Slip flow in the hydrodynamic entrance region of microchannels

This paper is aimed at investigating the hydrodynamic entrance region of microchannels, within the slip flow regime, for gaseous flows. Rarefaction effects, characterized by Knudsen number in the range 0.001 – 0.1, are determined in the hydrodynamic entry region, in laminar flow, for rectangular microchannels with different values of aspect ratio. The numerical results are obtained by a solver based on finite element method. The system of differential equations (continuity and Navier Stokes) in a 3-D rectangular domain, are solved with first order slip boundary conditions. Pressure and velocity profiles are presented in some graphs, and the main physical parameters for the entry region are calculated (apparent friction factor or apparent Poiseuille number Poapp, incremental pressure drop number or Hagenbach’s factor K(∞) , momentum flux correction factor Kd , kinetic energy correction factor Ke). The developing numbers Poapp, Kd , Ke are presented in some Tables, as a function of the longitudinal coordinate, in the entrance region. The numerical results are validated with available solutions in literature. Friction factors are found to be decreasing with increasing Knudsen number; the reduction in friction is more pronounced for small aspect ratios, proving that friction coefficients are less sensitive to rarefaction effects in corner-dominated flows (as in square channels). The results may be useful to predict pressure drop in microchannels with rectangular cross section, produced by microfabrication or chemical etching in silicon wafers for micro-electro-mechanical systems (MEMS).