Hall effect on thermosolutal instability of a Rivlin-Ericksen fluid in a porous medium

The thermosolutal instability of a Rivlin-Ericksen fluid in a porous medium is considered in the presence of uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the stable solute gradient and the magnetic field have stabilizing effects on the system, whereas the Hall currents have a destabilizing effect on the system. The medium permeability has both stabilizing and destabilizing effects on the system depending on the Hall parameter M. The kinematic viscoelasticity has no effect for stationary convection. Also, the dispersion relation is analysed numerically. The stable solute gradient and the magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system, which were nonexistent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.