In this work, the optimization for a radiative-convective annular fin of arbitrary profile with base wall thermal resistances is considered. A fourth order Runge-Kutta method is used to solve the associated non-linear governing equations. Further differentiations yield the optimum heat transfer and the optimum fin dimensions. To facilitate the thermal design, design charts for optimum dimensions are proposed. Furthermore, the fin effectiveness for the optimal annular radiative-convective fins is presented to check the practicality of the design.