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Mathematical Problems in Engineering
Volume 2013, Article ID 915781, 8 pages
Research Article

Numerical Study of Surface Roughness and Magnetic Field between Rough and Porous Rectangular Plates

1Department of Mathematics, Bangalore University, Bangalore 560001, India
2Department of Mathematics, JSSATE, Bangalore 560060, India
3Department of Mathematics, MSRIT, Bangalore 560054, India

Received 25 July 2013; Revised 30 October 2013; Accepted 31 October 2013

Academic Editor: Jun Jiang

Copyright © 2013 Ramesh B. Kudenatti 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.


This paper theoretically examines the combined effects of surface roughness and magnetic field between two rectangular parallel plates of which the upper plate has roughness structure and the lower plate has porous material in the presence of transverse magnetic field. The lubricating fluid in the film region is assumed to be Newtonian fluid (linearly viscous and incompressible fluid). This model consists of mathematical formulation of the problem with appropriate boundary conditions and solution numerically by finite difference based multigrid method. The generalized average modified Reynolds equation is derived for longitudinal roughness using Christensen’s stochastic theory which assumes that the height of the roughness asperity is of the same order as the mean separation between the plates. We obtain the bearing characteristics such as pressure distribution and load carrying capacity for various values of roughness, Hartmann number, and permeability parameters. It is observed that the pressure distribution and load carrying capacity were found to be more pronounced for increasing values of roughness parameter and Hartmann number; whereas these are found to be decreasing for increasing permeability compared to their corresponding classical cases. The physical reasons for these characters are discussed in detail.