G. C. Rana

Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection.

Stability of Stratified Rivlin-Ericksen Fluid in the Presence of Horizontal Magnetic Field and Uniform Horizontal Rotation in Porous Medium

The influence of viscosity, viscoelasticity and medium permeability on the stability of stratified Rivlin-Ericksen viscoelastic fluid is examined for viscoelastic polymeric solutions in the simultaneous presence of a uniform horizontal magnetic field (H, 0, 0) and uniform horizontal rotation (Ω,0,0). These solutions are known as Rivlin-Ericksen fluids and their rheology is approximated by the Rivlin-Ericksen constitutive relations, proposed by Rivlin and Ericksen [13]. The effects of Coriolis forces on the stability is chosen along the direction of the magnetic field and transverse to that of the gravitational field (o,o,-g). The system is found to be stable for all wave numbers for stable stratifications and unstable for unstable stratifications for the stratifications in density, viscosity, viscoelasticity, medium permeability and medium porosity. The system can be completely stabilized by large enough magnetic field, which was unstable in the absence of magnetic field; provided the initial configuration is top-heavy density wise. The kinematic viscosity and kinematic viscoelasticity have damping effects on the growth rates with the increase in kinematic viscosity and kinematic viscoelasticity, respectively, for a fixed wave number. The medium permeability has enhancing effects on the growth rates with its increase for a fixed wave number. The above results have also been shown graphically.

On the Onset of Electrohydrodynamic Instability of Rivlin-Ericksen Viscoelastic Dielectric Fluid Layer

In this paper we investigate the effect of AC electric field on the onset of instability of an elastico-viscous Rivlin-Ericksen dielectric fluid layer stimulated by the dielectrophoretic force due to the variation of dielectric constant with temperature. By applying linear stability theory and normal mode analysis method, we derive the dispersion relation describing the influence of viscelasticity and AC electric field. For the case of stationary convection, it is observed that Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid whereas AC electric field hastens the stationary convection. The present results are in good agreement with the earlier published results.

Thermal Instability of a Finite-Larmor-Radius Hall Plasma Under Rotation and Variable Gravitational Field in Porous Medium

Abstract The thermal instability of a rotating plasma in a porous medium is considered in the presence of a uniform vertical magnetic field to include the Hall-current, finite-Larmor-radius (FLR) and variable gravitational field effects. It is found that the principle of exchange of stabilities is valid in the absence of rotation and magnetic field (hence Hall-current). The uniform vertical magnetic field (and hence an FLR and Hall-current) and rotation effects introduce oscillatory modes in the system which were non-existent in their absence. The system is stable/unstable depending upon certain conditions in the presence of rotation, medium permeability and magnetic field (hence Hall-current and an FLR). The Rayleigh number is found to increase with the increase of the magnetic field (and hence an FLR and Hall-current), rotation and medium permeability.