Double-diffusive convection of compressible rotating Walters’ (B′) fluid with Hall currents saturating a porous medium

Abstract

Keeping in view the conflicting tendencies of rotation and Hall currents (magnetic field) while acting together; combined effects of Hall currents and rotation are considered on the hydromagnetic stability of a compressible Walters’ (Model B′) elastico-viscous fluid heated and soluted from below saturating a porous medium. Boussinesq approximation is used to simplify the complex hydromagnetic equations and the perturbation equations are analyzed in terms of normal modes. A dispersion relation governing the effects of visco-elasticity, salinity gradient, rotation, Hall currents and medium permeability is derived. It has been found that for stationary convection, Walters’ (Model B′) fluid behaves like an ordinary Newtonian fluid due to the vanishing of the visco-elastic parameter. Compressibility, solute gradient, rotation and magnetic field postpone the onset of instability as such their effect is to stabilize the system. Hall currents and medium permeability are found to hasten the onset of instability for permissible range of values of various parameters. The dispersion relation is analyzed numerically and the effects of various parameters for permissible range of values are depicted graphically. The visco-elasticity, solute gradient and Hall currents (hence magnetic field) introduce oscillatory modes in the system which were non-existent in their absence. Also the case of overstability is discussed and sufficient conditions for the non-existence of overstability are derived.

Keywords: Walters’ (Model B′) fluid, rotation, Hall currents, thermosolutal instability, compressibility, porous medium.