Annular generalized Couette flow of immiscible viscous fluids in an anisotropic porous medium

The present study concentrates on the flow of 2 immiscible fluids through space between 2 coaxial cylinders filled with 2 different layers of anisotropic porous mediums. The inner cylinder is impermeable, and we assumed that its surface is slippery. The permeability of both porous regions is different and depends on anisotropic parameters. The flow in porous regions is due to the applied pressure gradient and the movement of the outer cylinder in the axial direction with a constant speed. Velocity profiles of Couette flow, Poiseuille flow, and Couette-Poiseuille of the present problem are analytically obtained using appropriate boundary conditions. Further, the impacts of anisotropic parameters and other physical parameters are studied and graphically presented. It is found that increasing permeability ratio and anisotropic angles have increasing and decreasing impacts on velocity profiles, respectively and strongly influence the skin friction. In the no-slip case, there is greater skin friction on the surface of the inner cylinder than in the slip case. We found that a difference in the viscosities slows the velocity of the fluids, but a slippery surface enhances the velocity. Current findings about anisotropic permeability, viscosity ratio, and slip are used to study the flow mechanism in various industrial and engineering problems involving artificial porous materials.