Nonisothermal oscillatory cylindrical Couette gas flow in the slip regime: A computational study

Abstract

The oscillatory Couette flow between a stationary inner cylinder and an oscillating outer cylinder or a stationary outer cylinder and an oscillating inner cylinder is numerically investigated by using a continuum model with temperature-dependent transport coefficients based on the Navier–Stokes equations for compressible fluid, completed with the equations of continuity and energy transport. The first order velocity-slip boundary conditions, imposed at the outer cylinder wall, are linked to two types of motion of the outer cylinder—harmonic oscillations and stepwise oscillations. The first order slip conditions are also imposed at the inner cylinder combined with two types of energy transfer at the gas–wall interface. The first one is related to a constant wall temperature and the second one to an adiabatically isolated cylinder. Thus, the capabilities of model and numerical solution are extended to some cases, which might be important from a practical viewpoint. Calculated results for density, velocity, pressure and temperature variation are presented. The spectral characteristics of the gas flow oscillations in some interesting cases are analyzed. The numerical calculations for the case of harmonically oscillating inner cylinder are compared with the available analytical solution for incompressible viscous fluid and Direct Simulation Monte Carlo (DSMC) data. It is shown that for low speed oscillations the model of compressible viscous gas gives almost equivalent to incompressible fluid model solution for the macroscopic velocity profiles. At the same time noticeable temperature variations in the gas flow are observed that should be taken into consideration when the heat transfer in such a microfluidic system is analyzed. The presented results are interesting when non-planar microfluidic problems are considered.