Reynolds Equation for a Micro-Scale Lubrication of a Gas Between Eccentric Circular Cylinders with an Arbitrary Temperature Difference Based on Slip-Flow Theory

Micro-scale lubrication flow of a gas between eccentric circular cylinders with an arbitrary temperature difference is studied on the basis of the Navier–Stokes set of equations and the velocity slip and temperature jump boundary conditions. The dimensionless curvature, which is defined as the mean clearance divided by the radius of the inner cylinder, is small, the Knudsen number and the Reynolds number based on the mean clearance are small, and the temperature ratio is arbitrary. The Reynolds-type lubrication equation is derived analytically. For a verification of the equation, an assessment is conducted against the solution of the direct numerical analysis of the Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation in the author’s previous work [Doi, T. Phys. Fluids 2024, 36, 042016]. The solution of the lubrication equation agrees with that of the Boltzmann equation satisfactorily well over the slip flow regime, not only in the eccentric force and the torque but also in the local distribution of the temperature, flow velocity, and the normal stress. A superiority of the lubrication equation over the lubrication model proposed in the author’s previous work is also discussed.