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Abstract and Applied Analysis
Volume 2014, Article ID 172590, 7 pages
http://dx.doi.org/10.1155/2014/172590
Research Article

An Exact Solution for a Boundary Value Problem with Application in Fluid Mechanics and Comparison with the Regular Perturbation Solution

1Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
2Department of Mathematics, Faculty of Sciences, Helwan University, Cairo, Egypt
3Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Saudi Arabia

Received 29 January 2014; Accepted 2 March 2014; Published 6 April 2014

Academic Editor: Robert A. Van Gorder

Copyright © 2014 Abdelhalim Ebaid and S. M. Khaled. 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 exact solution for any physical model is of great importance in the applied science. Such exact solution leads to the correct physical interpretation and it is also useful in validating the approximate analytical or numerical methods. The exact solution for the peristaltic transport of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel has been achieved. The main advantage of such exact solution is the avoidance of any kind of restrictions on the viscosity parameter α, unlike the previous study in which the restriction α ≪ 1 has been put to achieve the requirements of the regular perturbation method. Hence, various plots have been introduced for the exact effects of the viscosity parameter, Daray’s number, porosity, amplitude ratio, Jeffrey fluid parameter, and the amplitudes of the waves on the pressure rise and the axial velocity. These exact effects have been discussed and further compared with those approximately obtained in the literature by using the regular perturbation method. The comparisons reveal that remarkable differences have been detected between the current exact results and those approximately obtained in the literature for the axial velocity profile and the pressure rise.