Gas flow in micro-channels using a boundary-layer approach

The present work numerically studies gaseous flow in micro-channels. The working fluids are nitrogen and helium. The proposed model assumes the fluid is a continuum but employs a slip boundary condition on the channel wall. Although slip flow in micro-channels can be investigated by solving numerically the compressible Navier-Stokes equations, as was done previously by several investigators, the hyperbolic-parabolic character of the equations makes it very inefficient. The results of present work show that they can be predicted accurately by solving the compressible boundary-layer equations. The parabolic character of the boundary-layer equations renders the present method a very efficient and accurate tool in studying slip flows. The results also demonstrate that diffusion is the dominant mechanism in momentum and energy transfers in micro-channel flows. The slip boundary condition is the result of rarefaction, which is due to the incomplete momentum and energy exchanges between gas molecules and the walls. The results show that the slip condition has decisive effects on the velocity and mass flow rate of the flow and has to be taken into account.