Fin efficiency analysis of convective straight fins with temperature dependent thermal conductivity using variational iteration method Safa Bozkurt Cos ßkun a, * , Mehmet Tarık Atay b a Department of Civil Engineering, Nig˘ de University, 51245 Nig˘ de, Turkey b Department of Mathematics, Nig˘ de University, 51245 Nig˘ de, Turkey Received 23 August 2007; accepted 17 January 2008 Available online 26 January 2008 Abstract For enhancing heat transfer between primary surface and the environment, utilization of radiating extended surfaces are common. Especially for large temperature differences; variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze the efficiency of convective straight fins with temperature dependent thermal con- ductivity. VIM produces analytical expressions for the solution of nonlinear differential equations. In order to show the effectiveness of variational iteration method (VIM), the results obtained from VIM analysis is compared with available solutions obtained using Ado- mian decomposition method (ADM) and the results from finite element analysis. This work assures that VIM is a promising method for the efficiency analysis of convective straight fin problems. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Straight fins; Efficiency; Variable thermal conductivity; Variational iteration method; Adomian decomposition method; Finite element method 1. Introduction Finned surfaces have enhanced heat transfer mechanism between the primary surface and its surrounding medium. Kern and Kraus made an extensive review on this issue [1]. Aziz and Hug [2] obtained a closed form solution for a straight convective fin with variable thermal conductivity using regular perturbation method. Yu and Chen [3] solved nonlinear conducting-convecting-radiating heat transfer equation assuming a linear variation for thermal conduc- tivity. Yu and Chen [4] studied optimum fin length problem of a convective-radiative straight fin with variable thermal conductivity. Sohrabpour and Razani [5] investigated opti- mum convective fin with variable thermal conductivity and variable heat transfer coefficient. Razelos and Imre [6] took a variable convective heat transfer coefficient into account in fin problem. Laor and Kalman [7] analyzed different fins with temperature dependent heat transfer coefficient. Bou- aziz et al. [8] analyzed the efficiency of longitudinal fins with temperature dependent thermo-physical properties. Arslantu¨rk [9] used ADM to obtain analytical expressions for dimensionless temperature and fin efficiency with tem- perature-dependent thermal conductivity. Arslantu¨rk [10,11] also studied the optimization problems for annu- lar fins. Recently Cos ßkun and Atay [12] used VIM for analyzing variation of temperature in straight and radial fins. ADM has been used extensively for the analysis various nonlinear problems in heat transfer [13–17]. The method is a technique for obtaining analytical expressions in the solu- tion of nonlinear differential equations [18] which depend 1359-4311/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.01.012 * Corresponding author. Tel.: +90 388 2252284. E-mail address: sbcoskun@nigde.edu.tr (S.B. Cos ßkun). www.elsevier.com/locate/apthermeng Available online at www.sciencedirect.com Applied Thermal Engineering 28 (2008) 2345–2352