%0 Journal Article %A Alloui, Zineddine %A Vasseur, Patrick %D 2016 %I Begell House %K natural convection, porous medium, parallel flow approximation %N 2 %P 163-176 %R 10.1615/ComputThermalScien.2016011763 %T NATURAL CONVECTION IN TALL AND SHALLOW POROUS RECTANGULAR ENCLOSURES HEATED FROM BELOW %U https://www.dl.begellhouse.com/journals/648192910890cd0e,2588198a050b6dad,72460bbe776a6c62.html %V 8 %X The Darcy model with the Boussinesq approximation is used to study both analytically and numerically natural convection in a porous medium saturated by a Newtonian fluid. The geometry considered is a rectangular cavity heated from below and cooled from above by a constant heat flux while the sidewalls are maintained adiabatic. The governing parameters for the problem are the thermal Darcy-Rayleigh number R and the aspect ratio of the cavity A. In the limit of extremely confined geometries the parallel flow approximation is used to predict the flow behavior in the case of a tall vertical layer (A >> 1) or shallow horizontal one (A << 1). For a tall cavity, the existence of multicellular flow patterns, consisting of m vertical cells, is predicted by the present analytical model. Also, for a shallow cavity, it is demonstrated that the flow pattern can be either unicellular or multicellular. This is confirmed by the numerical results obtained by solving the full governing equations. %8 2016-09-07