Analytical Solution for Nonlinear Convective–radiative Heat Transfer in a Straight Fin using Series Expansion Integration Method

Abstract

In this work, analytical solutions of nonlinear heat transfer equation in a convective–radiative longitudinal rectangular fin is developed using series expansion integration method. The results of the solution of the series expansion integration method are good agreement with the numerical solution. With the aid of the analytical solution, the effects of convective and radiative heat transfer parameters on the temperature distribution, rate of heat transfer, and thermal efficiency of the longitudinal rectangular fin are investigated. From the results, it is established that the thermal performance of the fin is greatly enhanced under the combined modes of convective and radiative heat transfers. The results obtained in this study serve as the basis for determining the level of accuracy of any other approximation method used in the analysis of the problem. Also, it could be used to improve the design of convecting–radiating fin in heat transfer equipment.