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Kelvin - Helmholtz instability of two superposed Oldroydian viscoelastic fluid layers in a horizontal magnetic field

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EN
Abstrakty
EN
The Kelvin-Helmholtz instability of the plane interface separating two superposed viscous electrically conducting streaming Oldroydian fluids permeated with surface tension and magnetic field in a porous medium is considered. The stability motion is also assumed to have uniform two dimensional streaming velocity. The stability analysis has been carried out for two highly viscous fluids. By applying the normal mode technique to the linearized perturbation equations, the dispersion relation has been derived. As in the case of superposed Newtonian fluids, the system is stable in the potentially stable case and unstable in the potentially unstable case, that holds also for the present case. The behavior of growth rate with respect to kinematic viscosity, elasticity, permeability of porous medium, surface tension and streaming velocity are examined numerically and discussed in detail in section 5.
Rocznik
Strony
1129--1142
Opis fizyczny
Bibliogr. 34 poz., wykr.
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autor
autor
autor
  • Department of Mathematics and Statistics, J.N.V. University Lachoo Memorial College of Science and Technology Jodhpur, INDIA, draiyubkhan@gmail.com
Bibliografia
  • Allah M.H.D. (1998): The effect of magnetic field and mass and heat transfer on Kelvin-Helmholtz stability. - Proceedings of National Academy of Science India,vol.68(A), No.2, pp.163-173.
  • Allah M.H.D. (2002): Rayleigh Taylor instability with surface tension. Porous medium rigid planes and exponential densities. - Indian Journal of Pure and Applied Mathematics, vol.33, No.9, pp.1391-1404.
  • Benjamin T.B. and Bridges T.J. (1997): Reappraisal of the Kelvin-Helmholtz problem Part I Hamiltonian structure - Journal of Fluid Mechanics, vol.333, No.4, pp.301-326.
  • Bhatia P.K. and Sharma A. (2003): Kelvin-Helmholtz instability of two viscous superposed conducting fluids. - Proceedings of National Academy of Science India,vol.73(A), No.4, pp.497-520.
  • Bhatia P.K. and Khan A. (1995): Stability of an Oldroydian fluid layer in a horizontal magnetic field, Revista Technica. - De La Facultad De Ingeneria Universidad Del Zulia, vol.18, No.3, pp.305-311.
  • Bhatia P.K. and Steiner J.M. (1974): On the Kelvin-Helmholtz discontinuity in two superposed plasmas. - Australian Journal of Physics, vol.27, pp.53-57.
  • Chandrasekhar S. (1961): Hydrodynamics and Hydromagnetic Stability. - New York, USA: Clarendon Press.
  • D'Angelo N. and Goeler S.V. (1966): Investigation of the Kelvin-Helmholtz instability in a cesium plasma. - Physics of Fluids, vol.2, No.2, pp.309-313.
  • D'Angelo N. (1965): Kelvin-Helmholtz instability in a fully ionized plasma in a magnetic field. - Physics of Fluids, vol. 8, No.9, pp.1748-1750.
  • Drazin P.G. and Reid W.H. (2004): Hydrodynamic Stability. - UK: Cambridge University Press.
  • Gerwin R.A. (1968): Hydromagnetic surface waves in a conducting liquid surrounded by a flowing gas. - Physics of Fluids, vol.11, pp.1699-1708.
  • Ingham D.B. and Pop I. (1998): Transport Phenomena in Porous Medium. - Oxford, UK: Pergamon Press.
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  • Kalra G.L. and Kathuria S.N. (1970): Effect of Hall current and resistivity on the stability of a gas-liquid system. - Journal of Plasma Physics, vol.4, pp.451.
  • Khan A. and Bhatia P.K. (2001): Stability of two superposed visco-elastic fluids in a horizontal magnetic field. - Indian Journal of Pure and Applied Mathematics, vol.32, No.1, pp.99-108.
  • Kumar Lal R. and Singh M. (2007): Hydrodynamic and hydromagnetic stability of two stratified Rivlin-Ericksen elastico-viscous superposed fluids. - International Journal of Applied Mechanics and Engineering, vol.12, No.3, pp.645-653.
  • McDonnel J.A.M. (1978): Cosmic Dust. - John Wiley and Sons. - Toronto, pp.330.
  • Nield D.A. and Bejan A. (2005): Convection in Porous Medium. - New York: Springer Verlag.
  • Oldrod J.G. (1958): Non-newtonian effects in steady motion of some idealized elastico-viscous liquids. - Proceedings of Royal Society London, Series A, vol.245 A, pp.278-297.
  • Oza S. and Bhatia P.K. (1993): Rayleigh-Taylor instability of stratified rotating fluid through a porous medium in 2D horizontal magnetic field. - Astrophysics and Space Science, vol.199, pp.279-288.
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  • Sayeed M.F., El (1997): Electrohydrodynamic instability of two superposed viscous streaming fluid through porous medium. - Canadian Journal of Physics, vol.75, No.7, pp.499-508.
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  • Sharma N., Khan A. and Bhatia P.K. (2008): Kelvin Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field. - Thermal Science, vol.12, No.3, pp.103-110.
  • Sharma N., Khan A. and Bhatia P. K. (2007): Rayleigh Taylor instability of Rivlin Ericksen elasticoviscous fluids in a uniform horizontal magnetic field through porous medium. - Journal of Indian Academy of Mathematics, vol.29, No.2, pp.379-390.
  • Sharma R.C. and Kumar P. (1997): Thermal instability in Rivlin Ericksen elastico-viscous fluid in hydromagnetics. - Zeitschrift für Naturforsch, vol.52 A, pp.369-371.
  • Shivamoggi B.K. (1981):Kelvin Helmholtz instability of a plasma in a magnetic field: Finite resistivity effect. - Physica Scripta, vol.24, pp.49-51.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0015-0011
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