EMPIRICAL-EVALUATION OF AN IMPORTANT APPROXIMATION FOR COMBINED-MODE HEAT-TRANSFER IN A PARTICIPATING MEDIUM USING THE FINITE-ELEMENT METHOD

An approximation common to many finite-element formulations for combined-mode heat transport is investigated. Although the approximation has been employed in the past, no discussion has been provided in the open literature regarding the implications of the approximation for solution accuracy. Two combined-mode problems involving conductive, convective, and radiative heat transfer modes in one and two dimensions are solved using two finite-element formulations. The first formulation employs a traditional Galerkin method while the second employs the approximation considered by this work. Results for the two benchmark problems are compared for accuracy and speed, and recommendations are made.