Journal of Applied Mathematics
Volume 2012 (2012), Article ID 869357, 12 pages
Research Article

Unsteady Unidirectional MHD Flow of Voigt Fluids Moving between Two Parallel Surfaces for Variable Volume Flow Rates

Department of Mechanical Engineering, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan

Received 21 March 2012; Accepted 15 May 2012

Academic Editor: Chein-Shan Liu

Copyright © 2012 Wei-Fan Chen 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.


The velocity profile and pressure gradient of an unsteady state unidirectional MHD flow of Voigt fluids moving between two parallel surfaces under magnetic field effects are solved by the Laplace transform method. The flow motion between parallel surfaces is induced by a prescribed inlet volume flow rate that varies with time. Four cases of different inlet volume flow rates are considered in this study including (1) constant acceleration piston motion, (2) suddenly started flow, (3) linear acceleration piston motion, and (4) oscillatory piston motion. The solution for each case is elaborately derived, and the results of associated velocity profile and pressure gradients are presented in analytical forms.