Journal of Porous Media, 14 (10): 865–882 (2011) COMBINED RADIATION AND NATURAL CONVECTION WITHIN AN OPEN-ENDED POROUS CHANNEL—VALIDITY OF THE ROSSELAND APPROXIMATION Abdesslem Jbara, 1 Khalifa Slimi, 2,* & Abdallah Mhimid 1 1 The National School of Engineers, Ibn Aljazzar Street, 5019, Monastir, Tunisia 2 Higher Institute of Transport and Logistics, 12 Abdullah Ibn Al-Zubeir Street, 4000, Sousse, Tunisia ∗ Address all correspondence to Khalifa Slimi E-mail: khalifa slimi@yahoo.fr Original Manuscript Submitted: 1/25/2010; Final Draft Received: 5/6/2010 The present article 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 assume 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: τD ≥100 and far from the bounding walls. A parametric study shows that this approximation can be used with high confidence for large Planck number values: N ≥5, for temperature ratios close to 1 and/or for single scattering albedo near or equal to 1. KEY WORDS: natural convection, porous medium, radiative transfer, Rosseland approximation, validity domain, finite volume method 1. INTRODUCTION Fluid flow and heat transfer by natural convection in porous media have been motivated by numerous applica- tions relevant to thermal insulation technology, ground- water hydrology, petroleum reservoir modeling, packed- bed heat exchangers, material processing, cooling of in- tegrated circuits, and storage of radioactive nuclear waste materials. In thermal insulation technology, for example, the coupling between radiation and convection is of great importance for correct accounting of the insulator perfor- mance. Radiative heat transfer is important especially when the operating fluid temperature is high and the partici- pating medium is a gas-saturated porous material, regard- less of other heat transfer modes. Unsteady multidimen- sional thermal problems taking into account thermal ra- diation have been numerically studied by relatively few researchers because of their mathematical difficulties and the requirement of large computational storage and time. Most published studies in this field are generally related to limited cases such as steady-state assumption, coupled radiation with conduction, and one-dimensional transfers, and are mainly limited to confined structures. A channel filled with a porous medium has theoretical and practical importance. One of the basic characteristics of buoyancy-induced flows in open-ended systems is the interactions and the influence of the inner (the medium 1091–028X/11/$35.00 c ⃝ 2011 by Begell House, Inc. 865