Abstract
Determination of wall heat flux for laminar flow inside a duct from the temperature measurement within the flow is a typical inverse heat convection problem which is ill-posed. In the present paper, an efficient method based on the Karhunen–Loève Galerkin procedure (Park and Cho, 1996, Chem. Engng Sci. 51, 81–98) is proposed for the solution of this kind of inverse heat transfer problems. Employing the Karhunen–Loève Galerkin procedure, which is a Galerkin method employing empirical eigenfunctions of the Karhunen–Loève decomposition, 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 a given system into a model with a minimum degree of freedom, resulting in drastic reduction of computation time. The performance of the present technique of inverse analysis using the Karhunen–Loève Galerkin procedure is evaluated by numerical experiments on the identification of unknown functions of wall heat flux, and is found to be very accurate as well as efficient.
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