Unsteady effects on natural convective heat transfer through porous media in cavity due to top surface partial convection

Numerical investigations of transient natural convection flow through a fluid-saturated porous medium in a rectangular cavity with a convection surface condition were conducted. 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 non-dimensionalized and then solved numerically under appropriate initial and boundary conditions using the finite difference method. The finite different equation handling the boundary condition of the open top surface is derived. The two-dimensional flow is characterized mainly by two symmetrical vortices driven by the effect of buoyancy. A lateral temperature gradient in the region close to the top wall induces the buoyancy force under an unstable condition. Unsteady effects of associated parameters were examined. It was found that the heat transfer coefficient, Rayleigh number and Darcy number considerably influenced characteristics of flow and heat transfer mechanisms. Furthermore, the flow pattern is found to have a local effect on the heat convection rate.