Stability of stratified Rivlin-Ericksen (model) fluid in magnetized quantum plasma saturating a porous medium

The present investigation is to focus on the quantum effects on the Rayleigh Taylor instability in an infinitely electrically conducting inhomogeneous stratified incompressible, viscoelastic fluid/plasma through a porous medium in the presence of a vertical magnetic field. After developing a mathematical formulation, the linear magneto hydrodynamic equations are solved by normal mode analysis to obtain the velocity perturbation. The linear growth rate is derived for the case when the plasma with exponential density, viscosity, viscoelasticity, quantum parameter distribution is confined between two rigid planes at z = 0, z = d. The behaviour of growth rates with respect to the kinematic viscoelasticity and the simultaneous presence of quantum effect and magnetic field are obtained in the presence of porous medium, the medium permeability and kinematic viscosity. It is observed that the vertical magnetic field beside the quantum effect yield more stability on the considered system.