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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1859693, 19 pages
https://doi.org/10.1155/2017/1859693
Research Article

Magnetohydrodynamic Three-Dimensional Couette Flow of a Maxwell Fluid with Periodic Injection/Suction

1Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad, Pakistan
2COMSATS Institute of Information Technology, Kamra Road, Attock 43600, Pakistan

Correspondence should be addressed to Y. Ali; moc.liamg@5risayr

Received 26 December 2016; Accepted 14 March 2017; Published 13 April 2017

Academic Editor: Eusebio Valero

Copyright © 2017 Y. Ali et al. 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

A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible Maxwell fluid is developed and analyzed theoretically. The application of transverse sinusoidal injection at the lower stationary plate and its equivalent removal by suction through the uniformly moving upper plate lead to three-dimensional flow. Approximate solutions for velocity field, pressure, and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, and the Deborah number on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to control the skin friction component along the main flow direction.