Abstract
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.