Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures, while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the ratio of wall thickness to its width , the wall to porous thermal conductivity ratio , the internal heating , and the local heating exponent parameters . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls.