A new branch solution for the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

作者：Shivanian Elyas^*; Ghoncheh S J Hosseini

来源：European Physical Journal Plus, 2017, 132(2): 97.

DOI：10.1140/epjp/i2017-11365-4

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.

• 出版日期2017-2-24