THERMAL SCIENCE

International Scientific Journal

Aiyub Khan

,

Neka SharmaORCID

,

P K BhatiaORCID

KELVIN-HELMHOLTZ DISCONTINUITY IN TWO SUPERPOSED VISCOUS CONDUCTING FLUIDS IN A HORIZONTAL MAGNETIC FIELD

ABSTRACT
The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.
KEYWORDS
viscosity, porous medium, streaming velocity, magnetic field, surface tension, instability
PAPER SUBMITTED: 2008-03-23
PAPER REVISED: 2008-05-10
PAPER ACCEPTED: 2008-05-15
DOI REFERENCE: https://doi.org/10.2298/TSCI0803103K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2008, VOLUME 12, ISSUE No. 3, PAGES [103 - 110]
REFERENCES
[1] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, USA, 1981
[2] Bhatia, P. K., Rayleigh-Taylor Instability of Two Viscous Superposed Conducting Fluids, Nuov. Cim. 19B (1974), 2, pp. 161-168
[3] Drazin, P. G., Reid, W. H., Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, 1981
[4] Joseph, D. D., Stability of Fluid Motion II, Springer-Verlag, New York, USA, 1976
[5] Phillips, O. M., Flow and Reaction in Permeable Rocks, Cambridge University Press, Cambridge, UK, 1991
[6] Ingham, D. B., Pop, I., Transport Phenomena in Porous Medium, Pergamon Press, Oxford, UK, 1998
[7] Nield, D. A., Bejan, A., Convection in Porous Medium, 2nd ed., Springer Verlag, New York, USA, 1999
[8] Wooding, R. A., Rayleigh Instability of a Thermal Boundary Layer in Flow through a Porous Medium, J. Fluid Mech., 9 (1960), 2, pp. 183-192, 10.1017/s0022112060001031
[9] Kumar, P., Stability of Two Superposed Viscoelastic (Walters B') Fluid- Particle Mixture in Porous Medium, Z. Naturforsch., 54a (1998), 5, pp. 343-347
[10] Sharma, R. C., Kango, S. K., Stability of Two Superposed Walters B' Viscoelastic Fluids in the Presence of Suspended Particles and Variable Magnetic Field in Porous Medium, Appl. Mech. Engng. 4 (1999), 2, pp. 255-269, 10.2298/tsci0701093k
[11] Khan, A., Bhatia, P. K., Stability of Two Superposed Viscoelastic Fluid in a Horizontal Magnetic Field, Indian J. Pure Appl. Math., 32 (2001), 1, pp. 98-108
[12] Kumar, P., Singh, M., Instability of Two Rotating Viscoelastic (Walter B') Superposed Fluid with Suspended Particle in Porous Medium, Thermal Science, 11 (2007), 1, pp. 93-102
[13] Bhatia, P. K., Sankhla, V. D., Kelvin-Helmholtz Discontinuity in Two Superposed Viscous Conducting Fluids, Astrophysics and Space Sci., 103 (1984), 1, pp. 33-38, 10.2298/tsci0803103k
[14] D'Angelo, N., Song, B., Kelvin-Helmholtz Instability in a Plasma with Negative Ions, IEEE Transectors Plasma Sci., 19 (1991), 1, pp. 42-46.
[15] D'Angelo, N., Song, B., The Kelvin-Helmholtz Instability in Dust Plasmas, Planet Space Sci., 38 (1990), 12, pp. 1577-1579
[16] Benjamin, T. B., Bridges, T. J., Reappraisal of the Kelvin-Helmholtz Problem, Part I: Hamiltonian Structure, J. Fluid Mech., 333 (1997), 4, pp. 301-325
[17] Allah, M. H. O., The Effects of Magnetic Field and Mass and Heat Transfer on Kelvin-Helmholtz Stability, Proc. Nat. Acad. Sci., 68 (1998), II, pp. 163-173
[18] El-Sayed, M. F., Electrohydrodynamic Instability of Two Superposed Viscous Streaming Fluids through Porous Media, Canad. J. Phys., 75 (1997), 7, pp. 499-508
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Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

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