Analysis of MHD rayleigh-taylor instability in a walter's B fluid with thermal and mass diffusion effects

An analytical and numerical investigation of Rayleigh-Taylor instability has been carried out within a planner configuration under the influence of a vertically imposed magnetic field, through viscous potential flow theory. The instability is examined for the configuration in which a Walter's B viscoelastic fluid overlies a Newtonian viscous fluid embedded in a porous medium, with simultaneous heat and mass transfer permitted across the interface. The dispersion relation between perturbation growth rate and wave number is established via normal mode analysis. This relation is investigated using the Newton-Raphson method, which facilitates the identification of the influence of various non-dimensional physical parameters, determining whether they suppress or amplify the perturbation growth. The study reveals that a vertically oriented magnetic field and an increased porosity of the medium enhance the amplification of perturbations, while an increased thermal flux across the interface counteracts this tendency, thereby diminishing the growth of instability.