Effect of Magnetic Field on Thermal Instability of Oldroydian Viscoelastic Rotating Fluid in Porous Medium

In this paper, we investigate the effect of a vertical magnetic field on thermal instability of an Oldroydian visco-elastic rotating fluid in a porous medium. By applying the normal mode analysis method, the dispersion relation governing the effects of rotation, magnetic field and medium permeability is derived and solved analytically and numerically. For the case of stationary convection, the Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has a stabilizing effect while the magnetic field and medium permeability have a stabilizing/destabilizing effect under certain conditions on thermal instability of the Oldroydian viscoelastic fluid in a porous medium. The oscillatory modes are introduced due to the presence of rotation, the magnetic field and gravity field. It is also observed that the ‘principle of exchange of stability’ is invalid in the presence of rotation and the magnetic field.

REFERENCES (12)

Bhatia P.K. and Steiner J.M. (1972): Convective instability in a viscoelastic fluid layer. - J. Angew. Math. Mech., vol.52, pp.321-32.

Google Scholar

Chandrasekhar S. (1981): Hydrodynamic and Hydromagnetic Stability. - New York: Dover Publications.

Google Scholar

Green P. (1968): Convective instability of viscoelastic fluid heated from below. - Phy. Fluids, vol.11, pp.1410.

Google Scholar

Ingham D.D. and Pop L. (1981): Transport Phenomena in Porous Media. - New York: Elsevier.

Google Scholar

Nield D.A. and Bejan A. (2006): Convection in Porous Medium. - New York: Springer.

Google Scholar

Rana G.C. and Kumar S. (2010): Thermal instability of Rivlin-Ericksen rotating fluid permeated with suspended particles under variable gravity field in porous medium. - Studia Geotechnica et Mechanica, vol. XXXII, pp.39-54.

Google Scholar

Rana G.C. and Kango S.K. (2011): Effect of rotation on thermal instability of compressible Walters, (Model B’) fluid in porous medium. - Vol.3, pp.44-53.

Google Scholar

Sharma R.C. (1975): Effect of rotation on thermal instability of a viscoelastic fluid. - Acta Physica Hungarica, vol.40, pp.11-17.

Google Scholar

Sharma R.C. (1975): Effect of magnetic field on thermal instability of a viscoelastic fluid. - Acta Physica Hungarica, vol.33, pp.293.

Google Scholar

10.

Vafai K. and Hadim H.A. (2000): Hand Book of Porous Media. - New York: Mureel Decker.

Google Scholar

11.

Vest C.M. and Arpaci V. (1969): Overstability of viscoelastic fluid heated from below. - J. Fluid Mech., vol.36, pp.613.

Google Scholar

12.

Wooding R.A. (1960): Rayleigh instability of a thermal boundary layer in flow through a porous medium. - J. Fluid Mech., vol.9, pp.183-192.

Google Scholar

Submit your paper

eISSN:	2353-9003
ISSN:	1734-4492