Porous journal bearings are broadly used in numerous industrial applications such as jet engine manufacturers, compressors and turbines. The most important advantage of these sorts of bearings is that they need no exterior oil supply. Low friction factor makes them very desirable in industry. Many investigations are carried out in this field based on Darcy's law using Newtonian lubricant. This work investigates numerically the viscous shear effects on finite porous elastic journal bearings lubricated with non-Newtonian couple stress fluid.

Based on Stokes micro-continuum mechanics, and considering bearing elastic deformation determined by Winkler model, an elastohydrodynamic modified Reynolds equation type is derived. The porous bearing flow is described by the complete Darcy-Brinkman model including viscous shearing forces. The film and porous governing equations are coupled at the porous elastic interface by the continuity of pressure, velocities and viscous shear stresses. As this fluid-porous bearing interaction problem necessitates numerical solution, the equations are discretized employing finite differences, and the successive over-relaxation scheme is used to solve iteratively the obtained algebraic equations. The fixed-point technique is advocated to solve sequentially this coupled problem. To show the viscous shear effects, bearing characteristics including load capacity and friction factor are compared to those obtained from Darcy model with Beavers-Joseph slip conditions, and discussed for different couple stress values, permeabilities and elastic deformation parameters.