Analysis of combined conductive-radiative heat transfer in a two-dimensional rectangular enclosure with a gray medium

Abstract

Combined conductive-radiative heat transfer in a two-dimensional enclosure is considered. The numerical procedure is based on a combination of two previous techniques that have been demonstrated to be successful for a two-dimensional pure radiation problem and a one-dimensional combined conductive-radiative heat transfer problem, respectively. Both temperature profile and heat transfer distributions are generated efficiently and accurately. Numerical data are presented to serve as benchmark solutions for two-dimensional combined conductive-radiative heat transfer. The accuracy of two commonly used approximation procedures for multidimensional combined conductive-radiative heat transfer is assessed. The additive solution, which is effective in generating approximation to one-dimensional combined conductive-radiative heat transfer, appears to be an acceptable empirical approach in estimating heat transfer in the present two-dimensional problem. The diffusion approximation, on the other hand, is shown to be generally inaccurate. For all optical thicknesses and conduction-radiation parameters considered (including the optically thick limit), the diffusion approximation is shown to yield significant errors in both the temperature and heat flux predictions.