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Vorticity transport analysis in magnetic viscoelastic fluid

Kumar P., Mohan H., Hoshoudy G.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 1

127--133

EN

Results of investigation on the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles is presented here. Equations governing the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles are obtained from the equations of magnetic fluid flow. From these equations it follows that the transport of solid vorticity is coupled with the transport of fluid vorticity. Further, we find that because of thermokinetic process, fluid vorticity may exist in the absence of solid vorticity, but when fluid vorticity is zero, then solid vorticity is necessarily zero. A two-dimensional case is also studied and found that the fluid vorticity is indirectly influenced by the temperature and the magnetic field gradient.

2

Hall effect on thermal instability of viscoelastic dusty fluid in porous medium

Singh M., Gupta R. K.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

871--886

EN

The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters.

3

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.