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. 1. Introduction Magnetohydrodynamic (MHD) flow of a fluid in squeeze-film lubrication is of interest, because it prevents the unexpected variation of lubricant viscosity with temperature under severe operating conditions. The effects of magnetic field in squeeze lubrication have been encouraging because magnetic field has important applications in the industry with obvious relevance to technology-based world. The MHD lubrication in an externally pressurized thrust bearing has been investigated both theoretically and experimentally by Maki et al. [1]. Limited studies of MHD lubrication are available in the literature which includes MHD slider bearings [2, 3], MHD journal bearings [4, 5], and MHD squeeze film bearings [6]. Hamza [7] has shown the effects of MHD on a fluid film squeezed between two rotating surfaces. Bujurke and Kudenatti [8] have theoretically explored the effect of rough on electrically conducting fluid between two rectangular plates, in which an upper plate has a roughness structure. They modified the classical Reynolds equation to include the effects of roughness and magnetic field and solved it using a multigrid method. They showed that the effect of roughness and Hartmann number is to increase the pressure distribution and hence the load carrying capacity for increasing roughness and magnetic parameters. Self-lubricating porous bearings have been studyied in the last few decades because of their industrial applications and machine manufacturing. These bearings have
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