Numerical Investigation of Combined Effects of Rarefaction and Compressibility for Gas Flow in Microchannels and Microtubes

In this paper, first, the Navier–Stokes equations for incompressible fully developed flow in microchannels and microtubes with the first-order and second-order slip boundary conditions are analytically solved. Then, the compressible Navier–Stokes equations are numerically solved with slip boundary conditions. The numerical methodology is based on the control volume scheme. Numerical results reveal that the compressibility effect increases the velocity gradient near the wall and the friction factor. On the other hand, the increment of velocity gradient near the wall leads to a much larger slip velocity than that for incompressible flow with the same value of Knudsen number and results in a corresponding decrement of friction factor. General correlations for the Poiseuille number $(fRe)$⁠, the Knudsen number (Kn), and the Mach number (Ma) containing the first-order and second-order slip coefficients are proposed. Correlations are validated with available experimental and numerical results.