Magneto-convection of a stratified dusty Rivlin-Ericksen fluid in porous medium: An analytical and computational study for moderate and high rotation

To study the conflicting tendencies of rotation and magnetic field while acting together and keeping in mind the applications of flow through porous medium in geophysics, particularly in the study of earth's core and the presence of dust/suspended particles therein; the hydromagnetic stability of stratified Rivlin-Ericksen fluid-particle mixture in the presence of rotation in porous medium is considered. The relevant hydromagnetic equations are linearized using Boussinesq approximation and the perturbed quantities are analysed in terms of normal modes. Dispersion relation governing the effects of rotation, magnetic field, medium permeability and suspended particles is derived. The system is found to be stable for the case of stable stratification. For the case of unstable stratification, magnetic field succeeds in stabilizing the otherwise unstable system for certain wave number range. Computational study has been carried out to discuss the behavior of growth rates with respect to kinematic viscoelasticity, Alfvén velocity, medium permeability and suspended particles for moderate as well as high rotation.