Magnetohydrodynamic flow due to noncoaxial rotations of a porous disk and a fourth-grade fluid at infinity

The governing equations for the unsteady flow of a uniformly conducting incompressible fourth-grade fluid due to noncoaxial rotations of a porous disk and the fluid at infinity are constructed. The steady flow of the fourth-grade fluid subjected to a magnetic field with suction/blowing through the disk is studied. The nonlinear ordinary differential equations resulting from the balance of momentum and mass are discretised by a finite-difference method and numerically solved by means of an iteration method in which, by a coordinate transformation, the semi-infinite physical domain is converted to a finite calculation domain. In order to solve the fourth-order nonlinear differential equations, asymptotic boundary conditions at infinity are augmented. The manner in which various material parameters affect the structure of the boundary layer is delineated. It is found that the suction through the disk and the magnetic field tend to thin the boundary layer near the disk for both the Newtonian fluid and the fourth-grade fluid, while the blowing causes a thickening of the boundary layer with the exception of the fourth-grade fluid under strong blowing. With the increase of the higher-order viscosities, the boundary layer has the tendency of thickening.