The linearized Boltzmann equation with Cercignani-Lampis boundary conditions: Basic flow problems in a plane channel

European Journal of Mechanics, B/Fluids

Volumn 28, Issue 3, 2009, Pages 387-396

  Garcia, R D M ^a   Siewert, C E ^b  

^a HSH Scientific Computing   (Brazil)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Cercignani Lampis boundary condition; Couette flow; Linearized Boltzmann equation; Poiseuille flow; Rarefied gas dynamics; Thermal creep flow

Indexed keywords

BOUNDARY CONDITIONS; CHANNEL FLOW; COMPUTATIONAL FLUID DYNAMICS; CREEP; DYNAMICS; GAS DYNAMICS; GASES; LINEARIZATION;

CERCIGNANI-LAMPIS BOUNDARY CONDITION; COUETTE FLOW; LINEARIZED BOLTZMANN EQUATION; POISEUILLE FLOW; RAREFIED GAS DYNAMICS; THERMAL-CREEP FLOW;

BOLTZMANN EQUATION;

EID: 62349090708     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2008.12.001     Document Type: Article

References (43)

1. Siewert C.E. The linearized Boltzmann equation: a concise and accurate solution of the temperature-jump problem. J. Quant. Spectros. Radiat. Transfer 77 (2003) 417-432
2. Siewert C.E. The linearized Boltzmann equation: concise and accurate solutions to basic flow problems. J. Appl. Math. Phys. (ZAMP) 54 (2003) 273-303
3. Siewert C.E. Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani-Lampis boundary condition. Phys. Fluids 15 (2003) 1696-1701
4. Siewert C.E. Heat transfer and evaporation/condensation problems based on the linearized Boltzmann equation. Eur. J. Mech. B Fluids 22 (2003) 391-408
5. Garcia R.D.M., and Siewert C.E. The linearized Boltzmann equation: sound-wave propagation in a rarefied gas. J. Appl. Math. Phys. (ZAMP) 57 (2006) 94-122
6. Garcia R.D.M., and Siewert C.E. The temperature-jump problem based on the linearized Boltzmann equation for a binary mixture of rigid spheres. Eur. J. Mech. B Fluids 26 (2007) 132-153
7. Garcia R.D.M., and Siewert C.E. The viscous-slip, diffusion-slip, and thermal-creep problems for a binary mixture of rigid spheres described by the linearized Boltzmann equation. Eur. J. Mech. B Fluids 26 (2007) 749-778
8. Garcia R.D.M., and Siewert C.E. Heat transfer between parallel plates: an approach based on the linearized Boltzmann equation for a binary mixture of rigid-sphere gases. Phys. Fluids 19 (2007) 027102
9. Garcia R.D.M., and Siewert C.E. Channel flow of a binary mixture of rigid spheres described by the linearized Boltzmann equation and driven by temperature, pressure, and concentration gradients. SIAM J. Appl. Math. 67 (2007) 1041-1063
10. Garcia R.D.M., and Siewert C.E. Couette flow of a binary gas mixture of rigid-sphere gases described by the linearized Boltzmann equation. Eur. J. Mech. B Fluids 27 (2008) 823-836
11. Barichello L.B., and Siewert C.E. A discrete-ordinates solution for a non-grey model with complete frequency redistribution. J. Quant. Spectros. Radiat. Transfer 62 (1999) 665-675
12. Chandrasekhar S. Radiative Transfer (1950), Oxford University Press, London
13. Cercignani C., and Lampis M. Kinetic model for gas-surface interaction. Transp. Theory Stat. Phys. 1 (1971) 101-114
14. Siewert C.E. Generalized boundary conditions for the S-model kinetic equations basic to flow in a plane channel. J. Quant. Spectros. Radiat. Transfer 72 (2002) 75-88
15. Sharipov F. Application of the Cercignani-Lampis scattering kernel to calculations of rarefied gas flows. I. Plane flow between two parallel plates. Eur. J. Mech. B Fluids 21 (2002) 113-123
16. Sharipov F., and Seleznev V. Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 (1998) 657-706
17. Cercignani C., Lampis M., and Lorenzani S. Variational approach to plane Poiseuille flow with general boundary conditions. In: Ketsdever A.D., and Muntz E.P. (Eds). Rarefied Gas Dynamics: 23rd International Symposium. Whistler, British Columbia, Canada, 20-25 July 2002. AIP Conference Proceedings vol. 663 (2003) 141-148
18. Bhatnagar P.L., Gross E.P., and Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (1954) 511-525
19. Cercignani C., Lampis M., and Lorenzani S. Plane Poiseuille flow with symmetric and nonsymmetric gas-wall interactions. Transp. Theory Stat. Phys. 33 (2004) 545-561
20. Knackfuss R.F., and Barichello L.B. Surface effects in rarefied gas dynamics: an analysis based on the Cercignani-Lampis boundary condition. Eur. J. Mech. B Fluids 25 (2006) 113-129
21. Loyalka S.K., and Hickey K.A. The Kramers problem: velocity slip and defect for a hard sphere gas with arbitrary accommodation. J. Appl. Math. Phys. (ZAMP) 41 (1990) 245-253
22. Loyalka S.K., and Hickey K.A. Plane Poiseuille flow: near continuum results for a rigid sphere gas. Physica A 160 (1989) 395-408
23. Loyalka S.K. Temperature jump and thermal creep slip: rigid sphere gas. Phys. Fluids A 1 (1989) 403-408
24. 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
25. Yasuda S., Takata S., and Aoki K. Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall. Phys. Fluids 16 (2004) 1989-2003
26. Ohwada T., Sone Y., and Aoki K. Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules. Phys. Fluids A 1 (1989) 1588-1599
27. 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) 2042-2049
28. Sone Y., Takata S., and Ohwada T. Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules. Eur. J. Mech. B Fluids 9 (1990) 273-288
29. Sone Y., Ohwada T., and Aoki K. Evaporation and condensation on a plane condensed phase: numerical analysis of the linearized Boltzmann equation for hard-sphere molecules. Phys. Fluids A 1 (1989) 1398-1405
30. Yasuda S., Takata S., and Aoki K. Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall. Phys. Fluids 16 (2004) 1989-2003
31. Takata S., Yasuda S., Kosuge S., and Aoki K. Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases. Phys. Fluids 15 (2003) 3745-3766
32. Takata S., Aoki K., Yasuda S., and Kosuge S. Temperature, pressure, and concentration jumps for a binary mixture of vapors on a plane condensed phase: numerical analysis of the linearized Boltzmann equation. Phys. Fluids 18 (2006) 067102
33. Williams M.M.R. A review of the rarefied gas dynamics theory associated with some classical problems in flow and heat transfer. J. Appl. Math. Phys. (ZAMP) 52 (2001) 500-516
34. Pekeris C.L. Solution of the Boltzmann-Hilbert integral equation. Proc. Natl. Acad. Sci. 41 (1955) 661-669
35. Cercignani C. Theory and Applications of the Boltzmann Equation (1975), Elsevier, New York
36. Sharipov F., and Kalempa D. Gas flow near a plate oscillating longitudinally with an arbitrary frequency. Phys. Fluids 19 (2007) 017110
37. Garcia R.D.M., and Siewert C.E. Some solutions (linear in the spatial variable) and generalized Chapman-Enskog functions basic to the linearized Boltzmann equation for a binary mixture of rigid spheres. J. Appl. Math. Phys. (ZAMP) 58 (2007) 262-288
38. Pekeris C.L., and Alterman Z. Solution of the Boltzmann-Hilbert integral equation II. The coefficients of viscosity and heat conduction. Proc. Natl. Acad. Sci. 43 (1957) 998-1007
39. Siewert C.E. On computing the Chapman-Enskog functions for viscosity and heat transfer and the Burnett functions. J. Quant. Spectros. Radiat. Transfer 74 (2002) 789-796
40. Gross E.P., and Jackson E.A. Kinetic models and the linearized Boltzmann equation. Phys. Fluids 2 (1959) 432-441
41. Barichello L.B., and Siewert C.E. Some comments on modeling the linearized Boltzmann equation. J. Quant. Spectros. Radiat. Transfer 77 (2003) 43-59
42. McCormack F.J. Construction of linearized kinetic models for gaseous mixtures and molecular gases. Phys. Fluids 16 (1973) 2095-2105
43. Siewert C.E. Poiseuille, thermal creep and Couette flow: results based on the CES model of the linearized Boltzmann equation. Eur. J. Mech. B Fluids 21 (2002) 579-597