Friction factor correlations of slip flow in micro-tubes

Poiseuille number, the product of friction factor and Reynolds number (f center dot Re) for quasi-fully developed flow in a micro-tube was obtained in slip flow regime. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers with two thermal boundary conditions: CWT (constant wall temperature) and CHF (constant heat flux), respectively. The tube diameter ranges from 3 to 10 mu m and the tube aspect ratio is 200. The stagnation pressure, p(stg) is chosen in such away that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at the atmospheric pressure. In slip flow, Mach and Knudsen numbers are systematically varied to determine their effects on f center dot Re. The correlation for f Re is obtained from numerical results. It was found that f center dot Re is mainly a function of Mach number and Knudsen number and is different from the values obtained by 64/(1+8Kn) for slow flow. The obtained f center dot Re correlations are applicable to both no-slip and slip flow regimes.