This study explains the effect of presence two adiabatic partitions fixed horizontally inside two dimensional enclosure filled with porous medium on natural convection heat transfer. The vertical walls of enclosure was insolated and the heat is transferred from the bottom to the above. A numerical study is used to solve the governing equations which represented by momentum, energy and continuity equations with finite difference method and it was in non-Darcian heat flow. The study included change in modified Rayleigh number (100 to 500), an inertia parameter (10-2 to 10-4), change the upper partition length at (30%-50%-70%) with stay the lower partition is constant at (30%) and opposite, change the lengths of two partitions at (30%-50%-70%) together, change the positions of two partitions at (20%-30%-40%) for the lower partition and (60%-70%-80%) for the upper partition and in addition to divergence between the two partition. The study at a constant aspect ration at (A=1.0). The results are showed the reduction in heat transfer compare with the no partitions. When the increase in the length of upper partition, the reduction in heat transfer of (68.2%) while when the increase in the length of lower partition the reduction reach to (66.4%) and the increase in the lengths of two partitions lead to the reduction to (73.2%). The reduction is (50%) when the two partitions near from both and when the upper partition near the cold wall and the lower partition near the hot wall, finally the heat transfer is reduced with (46.3%) when the change in the position of partitions toward the cold wall.