International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 408132, 12 pages
http://dx.doi.org/10.1155/2011/408132
Research Article

New Exact Solutions for an Oldroyd-B Fluid in a Porous Medium

I. Khan,1 M. Imran,1 and K. Fakhar1,2

1Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia
2Ibnu Sina Institute for Fundamental Science Studies, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia

Received 9 December 2010; Revised 21 March 2011; Accepted 13 April 2011

Academic Editor: Ricardo Estrada

Copyright © 2011 I. Khan 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

New exact solutions for unsteady magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid have been derived. The Oldroyd-B fluid saturates the porous space. Two different flow cases have been considered. The analytical expressions for velocity and shear stress fields have been obtained by using Laplace transform technique. The corresponding solutions for hydrodynamic Oldroyd-B fluid in a nonporous space appeared as the limiting cases of the obtained solutions. Similar solutions for MHD Newtonian fluid passing through a porous space are also recovered. Graphs are sketched for the pertinent parameters. It is found that the MHD and porosity parameters have strong influence on velocity and shear stress fields.