MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2004; 27:477–496 (DOI: 10.1002/mma.469) MOS subject classication: 76 A 05 Hydromagnetic rotating ow of a fourth-order uid past a porous plate Yongqi Wang 1; ∗; † and Tasawar Hayat 2 1 Institute of Mechanics; Darmstadt University of Technology; Hochschulstrasse 1; 64289 Darmstadt; Germany 2 Mathematics Department; Quaid-i-Azam University; Islamabad 45320; Pakistan Communicated by B. Straughan SUMMARY The rotating ow in the presence of a magnetic eld is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non-linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating ow of a fourth- order uid past a porous plate. The steady ow is governed by a boundary value problem in which the order of dierential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at innity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Eects of uniform suction or blowing past the porous plate, exerted magnetic eld and rotation on the ow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The ow behaviours of the Newtonian uid and second-, third- and fourth-order non-Newtonian uids are compared for the special ow problem, respectively. Copyright ? 2004 John Wiley & Sons, Ltd. KEY WORDS: fourth-order uid; non-Newtonian uid; hydromagnetic rotating ow 1. INTRODUCTION Rotation plays a signicant role in several important phenomenon in cosmical uid dynamics. Similarly, a great deal of meteorology depends upon the dynamics of a revolving uid. The large and moderate scale motions of the atmosphere are greatly aected by the vorticity of the earth’s rotation. In the case of an innitely extending liquid, rotating as a rigid body about an axis, the amount of energy possessed by the liquid is innitely large and it is of great interest to know how small disturbances propagate in such a liquid. The study of motions in a rotating and= or stratied conducting uid in the presence of a magnetic eld has greatly increased mainly due to the abundant applications in cosmical and geophysical uid dynamics. The order of magnitude analysis shows that the Coriolis force is very signicant as compared to the inertial and viscous forces involved in the basic eld ∗ Correspondence to: Yongqi Wang, Institute of Mechanics, Darmstadt University of Technology, Hochschulstrasse 1, 64289 Darmstadt, Germany. † E-mail: wang@mechanik.tu-darmstadt.de Copyright ? 2004 John Wiley & Sons, Ltd. Received 14 April 2003