General exact solution of the fin problem with the power law temperature-dependent thermal conductivity

Abstract

In this paper, the general exact implicit solution of the second-order nonlinear ordinary differential equation governing heat transfer in rectangular fin is obtained using Lie point symmetry method. General relationship among the fin efficiency, the rate of heat transfer from the entire fin, the fin effectiveness, and the thermo-geometric fin parameter is obtained for any value of the mode of heat transfer n and the constant β. Copyright © 2015 John Wiley & Sons, Ltd.