A scaling parameter for pressure losses and thermal effects in lubricant flows with viscous dissipation

The shearing of compressible fluids in a channel with parallel walls is studied to understand the impact of viscous dissipation and thermodynamics in thin lubricant films. Numerical simulations based on the compressible Navier-Stokes equations and Reynolds equation, both coupled with the energy equation, are performed for a lubricant oil. Particular attention is paid to the resulting pressure losses in the plane channel. It is shown that viscous effects, that alter the classical Couette velocity profile towards a Couette-Poiseuille one, scale with the parameter ξ=μ0Ul/(h2Pref), and that the pressure losses are proportional to the square of ξ.