×

Rarefied gas flow rate in Poiseuille flow through a circular capillary. (English. Russian original) Zbl 1333.76067

Fluid Dyn. 50, No. 5, 711-720 (2015); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2015, No. 5, 130-140 (2015).
Summary: The gas flow rate in slow isothermal Poiseuille flow through an infinitely long capillary with circular cross-section is determined as a function of the rarefaction parameter (inverse Knudsen number). An asymptotic expansion of the flow rate in a small inverse Knudsen number is obtained on the basis of a linearized model kinetic BGK equation.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] F.M. Sharipov and V.D. Seleznev, Channel and Microchannel Rarefied Gas Flows (Ural Branch of the RAS, Ekanerinburg, 2008) [in Russian].
[2] Sharipov, F.; Seleznev, V., Data on internal rarefied gas flows, J. Phys. Chem. Ref. Data, 27, 657-706, (1998)
[3] Cercignani, C.; Sernagiotto, F., Cylindrical Poiseuille flow of a rarefied gas, Phys. Fluids, 9, 40-44, (1966)
[4] Ferziger, J.H., Flow of a rarefied gas through a cylindrical tube, Phys. Fluids, 10, 1448-1453, (1967) · Zbl 0149.44601
[5] Sone, Y.; Yamamoto, K., Flow of rarefied gas through a circular pipe, Phys. Fluids, 11, 1672-1678, (1968) · Zbl 0182.28506
[6] Lo, S.S.; Loyalka, S.K., An efficient computation of near-continuum rarefied gas flows, J. Appl. Math. Phys. (ZAMP), 33, 419-424, (1982) · Zbl 0496.76070
[7] Lang, H.; Loyalka, S.K., Some analytical results for thermal transpiration and the mechanocaloric effect in a cylindrical tube, Phys. Fluids, 27, 1616-1619, (1984) · Zbl 0547.76087
[8] Valougeorgis, D.; Thomas, J.R., Exact numerical results for Poiseuille and thermal creep flow in a cylindrical tube, Phys. Fluids, 29, 423-429, (1986) · Zbl 0592.76110
[9] Graur, I.; Sharipov, F., Gas flow through an elliptical tube over the whole range of the gas rarefaction, Eur. J. Mech. B/Fluid, 27, 335-345, (2008) · Zbl 1154.76376
[10] Rykov, V.A.; Titarev, V.A.; Shakhov, E.M., Rarefied Poiseuille flow through a pipe of elliptic or rectangular cross-section, Fluid Dynamics, 46, 132-144, (2011) · Zbl 1235.76137
[11] Loyalka, S.K.; Hamoodi, S.A., Poiseuille flow of a rarefied gas in a cylindrical tube: solution of linearized Boltzmann equation, Phys. Fluids A, 3, 2825, (1991) · Zbl 0713.76089
[12] Knudsen, M., Die gesetze der molekularströmung und der inneren reibungsströmung der gase durch Röhren, Ann. Phys., 333, 75-130, (1909) · JFM 40.0825.02
[13] Sharipov, F.; Graur, I., General approach to transient flows of rarefied gases through long capillaries, Vacuum, 100, 22-25, (2014)
[14] Graur, I.; Sharipov, F., Non-isothermal flow of rarefied gas through a long pipe with elliptic cross section, Microfluid Nanofluid, 6, 267-275, (2009)
[15] Zhvick, V.V.; Friedlander, O.G., Poiseuille flow in a capillary at all regimes of rarefied gas flows, AIP Conf. Proc., 1501, 830-836, (2012)
[16] M. Abramovitz and I.A. Stegun, Handbook of Mathematical Functions (N.Y., Dover Publications, 1972; Nauka, Moscow, 1979).
[17] Wakabayashi, M.; Ohwada, T.; Golse, F., Numerical analysis of the shear and thermal creep flows of a rarefied gas over the planewall of a Maxwell-type boundary on the basis of the linearized Boltzmann equation for hard-sphere molecules, Eur. J. Mech. B/Fluids, 15, 175-201, (1996) · Zbl 0866.76078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.