Three dimensional numerical investigations are carried out to analyse the effect of different shapes of annular fin on heat transfer characteristics and pressure drop across a tube surface. Shear stress transport based k-ω turbulence model is used to analyse flow physics and heat transfer characteristics in flow domain. Weak zones of heat transfer across a circular tube surface are identified for 2500 < Re < 13000. Three different shapes of annular fin are considered to test the possibility of optimum heat transfer characteristics in weak zones. Results are compared with circular shape annular fin. Circular shape annular fin outperforms in terms of overall rate of heat transfer at the cost of highest pressure drop. The heat transfer rate decreases by 18%, 21% and 31% in sectorial fin, elliptical fin and sectional fin as compared to that of circular fin at 12965 Reynolds number, but at other end pressure drop across a tube surface in case of these fins also decrease as compared to that of circular annular fin. Potential rate, ratio of heat transfer rate to required pumping power, is calculated to evaluate optimum fin performance. Potential rate of an elliptical fin is highest among all the reported cases.