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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 135472, 14 pages
http://dx.doi.org/10.1155/2012/135472
Research Article

The One Step Optimal Homotopy Analysis Method to Circular Porous Slider

1School of Mathematical Science, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, Gomal University, Dera Ismail Khan, Pakistan

Received 4 August 2012; Revised 1 November 2012; Accepted 5 November 2012

Academic Editor: Xu Zhang

Copyright © 2012 Mohammad Ghoreishi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An incompressible Newtonian fluid is forced through the porous of a circular slider which is moving laterally on a horizontal plan. In this paper, we introduce and apply the one step Optimal Homotopy Analysis Method (one step OHAM) to the problem of the circular porous slider where a fluid is injected through the porous bottom. The effects of mass injection and lateral velocity on the heat generated by viscous dissipation are investigated by solving the governing boundary layer equations using one step optimal homotopy technique. The approximate solution for the coupled nonlinear ordinary differential equations resulting from the momentum equation is obtained and discussed for different values of the Reynolds number of the velocity field. The solution obtained is also displayed graphically for various values of the Reynolds number and it is shown that the one step OHAM is capable of finding the approximate solution of circular porous slider.