43
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Unified Approach for Variable Collision‐Frequency Models in Rarefied Gas Dynamics

&
Pages 227-260 | Published online: 15 Aug 2006

References

  • Arkilic , E. B. , Breuer , K. S. and Schmidt , M. A. 2001 . Mass flow and tangential momentum accommodation in silicon micromachined channels . Journal of Fluid Mechanics , 437 : 29 – 43 .
  • Barichello , L. B. , Bartz , A. C.R. , Camargo , M. and Siewert , C. E. 2002 . The temperature‐jump problem for a variable collision frequency model . Physics of Fluids , 14 : 382 – 391 .
  • Barichello , L. B. , Camargo , M. , Rodrigues , P. and Siewert , C. E. 2001 . Unified solutions to classical flow problems based on the BGK model . Zeitschrift für angewandte Mathematik und Physik , 52 : 517 – 534 .
  • Barichello , L. B. , Rodrigues , P. and Siewert , C. E. 2004 . On computing the Chapman‐Enskog and Burnett functions . Journal of Quantitative Spectroscopy and Radiative Transfer , 84 : 109 – 114 .
  • Barichello , L. B. and Siewert , C. E. 1999 . A discrete‐ordinates solution for a non‐grey model with complete frequency redistribution . Journal of Quantitative Spectroscopy and Radiative Transfer , 62 : 665 – 675 .
  • Barichello , L. B. and Siewert , C. E. 2000 . The temperature‐jump problem in rarefied‐gas dynamics . European Journal of Applied Mathematics , 11 : 353 – 364 .
  • Barichello , L. B. and Siewert , C. E. 2003 . Some comments on modeling the linearized Boltzmann equation . Journal of Quantitative Spectroscopy and Radiative Transfer , 77 : 43 – 59 .
  • Bhatnagar , P. L. , Gross , E. P. and Krook , M. 1954 . A model for collision processes in gases. I. Small amplitude processes in charged and neutral one‐component systems . Physics Review , 94 : 511 – 525 .
  • Busbridge , I. W. 1953 . Coherent and non‐coherent scattering in the theory of line formation . Monthly Nottices of the Royal Astronomical Society , 113 : 52 – 66 .
  • Camargo , M. 2003 . “ Unified solutions for variable collision frequency models of the rarefied gas dynamics (in Portuguese) ” . Porto Alegre, , RS, Brasil : Universidade Federal do Rio Grande do Sul . PhD. Thesis
  • Cassell , J. S. and Williams , M. M. R. 1972 . An exact solution of the temperature slip problem in rarefied gases . Transport Theory and Statistical Physics , 2 : 81 – 90 .
  • Cercignani , C. 1966 . The method of elementary solutions for kinetic models with velocity‐dependent collision frequency . Annals of Physics , 40 : 469 – 481 .
  • Karniadakis , G. E. and Beskok , A. 2002 . Micro flows New York : Springer‐Verlag .
  • Loyalka , S. K. and Ferziger , J. H. 1968 . Model dependence of the temperature slip coefficient . Physics of Fluids , 11 : 1668 – 1671 .
  • Loyalka , S. K. and Hickey , K. A. 1989 . Plane Poiseuille flow: near continuum results for a rigid sphere gas . Physica A , 160 : 395 – 408 .
  • Loyalka , S. K. and Hickey , K. A. 1990 . The Kramers problem: velocity slip and defect for a hard sphere gas with arbitrary accommodation . Zeitschrift für angewandte Mathematik und Physik , 41 : 245 – 253 .
  • Pekeris , C. L. and Alterman , Z. 1957 . “ Solution of the Boltzmann‐Hilbert integral equation II. The coefficients of viscosity and heat conduction ” . In Proceedings of the National Academy of Sciences of the United States of America Vol. 43 , 998 – 1007 .
  • Sharipov , F. 1999 . Non‐isothermal gas flow through rectangular microchannels . Journal of Micromechanics and Microengineering , 9 : 394 – 401 .
  • Siewert , C. E. 2001 . Kramers' problem for a variable collision frequency model . European Journal of Applied Mathematics , 12 : 179 – 191 .
  • Siewert , C. E. 2002a . On computing the Chapman‐Enskog functions for viscosity and heat transfer and the Burnett functions . Journal of Quantitative Spectroscopy and Radiative Transfer , 74 : 789 – 796 .
  • Siewert , C. E. 2002b . Poiseuille, Thermal Creep and Couette flow: results based on the CES model of the linearized Boltzmann equation . European Journal of Mechanics B/Fluids , 21 : 579 – 597 .
  • Siewert , C. E. 2003a . The linearized Boltzmann equation: a concise and accurate solution of the temperature‐jump problem . Journal of Quantitative Spectroscopy and Radiative Transfer , 77 : 417 – 432 .
  • Siewert , C. E. 2003b . The linearized Boltzmann equation: concise and accurate solutions to basic flow problems . Zeitschrift für angewandte Mathematik und Physik , 54 : 273 – 303 .
  • Siewert , C. E. and Sharipov , F. 2002 . Model equations in rarefied gas dynamics: viscous‐slip and thermal‐slip coefficients . Physics of Fluids , 14 : 4123 – 4129 .
  • Sone , Y. , Ohwada , T. and Aoki , K. 1989 . Temperature jump and Knudsen layer in a rarefied gas over a plane wall: numerical analysis of the linearized Boltzmann equation for hard‐sphere molecules . Physics of Fluids A , 1 : 363 – 370 .
  • Vasudevaiah , M. and Balamurugan , K. 2001 . Heat transfer of rarefied gases in a corrugated microchannel . International Journal of Thermal Sciences , 40 : 454 – 468 .
  • Willet , L. , Hashimi , S. , Thompson , R. V. and Loyalka , S. K. 1999 . Effect of surface heterogeneities on condensation on an aerosol particle . Journal of Aerosol Science , 30 : 569 – 585 .
  • Williams , M. M. R. 1971 . Mathematical Methods in Particle Transport Theory London : Butterworth .
  • Williams , M. M. R. 2001 . A review of the rarefied gas dynamics theory associated with some classical problems in flow and heat transfer . Zeitschrift für angewandte Mathematik und Physik , 52 : 500 – 516 .
  • Williams , M. M. R. and Loyalka , S. K. 1992 . Aerosol Science: Theory and Practice, with Special Applications to the Nuclear Industry Oxford, , England : Pergamon Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.