Porous and Magnetic Effects on Axial Couette Flows of Second Grade Fluids in Cylindrical Domains

Axial Couette flows of electrically conducting incompressible second grade fluids are analytically and numerically investigated through a porous medium in the presence of a constant magnetic field. General exact analytical expressions are derived for the dimensionless velocities corresponding to unidirectional unsteady motions in an infinite circular cylinder and between two infinite coaxial circular cylinders. They can be immediately particularized to give similar results for Newtonian fluids in same flows. Exact expressions for steady velocities of a large class of flows were provided. Due to the generality of boundary conditions the problems in discussion are completely solved. For illustration, some case studies with engineering applications are considered and the corresponding velocity fields are provided. Their correctness is graphically proved. It was also proved that the fluid flows slower and the steady state is rather touched in the presence of a magnetic field or porous medium. Moreover, the steady state is rather touched in the case of the motions between circular coaxial cylinders as compared with same motions in an infinite circular cylinder.