Communications in Mathematical Sciences

Volume 9 (2011)

Number 3

Stability behavior of three non-Newtonian magnetic fluids in porous media

Pages: 767 – 796

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n3.a6

Authors

Sameh A. Alkharashi (Department of Mathematics, Tanta University, Egypt)

Magdy A. Sirwah (Department of Mathematics, Tanta University, Egypt)

Kadry Zakaria (Department of Mathematics, Tanta University, Egypt)

Abstract

The present study deals with stability properties of two-dimensional non-Newtonian fluid layers moving in porous media, under the influence of uniform magnetic field. The system is composed of a middle fluid embedded between two semi-infinite fluids. The limiting case of the stability of one interface between two viscoelastic fluids is discussed. The presented analysis takes into account the modified Darcy’s law. The principle aim of this work is to investigate the influence of fluid elasticity and the porosity effect on the growth rate in the presence of a magnetic field. The stability analysis is performed theoretically and stability diagrams are obtained. The stability analysis shows that non-Newtonian (viscoelastic) fluid layers have a higher growth rate than Newtonian fluid layers, indicating that non-Newtonian fluid sheets are more unstable than Newtonian fluid sheets. It is observed that in fluid sheets the fluid elasticity tends to damp the stability, whereas the fluid viscosity results in an enhancement of stability. The phenomenon of the dual role is found to increase the porous parameter as well as the magnetic permeability ratio. It has been found that the increase of the viscosity coefficient damps the growth rate, while increasing the Reynolds number has the opposite effect.

Keywords

modified Darcy’s law, non-Newtonian fluids, three layers stability, porous media

2010 Mathematics Subject Classification

76-xx

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