%0 Journal Article
%T Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity
%A A. Moradi
%A H. Ahmadikia
%J Mathematical Problems in Engineering
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/568263
%X Three different profiles of the straight fin that has a temperature-dependent thermal conductivity are investigated by differential transformation method (DTM) and compared with numerical solution. Fin profiles are rectangular, convex, and exponential. For validation of the DTM, the heat equation is solved numerically by the fourth-order Runge-Kutta method. The temperature distribution, fin efficiency, and fin heat transfer rate are presented for three fin profiles and a range of values of heat transfer parameters. DTM results indicate that series converge rapidly with high accuracy. The efficiency and base temperature of the exponential profile are higher than the rectangular and the convex profiles. The results indicate that the numerical data and analytical method are in agreement with each other. 1. Introduction Heat transfer through fin surfaces is widely used in many industrial applications. The majority of the physical phenomena in the real world are described by nonlinear differential equations, whereas large class of these equations do not have an analytical solution. The numerical methods are widely used in solving nonlinear equations. There are some analytic methods for solving differential equations, such as Adomian decomposition method (ADM), HAM (homotopy analysis method), sinh-cosh method, homotopy perturbation method (HPM), DTM, and variational iteration method (VIM). An analytical solution for straight fin with combined heat and mass transfer is applied by Sharqawy and Zubair [1]. They used the four different profiles for the fin and compared the temperature profile and fin efficiency for them. Sharqawy and Zubair [2] applied the analytical method for the annular fin with combined heat and mass transfer as well. The nonlinear similarity solution in fin equation is applied by Bokharie et al. [3]. Abbasbandy and Shivanian [4] obtained the exact analytical solution of a nonlinear equation arising in heat transfer. HAM is used by Khani et al. [5] to evaluate the analytical approximate solution and the nonlinear problem efficiency with temperature-dependent thermal conductivity and variable heat transfer coefficient. Arslanturk [6] and Rajabi [7] obtained efficiency and fin temperature distribution by ADM and the HPM with temperature-dependent thermal conductivity. An analytical method for determining of the optimum thermal design of convective longitudinal fin arrays is presented by Franco [8]. Lin and Lee [9] investigated boiling on a straight fin with linearly varying thermal conductivity. The concept of differential transformation method
%U http://www.hindawi.com/journals/mpe/2010/568263/