A phenomenological and extended continuum approach for modelling non-equilibrium flows

Continuum Mechanics and Thermodynamics

Volumn 19, Issue 5, 2007, Pages 273-283

  Mizzi, S ^a   Barber, R W ^a   Emerson, D R ^a   Reese, J M ^b   Stefanov, S K ^c  

^a DARESBURY LABORATORY   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^c INSTITUTE OF MECHANICS   (Bulgaria)

Author keywords

Flows in micro electromechanical systems (MEMS) and nano electromechanical systems (NEMS); Micro and nano scale flow phenomena; Non continuum effects; Non equilibrium gas dynamics; Rarefied gas dynamics

Indexed keywords

NON-CONTINUUM EFFECTS; NON-EQUILIBRIUM GAS DYNAMICS; RAREFIED GAS DYNAMICS; VISCOUS STRESS;

BOUNDARY CONDITIONS; CONTINUUM MECHANICS; GAS DYNAMICS; HEAT FLUX; MEMS; MONTE CARLO METHODS; NAVIER STOKES EQUATIONS; NEMS;

FLOW OF GASES;

EID: 34648840785     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-007-0054-9     Document Type: Article

References (20)

1. Barber R.W. and Emerson D.R. (2006). Challenges in modeling gas-phase flow in microchannels: from slip to transition. Heat Transf. Eng. 27(4): 3-12
2. Bird G.A. (1994). Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford
3. Cercignani C. (2000). Rarefied Gas Dynamics-From Basic Concepts to Actual Calculations. Cambridge University Press, Cambridge
4. Chapman S. and Cowling T.G. (1991). The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge
5. Gad-el-Hak M. (1999). The fluid mechanics of microdevices-The Freeman scholar lecture. ASME J. Fluids Eng. 121: 5-33
6. Grad H (1949). On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2: 331-407
7. Gu X.J. and Emerson D.R. (2007). A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions. J. Comput. Phys. 225: 263-283
8. Ikenberry E. and Truesdell C. (1956). On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory I & II. J. Ration. Mech. Anal. 5: 1-128
9. Kogan M.N. (1969). Rarefied Gas Dynamics. Plenum Press, New York
10. Liu I.-S.: On well-posedness of classical boundary conditions in extended thermodynamics. In: Wang, Y., Hutter, K. (eds.), Proceedings of the XIVth International Symposium on Trends in Applications of Mathematics to Mechanics, pp. 225-233, Shaker Verlag, Aachen, 2005
11. Liu I.-S. (2007). A method of differential iteration for boundary value problems in extended thermodynamics. Nonlinear Anal. Real World Appl. 8: 1113-1131
12. Liu I.-S. and Rincon M.A. (2004). A boundary value problem in extended thermodynamics-one-dimensional steady flows with heat conduction. Continuum Mech. Thermodyn. 16: 109-124
13. Lockerby D.A., Reese J.M. and Gallis M.A. (2005). Capturing the Knudsen layer in continuum-fluid models of non-equilibrium gas flows. AIAA J. 43(6): 1391-1393
14. Lockerby, D.A., Reese, J.M., Gallis, M.A.: The usefulness of higher-order constitutive relations for describing the Knudsen layer. Phys. Fluids 17, Art. No. 100609 (2005)
15. Maxwell J.C. (1879). On stresses in rarefied gases arising from temperature inequalities. Phil. Trans. R. Soc. Ldn 170: 231-256
16. Pfahler J.N.: Liquid transport in micron and submicron size channels. Ph.D. Thesis. University of Pennsylvania, PA, USA, 1992
17. Rapaport D.C. (2004). The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge
18. Struchtrup H. (2005). Macroscopic Transport Equations for Rarefied Gas Flows. Springer, Germany
19. von Smoluchowski M. (1898). Über Wärmeleitung in verdünnten Gasen. Ann. Phys. Chem. 64: 101-130
20. Woods L.C. (1993). An Introduction to the Kinetic Theory of Gases and Magnetoplasmas. Oxford University Press, Oxford