Journal
JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME
Volume 131, Issue 10, Pages -Publisher
ASME
DOI: 10.1115/1.3215941
Keywords
compressible flow; friction; Knudsen flow; Mach number; microchannel flow; Navier-Stokes equations; pipe flow; Poiseuille flow; slip flow
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Funding
- National Natural Science Foundation of China [50376050]
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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.
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