THE STUDY BASED ON THE CONTINUUM MODEL FOR THE MICRO-SCALE POISEUILLE FLOW

In this paper, the planar microchannel force-driven Poiseuille flow was analyzed by using the gas kinetic theory and the macroscopic continuous flow theory, respectively. In the kinetic theory, the direct simulation Monte Carlo (DSMC) method was used where the body force was a substitute for the pressure gradient in order to ignore the length effect of the channel. In the continuous flow theory, the Burnett and super-Burnett constitutive relations were adopted and nonlinear ordinary differential equations of higher-orders were obtained by the hypothesis of parallel flow. Then, the equations were solved by Runge-Kutta method with the necessary boundary conditions. It was shown that the pressure distribution predicted by the high order continuous model could agree very well with that by DSMC even when the flow was in the transition region. And deviation of the velocity would exist near the wall when the Knudsen number is larger than 0.2. The temperature dip can not be obtained by Burnett model what will revert to the Navier-Stokes model for temperature distribution. The super-Burnett model can capture the temperature dip, similar to the DSMC result, while the temperature profile near the wall is quite different from the DSMC result. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model.