The conjugate natural convection heat transfer in a partially heated porous enclosure had been studied numerically. The governing dimensionless equations are solved using finite element method using Darcy model. The considering dimensionless parameters are modified Rayleigh number (10 ≤ Ra ≤ 10³), finite wall thickness (0.02 ≤ D ≤ 0.5), thermal conductivity ratio (0.1 ≤ K_r ≤ 10), and the aspect ratio (0.5 ≤ A≤ 10). The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that heat transfer can be enhanced by increasing the modified Rayleigh number, thermal conductivity ratio. Wall thickness effects on the heat transfer mechanism had been studied and it is found that as the Wall thickness increases, the conduction heat transfer mechanism will be dominated. Also, increasing aspect ratio will increase the stream function and reduced the heat transfer rate.