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

Abstract

The modeling of combined radiative and conductive heat transfer in three-dimensional enclosures with participating media is challenging since the problem is always implicit in temperature, as the heat conduction equation has the divergence of radiative flux as a source term and the radiative transfer equation has the black body intensity as a source. The degree of freedom or the number of equations in these systems is tremendously large especially 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 must reduce the number of equations to be solved before implementing on these systems modern techniques of estimation of parameters or inverse problem which requires repeated computation of governing equations. In the present paper, we apply the Karhunen–Loève Galerkin procedure to reduce the governing 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 drastically reduced computational cost. This technique is expected to facilitate the implementation of many techniques of estimation of parameters and the solution of inverse problems of the radiative heat transfer.