Stochastic reynolds equation for magnetohydrodynamics micropolar fluid and surface roughness in squeeze-film lubrication characteristics of rough parallel rectangular plates

This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.