Mathematical modeling rarefied gas flow in a rectangular channel with an inner cylindrical element
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 518-527.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article proposes method of solving the problem of heat and mass transfer in a long rectangular channel with an inner cylindrical element. A rarefied gas flow trough cross section is studied on the basis of kinetic equation in the free molecular. Diffuse reflection model for the boundary condition at the channel walls is used. The expression for the mass flux is obtained as a linear function of a pressure gradient supported in the channel.
Keywords: model of diffuse reflection, kinetic equation, free molecular regime.
@article{SEMR_2017_14_a106,
     author = {O. V. Germider and V. N. Popov},
     title = {Mathematical modeling rarefied gas flow in a rectangular channel with an inner cylindrical element},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {518--527},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a106/}
}
TY  - JOUR
AU  - O. V. Germider
AU  - V. N. Popov
TI  - Mathematical modeling rarefied gas flow in a rectangular channel with an inner cylindrical element
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 518
EP  - 527
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a106/
LA  - ru
ID  - SEMR_2017_14_a106
ER  - 
%0 Journal Article
%A O. V. Germider
%A V. N. Popov
%T Mathematical modeling rarefied gas flow in a rectangular channel with an inner cylindrical element
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 518-527
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a106/
%G ru
%F SEMR_2017_14_a106
O. V. Germider; V. N. Popov. Mathematical modeling rarefied gas flow in a rectangular channel with an inner cylindrical element. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 518-527. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a106/

[1] J. Kim, A. J. H. Frijns, S. V. Nedea, A. A. A. Steenhoven, “Geometry effects on rarefied nanochannel flows”, Microfluid Nanofluid, 15 (2013), 661–673 | DOI

[2] V. A. Titarev, E. M. Shakhov, “Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S-Model”, Computational Mathematics and Mathematical Physics, 50:12 (2010), 2131–2144 | DOI | MR | Zbl

[3] O. V. Germider, V. N. Popov, “Mathematical modeling of heat transfer process in a rectangular channel in the problem of Poiseuille flow”, Siberian Electronic Mathematical Reports, 13 (2016), 1401–1409 | MR

[4] I. Graur, M. T. Ho, “Rarefied gas flow through a long rectangular channel of variable cross section”, Vacuum, 101 (2014), 328–332 | DOI

[5] F. M. Sharipov, “Rarefied gas flow through a long rectangular channel”, J. Vac. Sci. Technol. A, 17:5 (1999), 3062–3066 | DOI

[6] S. Pantazis, S. Varoutis, V. Hauer, C. Day, D. Valougeorgis, “Gas-surface scattering effect on vacuum gas flows through rectangular channels”, Vacuum, 85 (2011), 1161–1164 | DOI

[7] V. A. Titarev, E. M. Shakhov, “Kinetic analysis of the isothermal flow in a long rectangular microchannel”, Computational Mathematics and Mathematical Physics, 50:7 (2010), 1221–1237 | DOI | MR | Zbl

[8] S. Boutebba, W. Kaabar, “Slip flow and heat transfer through a rarefied nitrogen gas between two coaxial cylinders”, J. Chem. Pharm. Res., 8:8 (2016), 495–501

[9] O. V. Germider, V. N. Popov, “Mathematical modelling of the mass transfer process between two coaxial cylinders in the problem of thermal creep”, IOP Conf. Series: Materials Science and Engineering, 158 (2016), 1–7

[10] P. Taheri, H. Struchtrup, “Poiseuille flow of moderately rarefied gases in annular channels”, International Journal of Heat and Mass Transfer, 55 (2012), 1291–1303 | DOI | MR | Zbl

[11] I. Graur, F. Sharipov, “Gas flow through an elliptical tube over the whole range of the gas rarefaction”, European Journal of Mechanics V Fluids, 27 (2008), 335–345 | DOI | MR | Zbl

[12] I. Graur, F. Sharipov, “Non-isothermal flow of rarefied gas through a long pipe with elliptic cross section”, Microfluid Nanofluid, 6 (2009), 267–275 | DOI

[13] O. V. Germider, V. N. Popov, A. A. Yushkanov, “Heat transfer process in an elliptic channel”, Matem. Mod., 29:1 (2017), 84–94

[14] V. A. Rykov, V. A. Titarev, E. M. Shakhov, “Rarefied poiseuille flow in elliptical and rectangular tubes”, Fluid Dyn., 46:3 (2011), 456–466 | DOI | MR | Zbl

[15] O. V. Germider, V. N. Popov, A. A. Yushkanov, “Computation of the heat flux in a cylindrical duct within the framework of the kinetic approach”, J. Eng. Phys. Thermophy, 89:5 (2016), 1338–1343 | DOI

[16] C. E. Siewert, D. Valougeorgis, “An analytical discrete-ordinates solution of the S-model kinetic equations for flow in a cylindrical tube”, J. Quant. Spectrosc. Radiat. Transf., 72 (2002), 531–550 | DOI

[17] C. H. Kamphorst, P. Rodrigues, L. B. Barichello, “A Closed-Form Solution of a Kinetic Integral Equation for Rarefied Gas Flow in a Cylindrical Duct”, Applied Mathematics, 5 (2014), 1516–1527 | DOI

[18] A. V. Proskurin, A. M. Sagalakov, “Modeling Duct Flow by the R-Function Method”, Journal of Applied and Industrial Mathematics, 10:3 (2016), 429–434 | DOI | MR | Zbl

[19] M. N. Kogan, Rarefied gas dynamics. Kinetic theory, Nauka, M., 1967

[20] F. M. Sharipov, V. D. Seleznev, Motion of rarefied gases in channels and microchannels, UrO RAN, Yekaterinburg, 2008

[21] P. Courant, Partial Differential Equations, Mir, M., 1964 | MR | Zbl

[22] J. Bernsten, T. O. Espelid, A. Genz, “Algorithm 698: DCUHRE: an adaptive multidemensional integration routine for a vector of integrals”, ACM Transactions on Mathematical Software (TOMS), 17 (1991), 452–456 | DOI | MR