Entropy generation due to natural convection has been computed for a wide range of Rayleigh number based on fin spacing, RaS in the entire laminar range 5 ≤ RaS ≤ 108, for diameter ratio, 2 ≤ D/d ≤ 5 for an isothermal horizontal cylinder fitted with vertical annular fins. Entropy generation in the tube-fin system is predominantly due to heat transfer rather than of fluid friction. 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 show 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 heat transfer is maximum. A detailed view of the entropy generation around the finned cylinder has been shown for various S/d at a particular D/d and Rayleigh number, which explains the nature and reason of entropy production.