Entropy generation due to natural convection has been calculated for a wide range of Rayleigh number (Ra) in both laminar (10^{4 }≤ Ra ≤ 10^{8}) and turbulent (10^{10 }≤ Ra ≤ 10^{12}) flow regimes, for diameter ratio of 2 ≤ D/d ≤ 5, for an isothermal vertical cylinder fitted with annular fins. In the laminar regime, the entropy generation was predominantly caused by heat transfer (conduction and convection) and the viscous contribution was negligible with respect to heat transfer. But in the turbulent regime, entropy generation due to fluid friction is significant enough although heat transfer entropy generation is still dominant. The results demonstrate that the degree of irreversibility is higher in case of finned configuration when compared with unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to delineate the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)_{finned}/(I/Q)_{unfinned}. The ratio (I/Q)_{finned}/(I/Q)_{unfinned} gets its minimum value at optimum fin spacing where maximum heat transfer occurs in turbulent flow, whereas in laminar flow the ratio (I/Q)_{finned}/(I/Q)_{unfinned} decreases continuously with the increase in number of fins.