A numerical investigation has been made of two-dimensional natural convection of air in an externally heated vertical or inclined square box containing uniformly distributed internal energy sources. Results have been obtained for Rayleigh numbers (both internal and external) up to 107 and inclination angles of 30, 60, and 90 deg from the horizontal. Two distinct flow pattern systems are observed: one, when the external Rayleigh number is larger than the internal Rayleigh number and the other, when the internal Rayleigh number is considerably greater than the external Rayleigh number. The average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot surface is observed to undergo large variations in the external Rayleigh number range associated with the transition from one flow pattern to another. The average heat flux ratio along the cold plate is found to increase with increasing external Rayleigh number and decreasing internal Rayleigh number. The local heat flux ratio along a surface attains its maximum value in the vicinity of the region where the heated (or cooled) fluid from the opposite wall or from the interior encounters the surface.