The present investigation deals with the quantum effects on the Rayleigh - Taylor
instability in an infinitely electrically conducting inhomogeneous stratified incompressible
viscoelastic fluid/plasma through a porous medium. The linear growth rate is derived for the
case where a plasma with exponential density, viscosity, viscoelasticity and quantum parameter
distribution is confined between two rigid planes. The solution of the linearized equations of
the system together with the appropriate boundary conditions leads to derive the dispersion
relation (the relation between the normalized growth rate and square normalized wavenumber)
using normal mode technique. The behavior of growth rate with respect to quantum effect and
kinematic viscoelasticity are examined in the presence of porous medium, medium permeability
and kinematic viscoelasticity. It is observed that the quantum effects bring more stability for a
certain wave number band on the growth rate on the unstable configuration.
Keywords: Rivlin-Ericksen (Model); viscoelastic; Rayleigh-Taylor instability; quantum plasma; porous medium.
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