Computational Thermal Sciences, 2(5):xxx–xxx, 2010 UNSTEADY NATURAL CONVECTION IN AN ANISOTROPIC POROUS MEDIUM BOUNDED BY FINITE THICKNESS WALLS H. S. Harzallah, 1 A. Zegnani, 1 H. Dhahri, 2 K. Slimi, 1,* & A. Mhimid 1 1 Ecole Nationale d’Ing´ enieurs, Rue Ibn Eljazzar, 5019, Monastir, Tunisia 2 Institut Pr´ eparatoire aux Etudes d’ing´ enieurs, Rue Ibn Eljazzar, 5019, Monastir, Tunisia * Address all correspondence to K. Slimi E-mail: khalifa slimi@yahoo.fr In this paper, a numerical study of unsteady natural convection in a fluid-saturated porous medium bounded by two equal-thickness walls has been made. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. The vertical walls are isothermal at different temperatures, the horizontal walls are adiabatic. For mod- eling fluid flow inside the porous material, the Darcy flow model is assumed to hold. For heat transfer, we assume the validity of the local thermal equilibrium assumption. The classical finite volume method is used to solve the resulting dimensionless governing equations. Satisfactory agreement was obtained between results that validate the used com- puter code. The governing parameters considered for the analysis are the permeability ratios, R px and R pz , the thermal conductivity ratios, Rcx and Rcz , the wall-to-porous medium heat capacity, σw, the wall-to-porous thermal conduc- tivity ratio, R w , and the ratio of the wall thickness to its height, D. The results show that lower values of R cz , and/or higher values of R px , have negligible effects on the heat transfer rate but they are strongly subordinate to R cx ,R pz ,R w , σw, and D. Moreover, small values of Rcx,Rw, and σw, or larger values of Rpz and Rw, enhance convection inside the enclosure. KEY WORDS: unsteady, natural convection, finite thickness walls, thermal anisotropy, mechanical anisotropy, porous medium, finite volume method 1. INTRODUCTION Recently, natural convection through anisotropic porous media has been of considerable interest in many applica- tions such as in high-performance thermal insulation for buildings, cold storage installations, geophysics, hydrol- ogy, oil extraction, and reservoir engineering, to name just a few. Anisotropy is generally a consequence of a prefer- ential orientation and/or asymmetric geometry of grains or fibers (Degan et al., 1995; Degan and Vasseur, 2003; Slimi et al., 2005; Saeid and Pop, 2005; Pakdee and Rat- tanadecho, 2006; Nield, 2007). Natural convection problems involving anisotropic ef- fects in the presence of porous materials coupled with the effect of the bounding walls have received relatively little attention despite their broad range of applications. Conjugate natural convection in a rectangular porous cav- ity surrounded by finite thickness conductive walls has been conducted by Chang and Lin (1994a). Their re- sults show that wall conduction decreases the overall heat transfer rate from the hot to cold sides of the porous enclosure. The effect of wall heat conduction on natu- ral convection in an enclosure filled with a non-Darcian porous medium has also been studied by Chang and Lin (1994b). Steady conjugate natural convection-conduction problems in a vertical porous enclosure limited with one finite wall thickness and sandwiched by finite thickness walls have been studied by Nawaf (2007a,b). It is found that as the wall thickness increases, the average Nusselt number decreases and the strength of the circulation of the operating fluid saturating the porous medium is much higher with thin walls. Vafai and Thiyagaraja (1987) have investigated the fluid flow and heat transfer rates at the in- terface region for three general and fundamental classes of convection in porous media. These are the interface re- gion between two different porous media, the interface 1940–2503/10/$35.00 c  2010 by Begell House, Inc. 1