Solution of an inverse heat transfer problem by means of empirical reduction of modes

Abstract

An efficent method of solving the inverse heat transfer problem of estimating the unknown function of wall heat flux for laminar flow inside a duct is proposed in the present paper. It is based on the Karhunen—Loeve Galerkin procedure which employs the empirical eigenfunctions of the Karhunen—Loeve decomposition as basis functions of a Galerkin procedure. With the empirical eigenfunctions, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and thus convert the governing equations to a model with a minimum degree of freedom, resulting in a drastic reduction of computation time without loss of accuracy. The performance of the present technique of inverse analysis using the Karhunen—Loeve Galerkin procedure is evaluated by several numerical experiments, and is found to be very accurate as well as efficient.