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In this study, a simple and accurate solution for the temperature distribution of convective-radiative straight rectangular fins with temperature-dependent thermal conductivity is presented using an analytical method called the Differential Transformation Method (DTM). The governing differential equation for the temperature distribution in present problem contains two nonlinear terms, one due to temperature-dependent thermal conductivity and the other due to surface radiation. Here, the concept of differential transformation method is briefly introduced and then it is used to derive solutions of highly nonlinear equation. The obtained results from DTM are compared with those from the numerical solution to verify the accuracy of the proposed method. The investigations reveal that the differential transformation method can achieve suitable results in predicting the solution of such strong nonlinear problem. After this verification, the effects of some physical applicable parameters in this problem such as convection-conduction parameter, thermal conductivity parameter and the radiation-conduction parameter on efficiency of the fin are presented and discussed.

The Efficiency of Convective-radiative Fin with Temperature-dependent Thermal Conductivity by the Differential Transformation Method