Application of finite-element-techniques to the interaction of conduction and radiation in an absorbing, scattering and emitting medium

In this paper, the authors demonstrate that a Galerkin finite element method of analysis, utilizing isoparametric elements, offers a viable means of solving continuum thermal radiation problems with conduction in a participating medium. The participating medium was considered to be a gray radiation medium exhibiting isotropic absorption, emission, and scattering characteristics and optical properties that are independent of temperature. The medium was considered to be bounded by infinite parallel opaque, gray surfaces with diffuse emission and reflection characteristics. In solving this problem, a finite element formulation was developed to describe a system in radiative equilibrium. Then the results of this first analysis were linked with a second finite element model which incorporated conduction into the analysis. The results of this study were found to be in good agreement with existing published data. The model offers the following advantageous features: geometric generality, a computational algorithm which is 'convenient' and 'computable', and a functional basis for extension of the radiation model to higher order approximation.