Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 87814, 14 pages
Research Article

Some New Parallel Flows in Weakly Conducting Fluids with an Exponentially Decaying Lorentz Force

Asterios Pantokratoras

School of Engineering, Democritus University of Thrace, Xanthi 67100, Greece

Received 8 March 2007; Revised 27 May 2007; Accepted 19 September 2007

Academic Editor: Mehrdad Massoudi

Copyright © 2007 Asterios Pantokratoras. 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.


We investigate the fully developed flow between two parallel plates and the film flow over a plate in an electrically conducting fluid under the action of a parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low-fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. Exact analytical solutions are derived for velocity, flow rate, and wall shear stress at the plates. The velocity results are presented in figures. All these flows are new and are presented for the first time in the literature.