Development of a finite element radiation model applied to two-dimensional participating media

Abstract

A finite element method (FEM) for radiative heat transfer has been developed and it is applied to 2D problems with unstructured meshes. The present work provides a solution for temperature distribution in a rectangular enclosure with black or gray walls containing an absorbing, emitting, isotropically scattering medium. Compared with the results available from Monte Carlo simulation and finite volume method (FVM), the present FEM can predict the radiative heat transfer accurately. © 2005 Radiative heat transfer is a major heat transfer model and it is usually strongly coupled with fluid dynamics in many high-temperature systems such as boilers, furnaces, rocket engines, etc. An accurate modeling of these systems requires a simultaneous solution of the radiative transfer equation (RTE) and the fluid dynamics equations. In the last several decades, many methods have been developed for solving the RTE. They include the zone method, Monte Carlo method, flux method, discrete transfer method, P-N method, discrete ordinates method (DOM), finite volume method (FVM), etc. Each of these methods has its own relative advantages and disadvantages and none of them is superior to the others in all aspects. However, many numerical complications may arise from incompatibilities between the radiative transport model and the discrete formulation employed for fluid dynamics and other heat transfer modes. The finite element formulation for RTE avoids many of these complications and has the advantage of greater compatibility with existing finite element based heat transfer software. Besides, the FEM could simplify the problems of complex geometries using unstructured meshes.