Nusselt number correlation is presented for vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium, heated from one side and cooled from other side, while its horizontal surfaces are insulated. Transient and steady-state patterns of stream function and temperature are presented. A two dimensional time-dependant numerical computation method has been developed to determine free convection in a vertical enclosure containing fluid and porous medium. It is found that the intensity of free convection is always much stronger in the fluid region, while the amount of fluid penetrating into the porous medium increases with increasing Darcy and Rayleigh numbers. For low Darcy-Rayleigh number, the flow takes place in the fluid layer and heat transfer in the porous layer is by conduction only. Velocities, temperatures and heat fluxes are assumed to be contineous across the fluid/porous-medium interface. The flow in the porous layer is modeled utilizing the Brinkman-Forchheimer-extended Darcy equations. The conservation equations for the fluid and the porous regions combined into a single set of equation for numerical solution. The present numerical model is verified by comparing with previous experiments. The agreement between the present model and experiments is, in general, good.