A challenge in Navier-Stokes-based continuum modeling: Maxwell-Burnett slip law

Physics of Fluids

Volumn 20, Issue 10, 2008, Pages

  Weng, Huei Chu ^a   Chen, Cha'o Kuang ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; DROPS; FLOW OF GASES; MASS TRANSFER; PRESSURE DROP;

CONTINUUM MODELING; CRITICAL KNUDSEN NUMBERS; CRITICAL VALUE; KNUDSEN NUMBERS; MASS FLOW RATE; PARALLEL PLATES; SECOND-ORDER SLIP; WORKING TEMPERATURES;

NAVIER STOKES EQUATIONS;

EID: 55849152018     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2998451     Document Type: Conference Paper

References (38)

1. J. Pfahler, J. C. Harley, H. Bau, and J. N. Zemel, "Gas and liquid flow in small channels," ASME Dyn. Syst. Control Div. ASMDEV 32, 49 (1991).
2. K. C. Pong, C. M. Ho, J. Liu, and Y. C. Tai, "Nonlinear pressure distribution in uniform microchannels," Proceeding of the ASME Fluids Engineering Division (FED) (ASME, New York, 1994), Vol. 197, p. 51.
3. J. C. Harley, "Compressible gas flow in micron and submicron sized channels," M.S. thesis, University of Pennsylvania, 1991.
4. J. C. Harley, Y. H. Huang, H. Bau, and J. N. Zemel, "Gas flow in microchannels," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112095000358 284, 257 (1995).
5. E. B. Arkilic, M. A. Schmidt, and K. S. Breuer, "Gaseous slip flow in long microchannels," J. Microelectromech. Syst. JMIYET1057-715710.1109/84.585795 6, 167 (1997).
6. A. Beskok, "Validation of a new velocity-slip model for separated gas microflows," Numer. Heat Transfer, Part B NHBFEE1040-779010.1080/104077901753306593 40, 451 (2001).
7. S. A. Schaaf and P. L. Chambré, Flow of Rarefied Gases (Princeton University Press, New York, 1961).
8. A. Beskok and G. E. Karniadakis, "A model for flows in channels, pipes, and ducts at micro and nano scales," Microscale Thermophys. Eng. MTENFP1089-395410.1080/108939599199864 3, 43 (1999).
9. T. Ewart, P. Perrier, I. Graur, and J. G. Méolans, "Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112007006374 584, 337 (2007).
10. S. Colin, P. Lalonde, and R. Caen, "Validation of a second-order slip flow model in rectangular microchannels," Heat Transfer Eng. HTEND20145-763210.1080/01457630490280047 25, 23 (2004).
11. H. Xue and Q. Fan, "A new analytic solution of the Navier-Stokes equations for microchannel flows," Microscale Thermophys. Eng.MTENFP1089-395410.1080/108939500404034 4, 125 (2000).
12. D. A. Lockerby and J. M. Reese, "On the modelling of isothermal gas flows at the microscale," J. Fluid Mech. JFLSA70022-1120 604, 235 (2008).
13. D. Jie, X. Diao, K. B. Cheong, and L. K. Yong, "Navier-Stokes simulations of gas flow in micro devices," J. Micromech. Microeng. JMMIEZ0960-131710.1088/0960-1317/10/3/311 10, 372 (2000).
14. C. Aubert and S. Colin, "High-order boundary conditions for gaseous flows in rectangular microducts," Microscale Thermophys. Eng.MTENFP1089-395410.1080/108939501300005367 5, 41 (2001).
15. G. E. Karniadakis and A. Beskok, Micro Flows (Springer-Verlag, New York, 2002).
16. N. G. Hadjiconstantinou, "Validation of a second-order slip model for dilute gas flows," Microscale Thermophys. Eng. MTENFP1089-395410.1080/10893950590945021 9, 137 (2005).
17. N. Dongari, A. Agrawal, and A. Agrawal, "Analytical solution of gaseous slip flow in long microchannels," Int. J. Heat Mass Transfer IJHMAK0017-931010.1016/j.ijheatmasstransfer.2007.01.048 50, 3411 (2007).
18. N. G. Hadjiconstantinou, "Comment on Cercignani's second-order slip coefficient," Phys. Fluids PHFLE61070-663110.1063/1.1587155 15, 2352 (2003).
19. C. Cercignani, "Higher order slip according to the linearized Boltzmann equation," University of California, Institute of Engineering Research Report No. AS-64-19, 1964.
20. R. G. Deissler, "An analysis of second-order slip flow and temperature jump boundary conditions for rarefied gases," Int. J. Heat Mass Transfer IJHMAK0017-931010.1016/0017-9310(64)90161-9 7, 681 (1964).
21. C. Cercignani and A. Daneri, "Flow of a rarefied gas between two parallel plates," J. Appl. Phys.JAPIAU0021-897910.1063/1.1729249 34, 3509 (1963).
22. A. K. Streekanth, "Slip flow through long circular tubes," Proceedings of the Sixth International Symposium on Rarefied Gas Dynamics (Academic, New York, 1969).
23. R. K. Agarwal, K. Y. Yun, and R. Balakrishnan, "Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition regime," Phys. FluidsPHFLE61070-663110.1063/1.1397256 13, 3061 (2001).
24. F. H. Qin, D. J. Sun, and X. Y. Yin, "Perturbation analysis on gas flow in a straight microchannel," Phys. FluidsPHFLE61070-663110.1063/1.2564671 19, 027103 (2007).
25. H. Schlichting, Boundary-Layer Theory (McGraw-Hill, New York, 1979).
26. H. C. Weng and C.-K. Chen, "Variable physical properties in natural convective gas microflow," ASME J. Heat Transfer JHTRAO0022-148110.1115/1.2927400 130, 082401 (2008).
27. A. Bejan, Convection Heat Transfer (Wiley, New York, 1995).
28. N. V. Suryanarayana, Engineering Heat Transfer (West, New York, 1995).
29. J. C. Maxwell, "On stress in rarefied gases from inequalities of temperature," Philos. Trans. R. Soc. London PTRSAV0370-231610.1098/ rstl.1879.0067 170, 231 (1879).
30. D. A. Lockerby, J. M. Reese, D. R. Emerson, and R. W. Barber, "Velocity boundary condition at solid walls in rarefied gas calculations," Phys. Rev. E PLEEE81063-651X10.1103/ PhysRevE.70.017303 70, 017303 (2004).
31. S. Chapman and T. Cowling, Mathematical Theory of Non-Uniform Gases (Cambridge University Press, London, 1970).
32. R. Schamberg, "The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems," Ph.D. thesis, California Institute of Technology, 1947.
33. A. Beskok, G. E. Karniadakis, and W. Trimmer, "Rarefaction, compressibility and thermal creep effects in micro-flows," Proceeding of the ASME Dynamic Systems and Control Division (DSC) (ASME, New York, 1995), Vol. 57, p. 877.
34. Y. T. Hsia and G. A. Domoto, "An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances," ASME J. Lubr. Technol. JLUTAT0022-2305 105, 120 (1983).
35. J. Maurer, P. Tabeling, P. Joseph, and H. Willaime, "Second-order slip laws in microchannels for helium and nitrogen," Phys. Fluids PHFLE61070-663110.1063/1.1599355 15, 2613 (2003).
36. S. Colin, "Rarefaction and compressibility effects on steady and transient gas flows in microchannels," Microfluid. Nanofluid. MNIAAR1613-498210.1007/s10404-004-0002-y 1, 268 (2005).
37. R. W. Barber and D. R. Emerson, "Challenges in modeling gas-phase flow in microchannels: From slip to transition," Heat Transfer Eng. HTEND20145-763210.1080/01457630500522271 27, 3 (2006).
38. E. B. Arkilic, K. S. Breuer, and M. A. Schmidt, "Mass flow and tangential momentum accommodation in silicon micromachined channels," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001004128 437, 29 (2001).