It is necessary for the heat transfer problems to provide information about the critical parameters that affect the efficiency to improve the status of the system. Major part of these information can be obtained by the investigations of the heatlines and entropy generation. Therefore, the laminar free convection in an enclosure forming by a hot inner circular cylinder and cold sinusoidal outer cylinder at different amplitude (λ=1, 2, and 4) and Rayleigh Number range (103-106) is numerically studied. Heatlines, streamlines, isotherms, and entropy generation are obtained using finite element technique based on the Galerkin method. The inner and outer cylinders are assumed to be kept at a constant temperature. Air is the working fluid with Prandtl number (0.71). The results showed that the fluid circulations are governed by two combined facts; the first one is the buoyancy force that excited by the increasing of Rayleigh number producing bigger circulations and the second is the increasing in the nondimensional amplitudes which damps the flow.