Pressure, temperature, and heat flux in high speed lubrication flows of pressurized gases

We present approximate solutions to the compressible Reynolds equation and the corresponding temperature equation which are valid for large speed numbers in the dense and supercritical gas regime. The flows are taken to be two-dimensional, steady, compressible, single-phase and laminar. New results include explicit formulas for pressure, density, temperature, and heat flux in terms of the speed number, film thickness function, and the material functions. We have found that the first correction for finite speed number will depend on the local values of the effective bulk modulus and thermal expansion coefficient. Our approximations are compared to numerical solutions to the exact Reynolds theory. It was found that the first order approximation is necessary to obtain realistic pressure and temperature distributions.