M. Agoor. Bothaina - Faculty of Science El-Fayoum University, Fayoum, Egypt.
N. T. Eldabe - Department of Mathematics Faculty of Education, Ain Shams University, Cairo, Egypt.

The Rayleigh-Taylor instability (RIT) at the interface of two superposed Couple-stress Casson fluids flowing in porous medium and in the presence of a uniform normal magnetic field is studied. The fluids have different densities. For mathematical simplicity, the stability analysis based on fully developed approximations is used. The maximum wave numbers and the corresponding maximum frequency are obtained. The Growth rate of Rayleigh-Taylor instability in the case of non-Newtonian Casson fluid with couple-stress through porous medium is discussed. The effects of physical parameters of the problem such as the permeability parameter, magnetic parameter, non-Newtonian Parameter and couple-stress parameter on the regions of stability are discussed numerically and illustrated graphically through a set of figures.

Casson equation, Newtonian fluid, Non, Micropolar fluid, Porous medium, Permeability, Magnetic field, Viscosity