## THERMAL SCIENCE

International Scientific Journal

### RAYLEIGH TAYLOR INSTABILITY IN DUSTY MAGNETIZED FLUIDS WITH SURFACE TENSION FLOWING THROUGH POROUS MEDIUM

**ABSTRACT**

In this paper we investigate the effect of surface tension on hydromagnetic Rayleigh-Taylor (R-T) instability of two incompressible superimposed fluids in a porous medium with suspended dust particles immersed in a uniform horizontal magnetic field. The relevant linearized perturbation equations have been solved using normal mode technique and the dispersion relation is derived analytically for the considered system. The dispersion relation is influenced by the simultaneous presence of medium porosity, suspended dust particles, permeability, magnetic field and surface tension. The onset criteria of R-T stability and instability are obtained and discussed. The growth rate of R-T instability is calculated numerically and is affected by the simultaneous presence of surface tension and magnetic field. The effects of various parameters on the growth rate of the R-T instability are discussed.

**KEYWORDS**

PAPER SUBMITTED: 2013-10-27

PAPER REVISED: 2014-02-27

PAPER ACCEPTED: 2014-03-22

PUBLISHED ONLINE: 2014-04-05

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**1**, PAGES [119 - 130]

- Allen, A. J. & Hughes, P. A., The Rayleigh-Taylor Instability in Astrophysical Fluids, Monthly Notices of the Royal Astronomical Society 208,(1984) , pp. 609-621.
- Lindl, J.D. and Mead ,W.C., Two-Dimensional Simulation of Fluid Instability in Laser-Fusion Pellets,, Phys. Rev., Lett. 34 (1975), pp.1273-1276.
- Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Clarendon Press Oxford 1961.
- Kull, H.J. and Anisimov, S.I., Ablative Stabilization in the Incompressible Rayleigh-Taylor Instability, Phys. Fluids, 29(1986), 7, pp. 2067-2075.
- Kalra, G.K., Effect of Finite Ion Larmor Radius on the Stability of Superposed Fluids, Can. J. Phys., 45(1967), pp.1579-1586.
- Bhatia, P.K., Rayleigh Taylor Instability of Viscous Superposed Conducting Fluids, IL Nuovo Cimento, 19B (1974), 2 pp. 161-168.
- Gupta, A., Bhatia, P.K., Instability of Partially-Ionized Superposed Plasmas, Astrophys. Space Sci.,181 (1991), pp. 103-110.
- Michael, D.H., Kelvin-Helmholtz Instability of a Dusty Gas, Proc. Comb. Phil. Soc., 61 (1965), pp. 569-571 .
- Sharma, R.C., Sharma, K.C., Rayleigh-Taylor Instability of Two Superposed Conducing Fluids in the Presence of Suspended Particles, Acta Phys. Acad. Sci. Hung., 43 (1977), 3-4, pp. 251-258.
- Chhajlani, R.K., Sanghvi, R.K. and Purohit, P., Rayleigh Taylor Instability of a Stratified Magnetized Medium in the Presence of Suspended Particles, Z. Naturforsch., 39a, (1984), pp. 939-944.
- Sanghvi, R.K., Chhajlani, R.K., Hydromagnetic Kelvin-Helmholtz Instability in the Presence of Suspended Particles and Finite Larmor Radius Effect, Z. Naturforch., 49a (1994), pp. 1102-1110.
- Sharma, P.K., Chhajlani, R.K., Effect of Rotation on the Rayleigh-Taylor Instability of Two Superposed Magnetized Conducting Plasma, Phys. Plasmas, 5 (1998), 6, pp. 2203-2209.
- Prajapati, R.P., Soni, G.D., Sanghvi, R.K. and Chhajlani, R.K., Kelvin-Helmholtz and Rayleigh- Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles, Z. Naturforsch, 64a (2009), pp. 455 -466.
- McDonnel, J.A.M, Cosmic Dust, John Wiley and Sons Toronto, 1978.
- Sharma, R.C. and Sunil, Rayleigh Taylor Instability of Partially Ionized Plasma in Porous Medium in Presence of Variable Magnetic Field, Z. Naturforsch., 47(1992), 12, pp. 1227-1231.
- Sharma, R.C., Kumar, P., Rayleigh-Taylor Instability of Viscous-Viscoelastic Fluids Through Porous Medium, Indian J. Pure Applied Math., 24(1993), pp.563-569.
- Sunil and Chand, T., Rayleigh Taylor Instability of a Plasma in Presence of Variable Magnetic Field and Suspended Particles in Porous Medium, Indian J. Phys., 71B (1997), pp. 95-105.
- Wurm, G., Paraskov, G. and Krauss, O., On the Importance of Gas Flow Through Porous Bodies For the Formation of Planetesimals, J. Astrophysical, 606(2004), pp. 983-987.
- Kumar, P., Mohan, H. and Singh, G.J. Rayleigh Taylor instability of Rotating Magnetic Field, Transport in Porous Media, 56 (2004), 2, pp. 199-208.
- Kumar, S., The Instability of Streaming Walters Fluids in Porous Medium in Hydromagnetics, Int. J. Appl. Math and Mech., 7 (2011), 11, pp. 33-45.
- Sharma, P.K., Prajapati, R.P. and Chhajlani, R.K., Effect of Surface Tension and Rotation on Rayleigh-Taylor Instability of Two Superposed Fluids with Suspended Particles, Acta Phys. Pol., A118 (2010), 4 pp. 576 -584.
- Prajapati, R.P. and Chhajlani, R.K., Kelvin-Helmholtz and Rayleigh Taylor Instability of Streaming Fluids with Suspended Particles Flowing Through Porous Medium, J. Porous Media, 13 (2010), 9, pp. 765-777.
- Singh, V. and Dixit, S., Stability of Rotating Viscous Viscoelastic Superposed Fluids in Presence of Suspended Particles in Porous Medium, Inter. J. Fluids Engg., 3(2011), 2, pp. 211-220.
- William, S. L., Control System Fundamentals, CRC Press, 2011.