Computational analysis of coupled radiation-convection dissipative non-gray gas flow in a non-Darcy porous medium using the Keller-box implicit difference scheme

Abstract

The effects of thermal radiation parameter (F), transpiration (γ), Eckert number (Ec), Prandtl number (Pr), buoyancy (Grashof number Gr), a Darcy parameter (Re/Gr Da) and a Forcheimmer inertial parameter (Fs Re/Gr Da) on two-dimensional free convective flow of an optically thin, near-equilibrium, non-gray gas past a vertical surface in a non-Darcy porous medium, are studied using the robust Keller finite-difference technique incorporating Newtonian quasilinearization and block-tridiagonal elimination. The Darcy–Brinkman–Forcheimmer inertial-viscous flow model is used for the momentum equation and the Cogley–Vincenti–Giles formulation is adopted to simulate the radiation component of heat transfer. The one-dimensional thermal radiation model works successfully for gases in the optically thin limit. Pseudo-similarity transformations are employed to simplify the highly non-linear partial differential equations for momentum and heat transfer into numerically manageable pseudosimilar ordinary differential equations which are solved with Keller's box method. Effectively, the radiation contribution is seen to take the form of a linear temperature term Fθ coupled with the streamwise pseudo-similar variable ξ. Local wall shear stress and local heat transfer rates are systematically computed for a wide selection of radiation parameter F values. The results are presented graphically for different gases. © 1998 John Wiley & Sons, Ltd.