Numerical method for predicting three-dimensional steady compressible flow in long microchannels

Numerical results available in the literature for microchannel flow are either for incompressible flow or for two-dimensional compressible flow. Three-dimensional simulations are limited to very short channels due to the long computational time and large memory required. This study develops an efficient three-dimensional numerical procedure to calculate steady compressible flow in long microchannels, which has not previously been reported in the literature. The proposed numerical procedure solves the reduced compressible Navier-Stokes equations, which do not model the entrance region accurately, but this region is small for the long microchannels studied in this paper. The major advantage of the present numerical procedure is its fast speed due to the parabolic character of the governing equations. An efficient space marching algorithm is adopted to solve the governing equations. It is at least two to three orders of magnitude faster than the full Navier-Stokes simulation. This is because the unsteady Navier-Stokes equations are a mixed set of hyperbolic-parabolic equations that are integrated in time until a steady state solution is reached. This procedure is inefficient because of its time marching procedure. The calculated mass flow rate and pressure distribution were compared with a known analytical solution for a two-dimensional microchannel flow and experimental data. The agreement was very good. The slip effect plays an important role in the friction characteristic of microchannel flows. This effect was investigated for three-dimensional microchannel flows. The effect of channel aspect ratio on the friction characteristic was also studied. The present numerical procedure is an efficient and accurate tool in studying steady compressible flow in long microchannels.