A Two-Temperature Model for Predicting Heat and Fluid Flow by Natural Convection and Radiation within a Saturated Porous Vertical Channel

摘要

The present article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with a fluid-saturated porous medium and adopts a two-temperature model of microscopic heat transfer. The bounding walls of the channel are gray and kept at a constant hot temperature. In the present study, we suppose the validity of the Darcy law for motion. For heat transfer, two energy conservation equations for both fluid and solid phases are derived. The radiative coupling problem is solved numerically by the finite volume method. Present solutions are compared with known results from previous published works. Excellent agreement was obtained between results that validate the used computer code. The numerical results have allowed us to represent the time-space variations of the different state variables. The effects of some influencing parameters (i.e., the internal Biot number Bi{sub}(int), the Planck number N, the optical thickness % the wall's emissivity e, and the single-scattering albedo ω) on the validity domain of the local thermal equilibrium assumption are checked.