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Hydromagnetic thermal instability of compressible Walters' (Model B') rotating fluid permeated with suspended particles in porous medium

Rana G. C., Jamwal H. S.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 4

75--88

EN

In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions.

2

The instability of streaming viscous-viscoelastic fluids in a porous medium

Kumar P., Singh G. J.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 1

191-201

EN

The Kelvin-Helmholtz instability of a Newtonian viscous fluid overlying a viscoelastic fluid in a porous medium is considered separately for Walters B' and Rivlin-Ericksen viscoelastic fluids. It is found that for the special case when perturbations in the directions of streaming are ignored, the system is unstable for a potentially unstable configuration and the system is stable for a potentially stable configuration for Rivlin-Ericksen viscoelastic fluids, which is in contrast to the case of the Walters B' viscoelastic fluid, where the system can be stable or unstable depending upon kinematic viscoelasticity, medium porosity, relative density of the viscoelastic fluid and medium permeability, for both potentially unstable and potentially stable configurations. In every other direction, a minimum value of wave-number has been found. The system is unstable for all wave-numbers greater than this minimum wave number.

3

The instability of streaming Walters B' viscoelastic fluids in hydromagnetics through porous media

Kumar P., Sharma P.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 1

123-131

EN

The instability of streaming Walters B' elastico-viscous fluids in hydromagnetics through porous medium is considered. The case of two uniform streaming fluids separated by a common horizontal interface is considered. It is found that for the special case when perturbations in the direction of streaming are ignored, the system can be stable or unstable, depending upon kinematic viscoelasticity, medium porosity and medium permeability, for both potentially unstable and stable configurations. In all other directions, a minimum value of wave-number has been found and the system is unstable for all wave-numbers greater than this minimum wave number and the instability of the system is found to be postponed due to the presence of the magnetic field.