To examine the performance of the rough-porous Rayleigh step slider bearing lubricated with couple stress fluid considering the effect of MHD forms the crux of this article. The bearing surface roughness is assumed to be longitudinal as well as transversal. The expression for longitudinal and transversal roughness are derived by using the stochastic random variable. The modified Darcy's law is used to derive the pressure in the porous region, The space between the slider filled with couple stress fluid. The stochastic Reynolds equation is derived applying the Christensen's stochastic approach. Following this the expression for load carrying capacity, fictional force and coefficient of friction are derived. It is observed that work load and frictional force increases when compared with plate without roughness and porous and decreases for coefficient of friction.

This article examines the performance of squeeze film properties in various finite plates lubricated with couple-stress fluid and subjected to a transverse magnetic field and surface roughness. On the basis of Stokes couple-stress fluid theory and Christensen's stochastic model are used to derive a modified Reynolds equation. The squeeze film pressure and workload were calculated using the resultant equation with boundary conditions. The study found that the bearing systems with surface roughness performed better than those with a smooth surface when a magnetic field was present. Additionally, the presence of viscosity variation resulted in a significant increase in the workload of finite plates compared to nonviscosity variation cases. The study also revealed that the load was reduced in the presence of porosity compared to the non-porous case.