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

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.