Numerical analysis is made for the unsteady and steady, two-dimensional laminar natural convection in an enclosure caused simultaneously by the external heating and a local internal heat source. The velocities and temperature profiles are given, the average and local Nusselt numbers for the hot and cold surfaces obtained, and the equivalent relative intensity of the internal heat source, the critical equivalent relative intensity of the internal heat source and the transient control regime defined. The results show that there exist five flow patterns with changing the external or internal Rayleigh number, and the heat transfer performance for each flow pattern region is different.