R. C. Sharma

Effect of rotation on thermal instability of a viscoelastic fluid

The thermal instability of a layer ofOldroyd fluid acted on by a uniform rotation is considered. The rotation is found to have destabilizing as well as stabilizing effect under certain conditions in contrast to that of a Maxwell fluid where it has a destabilizing effect. The analytic conditions for non-existence of overstability are investigated.

Effect of rotation on ferromagnetic fluid heated and soluted from below saturating a porous medium

The effect of rotation on thermosolutal convection in ferromagnetic fluid saturating a porous medium is considered for a fluid layer heated and soluted from below in the presence of a uniform vertical magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, magnetization has a destabilizing effect whereas a stable solute gradient and rotation have stabilizing effects on the system. In the absence of rotation, the destabilizing effect of medium permeability is depicted but in the presence of rotation, medium permeability may have a destabilizing or stabilizing effect on the onset of instability. The critical wavenumber and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of magnetic parameter M1. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of stable solute gradient and rotation. The oscillatory modes are introduced due to the presence of the stable solute gradient and rotation, which were non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.

Effect of suspended particles on the onset of Bénard convection in hydromagnetics

The influence of suspended particles on the onset of Bénard convection is studied in the presence of a vertical magnetic field. The principle of exchange of stabilities is satisfied. The influence of suspended particles is to destabilize the layer whereas the effect of magnetic field is stabilizing. The effect of a uniform rotation is also studied and is found to have a stabilizing influence in the presence of suspended particles on the Bénard convection.

Thermal instability in a viscoelastic fluid in hydromagnetics

The stability of a layer of Oldroyd fluid heated from below and subject to a magnetic field is considered. The magnetic field is found to have a stabilizing influence. The analytic conditions for nonexistence of overstability are investigated.

Thermal Instability of Oldroydian Viscoelastic Fluid with Suspended Particles in Hydromagnetics in Porous Medium

Abstract The effect of suspended particles on the thermal instability of an Oldroydian viscoelastic fluid in hydromagnetics in porous medium is considered. The magnetic field, suspended particles, viscoelasticity, and porous medium effects create oscillatory modes in the system which did not exist previously. For stationary convection, the viscoelastic fluid behaves like a Newtonian fluid and the magnetic field has a stabilizing effect, whereas medium-permeability, suspended particles have destabilizing effects on the system. The sufficient conditions for the avoidance of overstability are obtained, and these also hold good for the case of a Maxwellian viscoelastic fluid.

The gravitational instability of flow through porous medium for some systems of astrophysical interest

The gravitational instability of flow through porous medium for some hydrodynamical and hydromagnetical systems of astrophysical interest is investigated. The effects of rotation, magnetic field, viscosity and finite electrical conductivity are studied for the gravitational instability through porous medium. The effect of suspended particles on the instability is also considered. It is found that Jeans criterion remains unchanged in the presence of porosity, viscosity, finite conductivity, rotation, magnetic field and suspended particles in the medium.

Rayleigh-taylor instability of two viscoelastic superposed fluids

The stability of the plane interface separating two viscoelastic superposed fluids of uniform densities has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the system is stable for stable configuration and unstable for unstable configuration. The behaviour of growth rates with respect to stress relaxation time and strain retardation time parameters are examined analytically.

The effect of magnetic-field-dependent viscosity on ferroconvection in a porous medium in the presence of dust particles

This paper deals with the theoretical investigation of the effect of magnetic-field-dependent (MFD) viscosity on the thermal convection in ferromagnetic fluid saturating a porous medium in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis. For the case of stationary convection, medium permeability and dust particles always have a destabilizing effect whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, magnetization may have a destabilizing or stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M1. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were nonexistent in their absence. A sufficient condition for the nonexistence of overstability is also obtained.

RAYLEIGH--TAYLOR INSTABILITY OF TWO SUPERPOSED CONDUCTING FLUIDS IN THE PRESENCE OF SUSPENDED PARTICLES

Rayleigh-Taylor instability of two superposed conducting fluids in the presence of suspended particles is studied. The prevalent magnetic field is assumed to be uniform and horizontal. The fluids are assumed to be highly viscous and of equal kinematic viscosities, for mathematical simplicity. The system is found to be stable for stable configuration and unstable for unstable configuration in the presence of suspended particles. This is in contrast to the thermal instability problem where the suspended particles have a destabilizing effect.

Thermal-convective instability through porous medium

Thermal-convective instability through porous medium has been investigated and a criterion for monotonic instability has been derived. The criterion for monotonic instability has been found to hold good in the presence of magnetic field and rotation. The radiative transfer and medium porosity effects have also been discussed on the thermal-convective instability.