The numerical solution of the laminar free convection of air around a horizontal cylinder with external longitudinal fins has been reported in this paper. The cylinder surface as well as the surfaces of each fin were assumed to be at a uniform temperature. The fluid drawn over a large angular domain moves out through a narrow, almost vertical strip known as plume, the thickness of which reduces with increasing buoyancy. The heat transfer increases with an increase in Grashof number, the number of fins, and fin length. For a constant fin surface, more fins of lower length result in a better heat transfer for Gr beyond about 10(3).