Dynamic simulation of thermal radiation in participating media by means ofmode reduction

The modeling of combined radiative and conductive heat transfer in three-di mensional enclosures with participating media is challenging since the prob lem is always implicit in temperature, as the heat conduction equation has the divergence of radiative flux as a source term and the radiative transfe r equation has the black body intensity as a source. The degree of freedom or the number of equations in these systems is tremendously large especiall y when the radiation field is resolved by the S-4 method which is known to yield reliable results for the whole range of optical thickness. But one mu st reduce the number of equations to be solved before implementing on these systems modern techniques of estimation of parameters or inverse problem w hich requires repeated computation of governing equations. In the present p aper, we apply the Karhunen-Loeve Galerkin procedure to reduce the governin g equations of these systems to a low-dimensional model which predicts the performance of these systems with the accuracy of S-4 method at a drastical ly reduced computational cost. This technique is expected to facilitate the implementation of many techniques of estimation of parameters and the solu tion of inverse problems of the radiative heat transfer. (C) 1999 Elsevier Science Ltd. All rights reserved.