Instability of MHD Fluid Flow through a Horizontal Porous Media in the Presence of Transverse Magnetic Field - A Linear Stability Analysis

Jump To References Section

Authors

  • Assistant professsor, Department of mathematics, M S Ramaiah Institute of Technology, MSR Nagar, Bangalore-560054 ,IN

DOI:

https://doi.org/10.18311/jims/2019/17898

Keywords:

Brinkman model, Chebyshev collocation, Porous media, Stability.
Fluid mechanics

Abstract

The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Prm for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Rec, the critical wave number αc and the critical wave speed cc are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

2019-08-22

How to Cite

Basavaraj, M. S. (2019). Instability of MHD Fluid Flow through a Horizontal Porous Media in the Presence of Transverse Magnetic Field - A Linear Stability Analysis. The Journal of the Indian Mathematical Society, 86(3-4), 241–258. https://doi.org/10.18311/jims/2019/17898
Received 2017-08-17
Accepted 2019-03-18
Published 2019-08-22

 

References

P. G. Drazin, W. H. Reid, Hydrodynamic stability, Cambridge, U. K: Cambridge University Press (2004).

R. C. Lock, the stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field, Proc. Roy. Soc. Lond., A233, (1955), 105.

Potter M. C and Kudtchey J. A., Stability of plane Hartmann ow subject to a transverse magnetic field,Phy. Fluids., 16(11), (1973), 1848.

J.T. Stuart, On the stability of viscous ow between parallel planes in the presence of a coplanar magnetic field, Proc. R. Soc. London, Ser. A 221 (1954), 189-206.

J.C.R. Hunt, On the stability of parallel ows with parallel magnetic fields, Proc. R. Soc. London, A293 (1966), 342-358.

F.D. Hains, Stability diagrams for magnetogasdynamics channel ow, Phy. Fluids, 8(1965) 2014-2019.

D. S Krasnov, E Zienicke and O Zikanov, Numerical study of the instability of the Hartmann layer, J. Fluid Mech, 504 (2004), 183- 211.

S. A Orszag, Accurate solution of the Orr-Sommerfeld stability equation, J. Fluid Mech, 50 (1974), 689-703.

M. Takashima, The stability of the modied plane Poiseuille ow in the presence of transverse magnetic field, Fluid Dyn. Res., 17 (1996), 293-310.

O. D Makinde , P.Y Mhone, Temporal stability of small disturbances in MHD JeeryHamel flows, Comp. Math. Appl., 53 (2007), 128-136.

O.D. Makinde , On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium, Int. J. Numer. Meth. Fluids, 59 (2009), 791-799.

D.A. Nield , The stability of flow in a channel or duct occupied by a porous medium, Int. J. Heat Mass Transfer, 46 (2003), 4351-4354.

B.M Shankar , J Kumar, I.S Shivakumara, C.O. Ng., Stability of fluid flow in a Brinkman porous medium - A numerical study, Journal of Hydrodynamics, 26 (2014), 681-688.

B. Straughan, A. J Harfash, Instability in Poiseuille ow in a porous medium with slip boundary conditions, Micro fluid Nano fluid, 15 (2013), 109-115.

A. A. Hill and B. Straughan , Stability of Poiseuille ow in a porous medium, Adv. Math. Fluid Mech. (2010), 287-293.

D. A Nield , A Bejan, Convection in porous media[M],New York: Springer Verlag, 2013.

A.V. Proskurin, A.M. Sagalakov, Stability of poiseuille ow in the presence of a longitudinal magnetic field, J. Appl. Mech. Tech. Phy., 49 (2008), 383-390.

P. M. Balagondar and M. S. Basavaraj, Magnetohydrodynamic stability of couple stress fluid flow in a horizontal channel, Int. J. Math. Arch., 5(6) (2014), 1-10.

P. M. Balagondar and M. S. Basavaraj, Stability of magnetohydrodynamic ow of viscous fluid in a channel occupied by a porous medium, Journal of Arts and Science, 3(28) (2014), 263-274.

M. Takashima, The stability of natural convection in a vertical layer of electrically conducting fluid in the presence of transverse magnetic field, Fluid Dyn. Res., 14 (1994), 121-134.