Transient natural convection flow through a fluid-saturated porous medium in a square enclosure with a partially cooling surface condition was investigated using a Brinkmann-extended Darcy model. The physical problem consists of a rectangular cavity filled with porous medium. The cavity is insulated, except the top wall that is partially exposed to an Outside ambient. The exposed surface allows convective transport through the porous medium, generating a thermal stratification and flow circulations. The formulation of differential equations is nondimensionalized and then solved numerically under appropriate initial and boundary conditions using the finite difference method. The finite difference equations handling the convection boundary condition of the open top surface are derived for cooling conditions. In addition to the negative density gradient in the direction of gravitation, a lateral temperature gradient in the region close to the top wall induces the buoyancy force under an unstable condition. The two-dimensional flow is characterized mainly by the clockwise and anti-clockwise symmetrical vortices driven by the effect of buoyancy. The directions of vortex rotation generated under the cooling condition are in the opposite direction as compared to the heating condition. Unsteady effects of associated parameters were examined. The modified Nusselt number (Nu) was systematically derived. This newly developed form of Nu captures the heat-transfer behaviors reasonably accurately. It was found that the heat-transfer coefficient, Rayleigh number, Darcy number, as well as flow direction strongly influenced characteristics of flow and heat-transfer mechanisms.
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