Int. J. Therm. Sci. 41 (2002) 73–81 Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation Ali J. Chamkha a,∗ , Camille Issa b , Khalil Khanafer c a Department of Mechanical Engineering, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait b Department of Civil Engineering, Lebanese American University, Byblos, Lebanon c Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210-1107, USA Received 18 January 2001; accepted 5 March 2001 Abstract Natural convection boundary-layer flow of an absorbing and electrically-conducting fluid over a semi-infinite, ideally transparent, inclined flat plate embedded in a porous medium with variable porosity due to solar radiation is considered. The governing equations are derived using the usual boundary-layer and Boussinesq approximations and accounting for the presence of an applied magnetic field and an applied incident radiation flux. To account for the heat loss from the plate surface, a convective-type boundary condition is employed there. These equations and boundary conditions are non-dimensionalized and transformed using a non-similarity transformation. The resulting non-linear partial differential equations are then solved numerically subject to the transformed boundary conditions by an implicit iterative finite-difference scheme. Graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed for various parametric conditions.  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Natural convcetion; Porous medium; Solar radiation; Inclined plate; Bedded Introduction Thermal buoyancy-induced flow and convective heat transfer in fluid-saturated porous media have been the sub- ject of numerous publications. This interest in the sub- ject stems from various engineering applications in geother- mal reservoirs, petroleum industries, transpiration cooling, storage of radioactive nuclear waste materials, separation processes in chemical industries, building thermal insula- tion, and solar heating systems. Early work on porous me- dia used the Darcy law that neglects important effects such as boundary and inertia effects. Vafai and Tien [1] have re- ported a pioneering work on the boundary and inertia ef- fects of porous media on convective flow and heat transfer situations. In recent years, enhanced models of porous me- dia have been reported. These models have been applied for simulating more generalized situations such as flow through packed and fluidized beds and liquid metal flow through * Correspondence and reprints. E-mail address: chamkha@kuc01.kuniv.edu.kw (A.J. Chamkha). dendritic structures in alloy casting (Nithiarasu et al. [2]). Some of these models deal with variable porosity effects near the boundary in which the porosity distribution exhibits a peak value there and then decays asymptotically beyond that value. The basis for these models was the early exper- imental work of Benenati and Brosilow [3] on void frac- tion distribution in packed beds. Examples of such models are reported and employed by Vafai [4], Vafai et al. [5], Poulikakos and Renken [6], and Nithiarasu et al. [2]. Other models have dealt with thermal dispersion or secondary flow effect in porous media which result from mixing and recircu- lation of local fluid particles through tortuous paths formed by the spherical particles in packed beds. Examples of these models have been reported by Cheng and Vortmeyer [7] and Amiri and Vafai [8]. Hydromagnetic flows and heat transfer in porous media have been considered extensively in recent years due to their occurrence in several engineering processes such as compact heat exchangers, metallurgy, casting, filtration of liquid met- als, cooling of nuclear reactors and fusion control. Ram [9] considered hydromagnetic heat and mass transfer through a porous medium in a rotating fluid. Takhar and Beg [10] 1290-0729/02/$ – see front matter  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII:S1290-0729(01)01305-9