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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 601917, 14 pages
http://dx.doi.org/10.1155/2012/601917
Research Article

Constant Accelerated Flow for a Third-Grade Fluid in a Porous Medium and a Rotating Frame with the Homotopy Analysis Method

1Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia
2Department of Mathematics, Faculty of Science, University of Kordofan, North Kordofan State, El-Obied 51111, Sudan
3Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, 31750 Tronoh, Malaysia

Received 2 October 2012; Accepted 7 November 2012

Academic Editor: Yuji Liu

Copyright © 2012 Zainal Abdul Aziz 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

The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of a constant accelerated flow for a third-grade fluid in a porous medium and a rotating frame. HAM is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. The approximate analytic solution for constant accelerated flow is obtained by using HAM. HAM contains the auxiliary parameter , which provides us with a straightforward way to obtain the convergence region of the series solution. Graphical results are plotted and the consequences discussed. The obtained solutions clearly satisfy the governing equations and all the imposed initial and boundary conditions. Many interesting results can be obtained as the special cases of the presented analysis. The influence of the material parameters of a third-grade fluid and rotation upon the velocity field is finally deliberated.