Efficient numerical treatment of a conductive-radiative fin with temperature-dependent thermal conductivity and surface emissivity

Abstract

A thorough study of the effects of ambient temperature and surface emissivity on the heat transfer of a conductive-radiative fin is presented in this article. A semi-analytical method based on Green’s function coupled with fixed point iterative schemes will be employed to solve a nonlinear energy equation that governs a straight rectangular fin. The method will be shown to converge for both Picard’s and Mann’s fixed point iteration schemes. The proposed method’s efficiency and accuracy will be tested against some of the widely used numerical approaches found in the literature.