Z. Naturforsch. **68a,** 635 – 645
(2013)

doi:10.5560/ZNA.2013-0040

Exact Solutions for Unsteady Magnetohydrodynamic Oscillatory Flow of a Maxwell Fluid in a Porous Medium

Ilyas
Khan,
Farhad
Ali,
Samiulhaq, and
Sharidan
Shafie

Department of Mathematical Sciences, Faculty of Science, University of Technology Malaysia, 81310 UTM Skudai, Malaysia

Received December 3, 2012 / revised May 27, 2013 / published online July 17, 2013

In this paper, exact solutions of velocity and stresses are obtained for the magnetohydrodynamic (MHD) flow of a Maxwell fluid in a porous half space by the Laplace transform method. The flows are caused by the cosine and sine oscillations of a plate. The derived steady and transient solutions satisfy the involved differential equations and the given conditions. Graphs for steady-state and transient velocities are plotted and discussed. It is found that for a large value of the time *t*, the transient solutions disappear, and the motion is described by the corresponding steady-state solutions.

*Key words:* Exact Solutions; MHD Flow; Maxwell Fluid; Porous Medium.