Combined Radiation And Natural Convection Within An Open ended Porous Channel—Validity Of The Rosseland Approximation

The present work deals with a numerical study of coupled fluid flow and heat transfer by transient natural convection and thermal radiation in a vertical channel opened at both ends and filled with a fluid-saturated porous medium. The bounding walls of the channel are isothermal and gray.

In the present study we suppose the validity of the Darcy flow model and the local thermal equilibrium assumption. In order to examine the validity of the Rosseland approximation, the radiative term in the energy conservation equation was expressed via two different approaches. The first is based on the resolution of the radiative transfer equation (RTE) in the most general case while the second is based on assuming the Rosseland approximation to be valid.

Numerical results show that the Rosseland approximation is valid only for optically thick media and far from the bounding walls. A parametric study shows that this approximation can be used with high confidence for large Planck number values, for temperature ratios close to 1 and/or for single scattering albedo near or equal to 1.