problem. Reverse heat transfer problem is formulated to determine the location of the heat source from some known temperature values elsewhere in the slab. A reasonably good solution is obtained from the said inverse problem using the proposed approach, whose performance is also compared with that of other two approaches.