Simple and accurate solution for convective–radiative fin with temperature dependent thermal conductivity using double optimal linearization

Abstract

A novel concept of double optimal linearization is introduced and used to obtain a simple and accurate solution for the temperature distribution in a straight rectangular convective–radiative fin with temperature dependent thermal conductivity. The solution is built from the classical solution for a pure convection fin of constant thermal conductivity which appears in terms of hyperbolic functions. When compared with the direct numerical solution, the double optimally linearized solution is found to be accurate within 4% for a range of radiation–conduction and thermal conductivity parameters that are likely to be encountered in practice. The present solution is simple and offers superior accuracy compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method. The fin efficiency expression resembles the classical result for the constant thermal conductivity convecting fin. The present results are easily usable by the practicing engineers in their thermal design and analysis work involving fins.