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Effect of variable viscosity on vortex instability of non-Darcy free convection boundary layer flow adjacent to a non-isothermal horizontal surface in a porous medium

Ahmed M Elaiw14*, Ahmed A Bakr24 and Fuad S Ibrahim35

Author Affiliations

1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha, Saudi Arabia

3 Department of Mathematics, University Collage in Makkah, Umm-Alqura University, Makkah, Saudi Arabia

4 Department of Mathematics, Faculty of Science, Al-Azhar University (Assiut Branch), Assiut, Egypt

5 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

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Boundary Value Problems 2012, 2012:26  doi:10.1186/1687-2770-2012-26

Published: 27 February 2012


In this article, we study the effect of variable viscosity on the flow and vortex instability of non-Darcian free convection boundary layer flow on a horizontal surface in a saturated porous medium. The wall temperature is a power function of the distance from the origin. The variation of viscosity is expressed as an exponential function of temperature. The transformed boundary layer equations, which are developed using a non similar solution approach, are solved by means of a finite difference method. The analysis of the disturbance flow is based on linear stability theory. The local Nusselt number, critical Rayleigh number and the associated wave number at the onset of vortex instability are presented over a wide range of wall to ambient viscosity ratio parameters μ*= μw/μ. The variable viscosity effect is found to enhance the heat transfer rate and destabilize the flow for liquid heating, while the opposite trend is true for gas heating.

vortex instability; porous media; variable viscosity; non-Darcy; free convection; finite difference method