A new branch solution for the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient
Department of Mathematics, Imam Khomeini International University, 34149-16818, Qazvin, Iran
2 Department of Basic Sciences, Pharmaceutical Sciences Branch, Islamic Azad University, Tehran, Iran
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Accepted: 25 January 2017
Published online: 24 February 2017
In this paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. A method based on the traditional shooting method and the homotopy analysis method is applied, the so-called shooting homotopy analysis method (SHHAM), to the governing nonlinear differential equation. In this technique, more high-order approximate solutions are computable and multiple solutions are easily searched and discovered due to being free of the symbolic variable. It is found that the solution might be empty, unique or dual depending on the values of the parameters of the model. Furthermore, corresponding fin efficiencies with high accuracy are computed. As a consequence, a new branch solution for this nonlinear problem by a new proposed method, based on the traditional shooting method and the homotopy analysis method, is obtained.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017