Numerical simulation of a mixed heat transfer convection in a lid-driven cavity of a rectangular cross section has been investigated. The cavity is considered to be filled with a water-saturated porous medium of a constant porosity and permeability values. Furthermore, the temperature gradient is sustained in the vertical direction by heating the bottom wall, whereas the two vertical walls were assigned an insulated boundary condition. The generalized form of the momentum equation was employed in conjunction with the single-energy equation model to simulate the transport processes in the cavity. Moreover, the thermal dispersion effect has been incorporated in the energy equation. The flow and temperature profiles were studied using some operational dimensionless parameters, such as Grashof number and Reynolds number. The results show a significant elevation in flow and energy activities as Grashof number increases. For very small Reynolds number, the results are similar to that of a pure natural convection heat transfer in a cavity.