Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 691802, 14 pages
http://dx.doi.org/10.1155/2012/691802
Research Article
Effect of Variable Viscosity on Vortex Instability of Non-Darcy Mixed Convection Boundary Layer Flow Adjacent to a Nonisothermal Horizontal Surface in a Porous Medium
1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt
3Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha, Saudi Arabia
4Department of Mathematics, University Collage in Makkah, Umm-Alqura University, Saudi Arabia
Received 6 July 2011; Accepted 11 November 2011
Academic Editor: Muhammad R. Hajj
Copyright © 2012 A. M. Elaiw 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
We study the effect of variable viscosity on the flow and vortex instability for non-Darcy mixed convection boundary layer flow on a nonisothermal horizontal plat surface in a saturated porous medium. The variation of viscosity is expressed as an exponential function of temperature. The analysis of the disturbance flow is based on linear stability theory. The base flow equations and the resulting eigenvalue problem are solved using finite difference schemes. It is found that the variable viscosity effect enhances the heat transfer rate and destabilizes the flow for liquid heating, while the opposite trend is true for gas heating.