Abstract: Effect of Ra number and Da number on steady laminar natural convection in square enclosure filled with heat generating porous medium is investigated by local thermal non-equilibrium model and non-Darcy model numerically with the effective fluid-to-solid thermal conductivity ratio as constant.It is found that the Nuf increases with the increasing of Da when Ra is constant;Moreover,Nuf increases with the increasing of Ra when Da is constant.However,the values of Nus of the four walls are almost the same and equal to a constant for the cases discussed.The absolute value of Nuf of left wall is equal to that of right wall,furthermore,both of them are less than that of the ceiling wall,the heat transfer between fluid and bottom wall is the smallest compared with those of the other three walls.The non-equilibrium effect is significant when dimensionless volume heat transfer coefficient H is quite small.