A constant wall temperature microbearing gas flow

Abstract

A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained.

Keywords

• microbearing
• non-isothermal
• slip flow
• inertia
• analytical solution
• low mach number
• high reynolds number