Friction Factor Correlations for Gas Flow in Slip Flow Regime

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure $pstg$ is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on $fRe$⁠. The correlation for $fRe$ for the slip flow is obtained from that of $fRe$ of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that $fRe$ is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.