Poiseuille number, the product of friction factor and Reynolds number (f·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 10μm and the tube aspect ratio is 200. The stagnation pressure, pstg 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·Re. The correlation for f·Re is obtained from numerical results. It was found that f·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·Re correlations are applicable to both no-slip and slip flow regimes.
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Friction Factor Correlations of Slip Flow in Micro-Tubes
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Hong, C, Asako, Y, & Faghri, M. "Friction Factor Correlations of Slip Flow in Micro-Tubes." Proceedings of the ASME 2007 5th International Conference on Nanochannels, Microchannels, and Minichannels. ASME 5th International Conference on Nanochannels, Microchannels, and Minichannels. Puebla, Mexico. June 18–20, 2007. pp. 365-372. ASME. https://doi.org/10.1115/ICNMM2007-30064
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