Journal of the Association of Engineers, India

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Stability of a Perfectly Conducting Viscoelastic Fluid with Continuous Viscosity & density Stratification in Presence of a Horizontal Magnetic Field


Affiliations
1 S.N. Bose Institute for Mathematics & Mathematical Sciences, C-34/4 Anadapur, Kolkata-700107, India
2 Department of Mathematics, Narula Institute of Technology, Agarpara, Kolkata- 700109, India
3 Department of Computer Application, B.P. Poddar Institute of Management & Technology, 137, V.I.P. Road, Kolkata- 700052, India
     

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Rayleigh-Taylor instability of a viscoelastic fluid in presence of a horizontal magnetic field has been investigated. The Graphical representations of numerical solution of the derived generating equations evolved have been presented with the analysis of results obtained and presentation of numerical data. It has been seen that effect of magnetic field under certain condition acts as a destabilising agent. When horizontal magnetic field varies in vertical direction, the magnetic field affects on two-dimensional disturbances perpendicular to the lines of force. The corresponding stability conditions, dependent on magnetic field and gravity wave, but independent of viscosity and viscoelasticity are derived. Also it is observed that the stability of equilibrium is dependent on sufficiently large magnetic field, viscosity and viscoelasticity for exponential density and viscosity stratification.

Keywords

Rayleigh–Taylor Instability, Viscoelastic Fluid, Horizontal Magnetic Field, Gravity Wave, Maxwell Model, Kelvin–Voigt Model, Standard Linear Solid Model, Generalized Maxwell Model
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  • Stability of a Perfectly Conducting Viscoelastic Fluid with Continuous Viscosity & density Stratification in Presence of a Horizontal Magnetic Field

Abstract Views: 344  |  PDF Views: 3

Authors

N. C. Ghosh
S.N. Bose Institute for Mathematics & Mathematical Sciences, C-34/4 Anadapur, Kolkata-700107, India
Pijush Basak
Department of Mathematics, Narula Institute of Technology, Agarpara, Kolkata- 700109, India
Abhijit Bhattacharya
Department of Computer Application, B.P. Poddar Institute of Management & Technology, 137, V.I.P. Road, Kolkata- 700052, India

Abstract


Rayleigh-Taylor instability of a viscoelastic fluid in presence of a horizontal magnetic field has been investigated. The Graphical representations of numerical solution of the derived generating equations evolved have been presented with the analysis of results obtained and presentation of numerical data. It has been seen that effect of magnetic field under certain condition acts as a destabilising agent. When horizontal magnetic field varies in vertical direction, the magnetic field affects on two-dimensional disturbances perpendicular to the lines of force. The corresponding stability conditions, dependent on magnetic field and gravity wave, but independent of viscosity and viscoelasticity are derived. Also it is observed that the stability of equilibrium is dependent on sufficiently large magnetic field, viscosity and viscoelasticity for exponential density and viscosity stratification.

Keywords


Rayleigh–Taylor Instability, Viscoelastic Fluid, Horizontal Magnetic Field, Gravity Wave, Maxwell Model, Kelvin–Voigt Model, Standard Linear Solid Model, Generalized Maxwell Model



DOI: https://doi.org/10.22485/jaei%2F2015%2Fv85%2Fi3-4%2F119861