Hall Effect on Thermal Instability of Viscoelastic Dusty Fluid in Porous Medium

Abstract

The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters.

Hall Effect on Bénard Convection of Compressible Viscoelastic Fluid through Porous Medium

“…Sunil et al [17,18] studied the Hall effect on thermosolutal instability of Rivlin-Ericksen and Walters' (model ) fluid in porous medium. In one study of Singh [19], Hall current effect on thermosolutal instability in a viscoelastic fluid flowing through porous medium and magnetic field stable solute gradient are found to have stabilizing effects on the system, whereas Hall current and medium permeability have a destabilizing effect on the system. The sufficient conditions for the nonexistence of overstability have also obtained.…”