Effect of Hall Currents and Suspended Particles on Critical Thermal Rayleigh Number for Compressible Walters’ (Model B') Fluid

A layer of a compressible, electrically conducting Walters' (Model B¢) elastico-viscous fluid permeated with suspended particles heated from below in the presence of a magnetic field and Hall currents is considered. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant hydromagnetic equations. A dispersion relation governing the effects of visco-elasticity, magnetic field, Hall currents and suspended particles has been obtained. For the case of stationary convection, Walters' (Model B¢) fluid behaves like a Newtonian fluid due to the vanishing of the visco-elastic parameter. The compressibility and magnetic field are found to have stabilizing effects on the system, that is, their effect is to postpone the onset of thermal instability whereas Hall currents and suspended particles are found to hasten the onset of thermal instability for permissible range of values of various parameters. The dispersion relation is also analyzed numerically. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behaviour of various parameters on critical thermal Rayleigh numbers has been depicted graphically.