Mathematical Problems in Engineering
Volume 2003 (2003), Issue 2, Pages 47-64
doi:10.1155/S1024123X03308026
Magnetohydrodynamic flow due to noncoaxial rotations of a
porous disk and a fourth-grade fluid at infinity
1Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2Institute of Mechanics, Darmstadt University of Technology, Hochschulstrasse 1, Darmstadt 64289, Germany
Received 24 October 2002
Copyright © 2003 Tasawar Hayat and Yongqi Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.