Mathematical Problems in Engineering
Volume 2003 (2003), Issue 2, Pages 47-64

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

Tasawar Hayat1 and Yongqi Wang2

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.


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.