Accurate Solution for Convective–Radiative Fin with Variable Thermal Conductivity and Nonlinear Boundary Condition by DTM

Abstract

In this paper, a convective–radiative straight fin with temperature-dependent thermal conductivity is analyzed. The tip of the fin is assumed to lose heat by convection and radiation to the same sink. The calculations are carried out using the differential transformation method (DTM) which is a semi-numerical-analytical solution technique that can be applied to various types of differential equations. The principle of differential transformation is briefly introduced, and then applied for the afore-mentioned equations. The current results are then compared with previously obtained results using the variational iteration method, the homotopy perturbation method, the homotopy analysis method, the double optimal linearization method and numerical solution to verify the accuracy of the proposed method. The findings reveal that the DTM can achieve more suitable than other methods in predicting the solution of such problems. After this verification, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as thermal conductivity, the convection–conduction parameter, the radiation–conduction parameter, convection sink temperature and radiation sink temperature.