Numerical Modeling of Gas Flow in Square Microchannels

In this paper, nitrogen gas flow in long microchannels with square cross section is simulated numerically with a three-dimensional continuum model. The governing equations of the model are solved by a control volume method. Numerical results are verified with analytical solutions for the range of hydraulic diameters investigated at constant L/D_h ratio of 1000 and pressure ratio of 1.0001. As the pressure ratio is small and therefore the compressibility effect is negligible in this study. A parametric study is conducted at the same L/D_h and pressure ratio. By reducing the hydraulic diameter down from 10000 μm to 0.01 μm, the gas flow inside the microchannels switches from continuum to free molecular flows. The no-slip flow simulation results provide a constant fRe = 54.8, which is very close to the analytical result of fRe = 57. Slip flow condition reduces the friction factor and starts to drop fRe at D_h = 60 μm in the continuum regime.