Stability of Stratified Viscoelastic Walters' (Model B′) Fluid/Plasma in the Presence of Quantum Pressure

Quantum effects on the Rayleigh-Taylor Instability in an inhomogeneous stratified incompressible, viscoelastic Walters' (model B') fluid/plasma are investigated. 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 at z=0, z=d. The solution of the linearized equations of the system together with the boundary conditions leads to derive the dispersion relation (the relation between the normalized growth rate and square normalized behavior wave number) using normal mode technique to explain the roles that play the variables of the problem. The behavior of growth rates with respect to the quantum effect and kinematic viscoelasticity are examined in the presence of kinematic viscosity.