Two‐dimensional calculations were performed for combined convection heat transfer in a channel with two ribs attached to one wall, following a previous study on the forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy‐assisted flow and buoyancy‐opposing flow. The effect of Reynolds number, ReL, and modified Richardson number, Ri*, was examined keeping the space between ribs, σ, and blockage ratio, τ, constant (σ = 3.0, τ = 0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculations are stabilized in both cases. Serious deterioration of Nusselt number on the second rib suddenly occurs in a certain range of Ri* due to the flow stabilization. This is because flow unsteadiness plays an important role for heat transfer enhancement as was described in a previous study. However, in buoyancy‐assisted flow, a similar deterioration of Nusselt number also appears on the second rib even if flow remains steady. This is caused by the disappearance of a strong rotating flow which exists in the cavity between both ribs and keeps the fluid in the cavity cooler. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 379–394, 1999