Thermosolutal instability of a compressible Rivlin–Erickson fluid in the presence of rotation and Hall currents saturating a porous medium

Abstract

The combined effect of Hall currents (hence magnetic field) and rotation on the stability of a layer of compressible Rivlin–Erickson elastico-viscous fluid heated and soluted from below is considered. Dispersion relation governing the effects of rotation, Hall currents, magnetic field, compressibility, solute gradient and medium permeability is derived. For the case of stationary convection, the Rivlin–Erickson fluid behaves like an ordinary Newtonian fluid due to the vanishing of the visco-elastic parameter. It has been found that the compressibility, solute gradient, rotation and magnetic field postpone the onset of thermosolutal instability. Hall currents and medium permeability hasten the onset of thermosolutal convection for the permissible range of values of various parameters. Also, the dispersion relation is analyzed numerically and the results depicted graphically. The compressibility and solute gradient introduce oscillatory modes in the system which were non-existent in their absence. The case of overstability is discussed and sufficient conditions for non-existence of overstability are derived.