A New Numerical Procedure for Coupling Radiation in Participating Media With Other Modes of Heat Transfer

Abstract

Traditionally, radiation in participating media is coupled to other modes of heat transfer using an iterative procedure in which the overall energy equation (EE) and the radiative transfer equation (RTE) are solved sequentially and repeatedly until both equations converge. Although this explicit coupling approach is convenient from the point of view of computer code development, it is not necessarily the best approach for stability and convergence. A new numerical procedure is presented in which the EE and RTE are implicitly coupled and solved simultaneously, rather than as segregated equations. Depending on the average optical thickness of the medium, it is found that the coupled solution approach results in convergence that is between 2–100 times faster than the segregated solution approach. Several examples in one- and two-dimensional media, both gray and nongray, are presented to corroborate this claim.