Mixed convection in a horizontal annulus is considered, and the effect of a forced flow on the natural convective flow is investigated. The inner cylinder is hotter than the outer cylinder, and the outer cylinder is rotating with constant angular velocity with its axis at the center of the annulus. The unsteady streamfunction-vorticity equation is solved with a finite difference method. For the fluid with Pr=0.7, there appear flows with two eddies, one eddy, or no eddy according the Rayleigh and Reynolds numbers. The rotation of the outer cylinder reduces the heat transfer rate at the wall of the annulus. The oscillatory multicellular flow of a low Prandtl number fluid with Pr=0.01 can be effectively suppressed by the forced flow.