Analysis of Stability of a Plasma in Porous Medium

The thermal convection of a plasma in porous medium is investigated in the presence of finite Larmor radius (FLR) and Hall effects. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of a magnetic field (and hence the presence of FLR and Hall effects) introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, the FLR may have a stabilizing or destabilizing effect, but a completely stabilizing one for a certain wave-number range. Similarly, the Hall currents may have a stabilizing or destabilizing effect but a completely stabilizing one for the same wave-number range under certain condition, whereas the medium permeability always has a destabilizing effect for stationary convection. Also it is found that the system is stable for 𝑔𝛼𝜅 𝜈𝛽 ≤ 27𝜋 4 4 and under the condition 𝑔𝛼𝜅 𝜈𝛽 > 27𝜋 4 4 , the system becomes unstable.

Analysis of Stability in Couple-Stress Magneto-Fluid

The aim of the present research was to study the effect of magnetic field on the layer of electrically conducting couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that the couple-stress parameter and magnetic field have stabilizing effect on the system whereas the medium permeability has a destabilizing effect on the system. The magnetic field introduces oscillatory modes in the system which was non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.

Stability Analysis in Couple-Stress Rotatory Fluid

The aim of the present research was to study the effect of uniform rotation on the layer of a couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that rotation has a stabilizing effect, whereas the couple-stress parameter and medium permeability have both stabilizing and destabilizing effects on the system. It is found that the presence of rotation introduces oscillatory modes in the system which were non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.

Numerical Investigations on Rotatry Micropolar Fluid in Hydromagnetics Permeated with Suspended Particles Saturating Porous Medium

This paper deals with the convection of micropolar fluids heated and soluted from below in the presence of suspended particles (fine dust) and uniform vertical rotation and uniform vertical magnetic field in a porous medium. Using the Boussinesq approximation, the linearized stability theory and normal mode analysis, the exact solutions are obtained for the case of two free boundaries. It is found that the presence of the suspended particles number density, the rotation parameter, stable solute, magnetic field intensity and medium permeability bring oscillatory modes which were non–existent in their absence. It is found that the presence of coupling between thermal and micropolar effects, rotation parameter, solute parameter and suspended particles may introduce overstability in the system. Graphs have been plotted by giving numerical values to the parameters accounting for rotation parameter , magnetic field solute parameter, the dynamic microrotation viscosity and coefficient of angular viscosity to depict the stability characteristics, for both the cases of stationary convection and overstability. It is found that Rayleigh number for the case of overstability and stationary convection increases with increase in rotation parameter, as well as with magnetic field intensity, solute parameter and decreases with increase in micropolar coefficients and medium permeability, for a fixed wave number, implying thereby the stabilizing effect of rotation parameter, magnetic field intensity ,solute parameter and destabilizing effect of micropolar coefficients and medium permeability on the thermosolutal convection of micropolar fluids.

Effect of Rotation on Thermosolutal Convection in Visco-elastic Nanofluid with Porous Medium

In this paper, we studied the rotation effect on the thermosolutal convection in visco-elastic nanofluid in the presence of porous medium using Walters` (model B`). To solve the conservation equation, we used the normal mode technique and Galerkin weighted residual method. For stationary convection, the onset criterion derived analytically and experiential that visco-elastic nanofluid behaves as a regular Newtonian nanofluid. The effect of rotation, thermo-nanofluid Lewis number, thermosolutal Lewis number and solutal Rayleigh number analyze analytically and graphically.