We have employed homotopy analysis method (HAM) to evaluate the approximate analytical solution of the nonlinear equation arising in the convective straight fins with temperature-dependent thermal conductivity problem. Solutions are presented for the dimensionless temperature distribution and fin efficiency of the nonlinear equation. The analytical results are compared with previous work and satisfactory agreement is noted. 1. Introduction The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system. Heat transfer includes the mechanisms of heat conduction, thermal radiation, and mass transfer. The analysis of extended surface heat transfer is extensively presented by Kraus et al. [1]. Arslanturk [2] used decomposition method to evaluate the temperature distribution and analytical expression for the fin efficiency. In the study of heat transfer, a fin is a surface that extends from an object to increase the rate of heat transfer to or from the environment by increasing convection. Incropera and Dewitt [3] presented a series of studies on the topic of heat transfer. Mokheimer [4] discussed a series of fin-efficiency curves for annular fins of rectangular, constant heat flow area, triangular, concave parabolic, and convex parabolic profiles for a wide range of radius ratios, and the dimensionless parameter based on the locally variable heat transfer coefficient. The optimum dimensions of circular fins with variable profile and temperature-dependent thermal conductivity have been obtained by Zubair et al. [5]. A new approach to calculate thermal performance of a singular fin with variable thermal properties has been presented by Kou et al. [6]. Joneidi et al. [7] studied an analytical solution of fin efficiency of convective straight fins with temperature-dependent thermal conductivity by the DTM. In this present paper, we first apply homotopy analysis method to obtain an approximation of analytical expression of fin efficiency of convective straight fins with temperature-dependent thermal conductivity. This problem is compared with Joneidi et al. [7]. 2. Mathematical Formulation of the Boundary Value Problem Consider a straight fin with a temperature-dependent thermal conductivity, arbitrary constant cross-sectional area ; perimeter and length ？？(see Figure 1). The fin is attached to a base surface of temperature and extends into a fluid of temperature , and its tip is
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