The present paper numerically studies natural convection in a partially cooled square enclosure filled with a porous medium. One of the enclosure walls is heated while the middle opposite wall is partially cooled. The remaining walls are adiabatic. The governing equations which are continuity, momentum and energy equations are solved using finite element method with FlexPDE 6.20 Professional. The relevant parameters for computations are Darcy numbers (Da = 10 −5 −10 −3 ), Rayleigh numbers (Ra = 10 4 −10 6 ), Prandtl numbers (P r = 0.70 − 10) and cold length (D = 0.50). The numerical results are present in terms of isotherms, streamlines and heatlines. It is found that varied Darcy and Rayleigh numbers can lead to difference temperature flow and heat fields. The results of this study can be use in the thermal insulation of buildings and cooling systems of electronic devices.