Rarefaction effects in thermally-driven microflows

Physica A: Statistical Mechanics and its Applications

Volumn 389, Issue 16, 2010, Pages 3069-3080

  Taheri, Peyman ^a   Struchtrup, Henning ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Grad's moment method; Kinetic theory of gases; Knudsen boundary layers; Rarefied gas flow; Thermal creep flow; Thermal transpiration flow

Indexed keywords

BOUNDARY LAYERS; CREEP; FLOW OF GASES; KINETIC THEORY OF GASES; LINEARIZATION; METHOD OF MOMENTS;

GRAD'S MOMENT METHODS; KNUDSEN; RAREFIED GAS FLOW; THERMAL CREEP FLOW; THERMAL TRANSPIRATION;

GASES;

EID: 77953319317     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2010.03.050     Document Type: Article

References (37)

1. Sone Y. Kinetic Theory and Fluid Dynamics (2002), Birkhäuser, Boston
2. Reynolds O. Experimental researches on thermal transpiration of gases through porous plates and on the law of transpiration and impulsion. Philos. Trans. R. Soc. Lon. 170 (1879) 727
3. Maxwell C. On stress in rarefied gases arising from inequalities of temperature. Philos. Trans. R. Soc. Lon. 170 (1879) 231
4. Knudsen M. Eine Revision der Gleichgewichtsbedingung der Gase. Thermische Molekularströmung. Ann. Phys. 31 (1910) 205-229
5. Knudsen M. Thermischer Molekulardruck der Gase in Röhren. Ann. Phys. 33 (1910) 1435
6. Sone Y., Waniguchi Y., and Aoki K. One-way flow of a rarefied gas induced in a channel with a periodic temperature distribution. Phys. Fluids 8 (1996) 227
7. Han Y.-L., Muntz E.P., Alexeenko A., and Young M. Experimental and computational studies of temperature gradient-driven molecular transport in gas flows through nano/microscale channels. Nano. Microscale Thermophys. Eng. 11 (2007) 151
8. Sharipov F., and Seleznev V. Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 3 (1998) 657-706
9. Loyalka S.K. Kinetic theory of thermal transpiration and mechanocaloric effect. i. J. Chem. Phys. 55 9 (1971) 4497-4503
10. Loyalka S.K. Comments on Poiseuille flow and thermal creep of a rarefied gas between parallel plates. Phys. Fluids 17 (1974) 1053
11. Loyalka S.K. Kinetic theory of thermal transpiration and mechanocaloric effect. ii. J. Chem. Phys. 63 9 (1975) 4054-4060
12. Loyalka S.K., Petrellis N., and Storvick T.S. Some exact numerical results for the BGK model: Couette, Poiseuille and thermal creep flow between parallel plates. J. Appl. Math. Phys. (ZAMP) 30 (1979) 514-521
13. Barichello L.B., Camargo M., Rodrigues P., and Siewert C.E. Unified solutions to classical flow problems based on the BGK model. J. Appl. Math. Phys. (ZAMP) 52 (2001) 517-534
14. Ohwada T., Sone Y., and Aoki K. Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules. Phys. Fluids A 1 (1989) 2042
15. Loyalka S.K., and Hickey K.A. Kinetic theory of thermal transpiration and the mechanocaloric effect: planar flow of a rigid sphere gas with arbitrary accommodation at the surface. J. Vac. Sci. Technol. A 9 (1991) 158-163
16. Struchtrup H. Macroscopic Transport Equations for Rarefied Gas Flows (2005), Springer, New York
17. Chapman S., and Cowling T.G. The Mathematical Theory of Nonuniform Gases (1970), Cambridge University Press, Cambridge
18. Grad H. On the kinetic theory of rarefied gases. Comm. Pure Appl. Math. 2 (1949) 325
19. Grad H. In: Flügge S. (Ed). Principles of the Kinetic Theory of Gases. Handbuch der Physik vol. 12 (1958), Springer, Berlin
20. Bobylev A.V. The Chapman-Enskog and grad methods for solving the Boltzmann equation. Sov. Phys. Dokl. 27 (1982) 29
21. Rosenau P. Extending hydrodynamics via the regularization of the Chapman-Enskog expansion. Phys. Rev. A 40 (1989) 7193
22. Zhong X., MacCormack R.W., and Chapman D.R. Stabilization of the Burnett equations and applications to hypersonic flows. AIAA J. 31 (1993) 1036
23. Jin S., and Slemrod M. Regularization of the Burnett equations via relaxation. J. Stat. Phys. 103 (2001) 1009
24. Müller I., Reitebuch D., and Weiss W. Extended thermodynamics - consistent in order of magnitude. Cont. Mech. Thermodyn. 15 (2003) 113
25. Bobylev A.V. Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations. J. Stat. Phys. 124 (2006) 371
26. Söderholm L.H. Hybrid Burnett equations: a new method of stabilizing. Trans. Theory Stat. Phys. 36 (2007) 495
27. Taheri P., Torrilhon M., and Struchtrup H. Couette and Poiseuille microflows: analytical solutions for regularized 13-moment equations. Phys. Fluids 21 (2009) 017102
28. Struchtrup H., and Torrilhon M. Higher-order effects in rarefied channel flows. Phys. Rev. E 78 (2008) 046301
29. Taheri P., Rana A.S., Torrilhon M., and Struchtrup H. Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics. Cont. Mech. Thermodyn. 21 (2009) 423-443
30. Struchtrup H. Stable transport equations for rarefied gases at high orders in the knudsen number. Phys. Fluids 16 (2004) 3921
31. Struchtrup H., and Torrilhon M. Regularization of grad's 13-moment equations: derivation and linear analysis. Phys. Fluids 15 (2003) 2668
32. Struchtrup H., and Thatcher T. Bulk equations and Knudsen layers for the regularized 13 moment equations. Cont. Mech. Thermodyn. 19 (2007) 177
33. Torrilhon M., and Struchtrup H. Regularized 13-moment equations: shock structure calculations and comparison to Burnett models. J. Fluid Mech. 513 (2004) 171
34. Torrilhon M., and Struchtrup H. Boundary conditions for regularized 13-moment equations for micro-channel flows. J. Comput. Phys. 227 (2008) 1982
35. Gu X., and Emerson D. A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions. J. Comput. Phys. 225 (2007) 263
36. Arkilic E.B., Schmidt M.A., and Breuer K.S. Gaseous slip flow in long microchannels. J. Microelectromech. Syst. 6 (1997) 167
37. Struchtrup H., and Torrilhon M. H theorem, regularization, and boundary conditions for linearized 13-moment equations. Phys. Rev. Lett. 99 (2007) 014502