Combined convection flow in square, circular, and semicircular ducts was numerically studied for axially uniform heat flux. The peripheral condition is that of the top half of the duct is insulated while the bottom half is heated. For the case of a square duct, dual solutions are obtained where the secondary flow is characterized either with two or four vortices. Regions of dual solutions have been mapped in the parameter space of aspect ratio and Grashof number. For the case of a circular duct, only the solution characterized by two vortices is obtained.