A major hindrance in the rapid quenching of heated substrates in applications such as forging, and cryogenic systems is the formation of a low conductivity vapor film around the heated substrate which retards the heat dissipation rate. Extended surfaces (fins) on heat transfer substrates alter the profile of the liquid-vapor interface in the film boiling regime leading to an increase in the heat transfer coefficient. In the present work we develop a theoretical model to determine the shape of the liquid-vapor interface during film boiling over a cylindrical metallic sample with equally spaced annular fins. The fins have a thickness of 1 mm and the distance between the annular fins is 5, 8 and 12 mm in the present study. The momentum and energy conservation equations in the vapor domain govern the shape of the liquid-vapor interface. Buoyancy is assumed to be the primary force in driving the vapor flow and hence influences the shape of the liquid vapor interface. We determine the influence of liquid subcooling on the evolution of the vapor film and observe that the curvature of the vapor film between two consecutive fins is prominent in the case of densely spaced fin arrays (~ 5 mm) as compared to that for sparser fins (~12 mm) during the entire range of film boiling. The theoretical prediction of the shape of the liquidvapor interface shows a good agreement with the shape of the vapor film profile obtained through experiments. The corresponding effect of the vapor film profile on the heat dissipation rate is analyzed by calculating the average heat transfer coefficient. The average heat transfer coefficient calculated using the present mathematical model is in close agreement with the experimentally obtained heat transfer coefficient.