Forced and mixed convection in 2-D, steady state, laminar flow and heat transfer around sinusoidal corrugated circular cylinder are numerically studied. Finite Element of Galerkin approach is used to analyze continuity, momentum and energy equation at Reynolds number (Re = 01 , 45, 100, 200), Richardson Number (Ri=0, 1, 2), corrugation number (G = ꚙ, 3, 4, 5, 10), amplitude values (λ= 0.1, 0.2, 0.3 and 0.6) for Prandtl number (Pr = 0.71). Results show the variation of corrugation number G and amplitude value λ have important effect on the streamline , isothermal lines, local and average Nusselt number around the sinusoidal cylinder. The heat transfer is reduced as 46% compared to circular cylinder at (G=5 and λ=0.6). But (G =3, 4 for λ = 0.6) have more obstruction area against flow. An agreement validation is obtained between present and previous numerical results.