Available online at www.ispacs.com/cna Volume 2012, Year 2012 Article ID cna-00114, 21 pages doi: 10.5899/2012/cna-00114 Research Article Tau–Homotopy Analysis Method for Solving Micropolar Flow due to a Linearly Stretching of Porous Sheet S. Kazem 1∗ , M. Shaban 2 (1) Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran (2) Department of Physics, Shahid Beheshti University, Evin, Tehran 19839, Iran Copyright 2011 c ⃝ S. Kazem, M. Shaban. This is an open access article distributed under the Creative Com- mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract A modification of the homotopy analysis method (HAM) for solving a system of nonlinear boundary value problems (BVPs) in semi–infinite domain, micropolar flow due to a linearly stretching of porous sheet, is proposed. This method is based on operational matrix of exponential Chebyshev functions to construct the derivative and product of the unknown function in the matrix form. In addition, by using Tau method the problem converts to algebraic equations to obtain the solution iteratively. In whole we can say, the computer oriented of this method is the most important aspect of it. During comparison between our methods and those previously reported, significant consequences are demonstrated. Keywords : Homotopy analysis method; Micropolar flow; Stretching sheet; Suction and injection; Chebyshev Tau method. 1 Introduction The homotopy analysis method (HAM) [21] is a powerful tool and has been already used for several nonlinear problems [1, 2, 3, 4, 5, 12, 13, 14, 15, 22, 28, 30, 34, 35]. The replace- ment of a nonlinear equation by a system of ordinary differential equations is the basic idea of the homotopy analysis method which prepare us to solve this system with the symbolic computation software such as Maple, Mathematica and Matlab. The solution of this system of ODEs is used to form a convergent series which, as proved in [21, 23], is the solution of the original nonlinear equation. In using the HAM, and in order to * Corresponding author. Email address: saeedkazem@gmail.com 1