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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 7, Pages 1285–1302 (Mi zvmmf4909)  

This article is cited in 23 scientific papers (total in 23 papers)

Kinetic analysis of an isothermal flow in a long microchannel with rectangular cross section

V. A. Titareva, E. M. Shakhovb

a Cranfild University, Cranfild, UK, MK43OAL
b Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 107005 Russia

Abstract: The linearized kinetic BGK model is used to study the steady Poiseuille flow of a rarefied gas in a long channel of rectangular cross section. The solution is constructed using the finite-volume method based on a TVD scheme. The basic computed characteristic is the mass flow rate through the channel. The effect of the relative width of the cross section is examined, and the difference of the solution from the one-dimensional flow between infinite parallel plates is analyzed. The numerical solution is compared to available results and to the analytical solution of the Navier–Stokes equations with no-slip and slip boundary conditions. The limits of applicability of the hydrodynamic solution are established depending on the degree of rarefaction of the flow and on the ratio of the side lengths of the channel cross section.

Key words: linearized kinetic equation, BGK model, finite-volume TVD method, gas channel flow.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:7, 1221–1237

Bibliographic databases:

UDC: 519.634
Received: 14.12.2009

Citation: V. A. Titarev, E. M. Shakhov, “Kinetic analysis of an isothermal flow in a long microchannel with rectangular cross section”, Zh. Vychisl. Mat. Mat. Fiz., 50:7 (2010), 1285–1302; Comput. Math. Math. Phys., 50:7 (2010), 1221–1237

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rykov V.A., Titarev V.A., Shakhov E.M., “Rarefied Poiseuille flow in elliptical and rectangular tubes”, Fluid Dynamics, 46:3 (2011), 456–466  crossref  mathscinet  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    2. Graur I., Ho M.T., “Rarefied Gas Flow Through a Long Rectangular Channel of Variable Cross Section”, Vacuum, 101:SI (2014), 328–332  crossref  adsnasa  isi  elib  scopus
    3. Yovanovich M.M., Khan W.A., “Similarities of Rarefied Gas Flows in Elliptical and Rectangular Microducts”, Int. J. Heat Mass Transf., 93 (2016), 629–636  crossref  isi  elib  scopus
    4. Germider O.V., Popov V.N., Yushkanov A.A., “Computation of the Heat Flux in a Cylindrical Duct Within the Framework of the Kinetic Approach”, J. Eng. Phys. Thermophys., 89:5 (2016), 1338–1343  crossref  isi  scopus
    5. Germider O.V., Popov V.N., Yushkanov A.A., “Computation of the gas mass and heat fluxes in a rectangular channel in the free molecular regime”, Tech. Phys., 61:6 (2016), 835–840  crossref  isi  elib  scopus
    6. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie protsessa perenosa tepla v pryamougolnom kanale v zadache o techenii Puazeilya”, Sib. elektron. matem. izv., 13 (2016), 1401–1409  mathnet  crossref
    7. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie protsessa perenosa tepla v pryamougolnom kanale v zavisimosti ot chisla Knudsena”, Zhurnal SVMO, 18:2 (2016), 85–93  mathnet  elib
    8. O. Germider, V. N. Popov, A. A. Yushkanov, “Heat transfer process in an elliptic channel”, Math. Models Comput. Simul., 9:4 (2017), 521–528  mathnet  crossref  elib
    9. Germider O.V. Popov V.N. Yushkanov A.A., “Mathematical simulation of heat transfer in an elliptic channel under the action of a pressure gradient”, Tech. Phys., 62:3 (2017), 355–358  crossref  mathscinet  isi  scopus
    10. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie techeniya razrezhennogo gaza v pryamougolnom kanale s vnutrennim tsilindricheskim elementom”, Sib. elektron. matem. izv., 14 (2017), 518–527  mathnet  crossref
    11. O. V. Germider, V. N. Popov, A. A. Yushkanov, “Mathematical modeling of transfer processes in an elliptical channel in the free molecular regime”, J. Appl. Industr. Math., 11:3 (2017), 347–353  mathnet  crossref  crossref  elib
    12. Germider O.V., Popov V.N., “Mathematical Simulation of Heat and Mass Transfer in a Cylindrical Channel Versus the Tangential Momentum Accommodation Coefficient”, Tech. Phys., 62:11 (2017), 1605–1610  crossref  isi  scopus
    13. Germider O.V. Popov V.N. Yushkanov A.A., “Analytical Solution of the Problem of Heat Transfer in Rarefied Gas Between Two Coaxial Cylinders”, J. Appl. Mech. Tech. Phys., 58:2 (2017), 285–290  crossref  mathscinet  zmath  isi  scopus
    14. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie protsessa perenosa massy v pryamougolnom kanale v zadache o teplovom kripe”, Sib. zhurn. chist. i prikl. matem., 17:4 (2017), 39–48  mathnet  crossref
    15. O. V. Germider, V. N. Popov, “Transport processes at part accommodation by the walls of a rectangular channel”, Math. Models Comput. Simul., 10:4 (2018), 512–518  mathnet  crossref  elib
    16. Guevel Y., Allain T., Girault G., Cadou J.M., “Numerical Bifurcation Analysis For 3-Dimensional Sudden Expansion Fluid Dynamic Problem”, Int. J. Numer. Methods Fluids, 87:1 (2018), 1–26  crossref  mathscinet  isi  scopus
    17. Huck Ch., Pleskun H., Bruemmer A., “Measurement and Simulation of Rarefied Couette Poiseuille Flow With Variable Cross Section”, J. Vac. Sci. Technol. A, 36:3 (2018), 031606  crossref  mathscinet  isi  scopus
    18. Duan Zh., He B., “Further Study on Second-Order Slip Flow Models in Channels of Various Cross Sections”, Heat Transf. Eng., 39:11 (2018), 933–945  crossref  isi  scopus
    19. O. V. Germider, V. N. Popov, A. A. Yushkanov, “Matematicheskoe modelirovanie protsessov perenosa tepla i massy gaza v pryamougolnom kanale v zavisimosti ot koeffitsienta akkomodatsii tangentsialnogo impulsa”, Sib. elektron. matem. izv., 15 (2018), 1011–1023  mathnet  crossref
    20. O. V. Germider, V. N. Popov, “Solution of the linearized problem of heat and gas mass transfer in the gap between two cylindrical surfaces under a longitudinal temperature gradient”, Comput. Math. Math. Phys., 58:10 (2018), 1610–1619  mathnet  crossref  crossref  isi  elib
    21. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie protsessov perenosa v tsilindricheskom kanale”, Zhurnal SVMO, 20:1 (2018), 64–77  mathnet  crossref  elib
    22. Germider V O. Popov V.N., “Nonisothermal Free-Molecular Flow of Gas in An Elliptic Channel With a Circular Cylindrical Element Inside”, Tech. Phys., 64:1 (2019), 19–23  crossref  isi
    23. O. V. Germider, V. N. Popov, “Metod kollokatsii i ego primenenie dlya resheniya linearizovannogo uravneniya Kholveya”, Matem. modelirovanie, 32:9 (2020), 3–19  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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