Abstract
Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.
Highlights
Extended surfaces are extensively used in various industrial applications
The mathematical complexity of the conservation energy equation is reduced by this assumption and well-established closed form analytical solutions can be obtained for a number of cases
The appropriate convergence study and comparison with previously published related articles, the results obtained using variational iteration method (VIM) [4, 30], Adomian decomposition method (ADM) [31], homotopy analysis method (HAM) [32], and numerical solution (NS), were employed in order to verify the accuracy of the proposed method
Summary
Extended surfaces are extensively used in various industrial applications. An extensive review on this topic is presented by Kraus et al [1]. Kulkarni and Joglekar [9] proposed and implemented a numerical technique based on residue minimization to solve the nonlinear differential equation, which governs the temperature distribution in straight convective fins having temperature-dependent thermal conductivity. Khani et al [10] used HAM to evaluate the analytical approximate solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. Khani and Aziz [13] used HAM to develop analytical solutions for the thermal performance of a straight fin of trapezoidal profile when both thermal conductivity and heat transfer coefficient are temperaturedependent. Ganji et al [29] applied DTM to the problem of convective-radiative straight fins with temperaturedependent thermal conductivity They considered zero dimensionless convective and radiative sink temperatures and without heat generation. Because a broad range of governing parameters are investigated, the results should be useful in a number of engineering applications
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