Analysis of Combined Conductive-Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure With a Gray Medium

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.