Design Charts for Circular Fins of Arbitrary Profile Subject to Radiation and Convection with Wall Resistances

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 equa- tions. 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 ra- diative-convective fins is presented to check the practicality of the design.