Subash Chand Pal et al IJMEIT Volume 2 Issue 12 December 2014 Page 922 IJMEIT// Vol. 2 Issue 12//December//Page No: 922-931//ISSN-2348-196x 2014 Fractional Homotopy Analysis Transform Method for a Fin with Temperature Dependent Internal Heat Generation and Constant Thermal Conductivity Authors Subash Chand Pal 1 , Mithilesh Kumar Sahu 2 , Pardeep Bishnoi 2 , M.K Paswan 3 Sunil Kumar 4 1 PG Scholar, Dept. of Mechanical Engg. , NIT Jamshedpur, INDIA 2 Ph.D. Scholars, Dept. of Mechanical Engg., NIT Jamshedpur, INDIA 3 Professor, Dept. of Mechanical Engg., NIT Jamshedpur, INDIA 4 Assistant Professor, Dept. of Mathematics, NIT Jamshedpur, INDIA Email: subashmiet105@gmail.com, manikant.nit@gmail.com Abstract Fractional Homotopy Analysis Transform Method (FHATM) is a new analytical technique for solving non homogeneous and homogeneous fin equation. The FHATM is an innovative adjustment in Laplace Transform Algorithm (LTA) and makes the calculation much easier. The non linear problem is solve by proposed technique without using adomian polynomials and He’s polynomial which can be consider as a clear advantage of this new algorithm over decomposition and homotopy perturbation transform method. In this paper it can be seen that the auxiliary parameter ħ which controls the convergence of the HATM approximate series solution and it also can be used in the predicting and calculating multiple solution. This is a basic technique which gives more qualitative difference in analysis between FHATM and other method. This indicate that the solution obtained by proposed method is easy to implement and computationally very attractive. This proposed method is illustrated by solving a fin with temperature dependent internal heat generation and constant thermal conductivity. Keywords: Fin, Fractional homotopy analysis transform method (FHATM), Temperature dependent internal heat generation, Temperature dependent thermal conductivity, homotopy analysis method, approximate analytical solution, Laplace transform algorithm (LTA). 1. Introduction The fractional calculus has a long history, starting from 30 September 1695 when Leibniz describes the derivative of order α = 1/2. The theory of derivatives and integrals of non integer order goes back to Leibniz, Liouville, Grunewald, Letnikov, and Riemann. Various important phenomena are well described by fractional differential equations in electro magnetics, acoustics, visco elasticity, electrochemistry, and materials science. Fractional order ordinary differential equations, as generalizations of classical integer-order ordinary differential equations, are increasingly used to model problems in fluid flow, mechanics, visco elasticity, biology, physics and engineering, and other applications. Fractional derivatives provide an excellent medium for the description of memory and hereditary properties of various materials and processes. It is more useful for the formulation of certain electro chemical problem by half-order derivatives than classical models [1- 6].The proposed method involves coupling of the HAM and Laplace transform method. The main advantage of this proposed method is its capability