Numerical Solution of the MHD Reynolds Equation for Squeeze-Film Lubrication between Porous and Rough Rectangular Plates

Abstract

The present theoretical study investigates the effects of surface roughness and couple-stress fluid between two rectangular plates, of which an upper rough plate has a roughness structure and the lower plate has a porous material in the presence of transverse magnetic field. The lubricant in the gap is taken to be a viscous, incompressible, and electrically conducting couple-stress fluid. This gap is separated by a film thickness H which is made up of nominal smooth part and rough part. The modified Reynolds equation in the film region is derived for one-dimensional longitudinal roughness structure and solved numerically using multigrid method. The numerical results for various physical parameters are discussed in terms of pressure distribution, load capacity, and squeeze film time of the bearing surfaces. Our results show that, the pressure distribution, load capacity and squeeze film time are predominant for larger values of Hartman number and roughness parameter, and for smaller values of couple-stress parameters when compared to their corresponding classical cases.

Modified Reynolds Equation for Different Types of Finite Plates with the Combined Effect of MHD and Couple Stresses

“…Many researchers have applied the hydromagnetic flow model and Stokes couple stress model to engineering problems. For example, Lin, et al (22), Naduvinamani, et al (23), and Ramesh Kudenatti, et al (24) have shown that the effect of applied magnetic field is more significant in increasing the load-carrying capacity and squeeze film time. Fathima,et al (25) have studied the combined effects of couple stresses and magnetic field in anisotropic plates.…”