Quantum Effects on the Magnetogravitational Instability of Viscoelastic Fluid through a Porous Medium

In the present analysis, the effect of quantum corrections on the gravitational instability of a viscoelastic fluid through porous medium in the presence of uniform magnetic field has been studied in the transverse and longitudinal mode of wave propagation. For the mathematical formulation of the physical problem Generalized Hydrodynamic and Hass model have been used. A general dispersion relation has been derived by using the normal mode analysis. The general dispersion relation is discussed separately for both the modes of wave propagation under the strongly and weakly coupling limits. It is found that the porosity of the medium and quantum effects modifies the Jeans criterion of instability for both the modes of wave propagation under the strongly and weakly coupling limits. Further, the effects of various parameters on the growth rate of gravitational instability has been numerically studied and depicted graphically.