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Example text
01, the presence of a thin layer near the wall, of thickness ~ A (Knudsen layer), influences the viscous layer in a significant way. This regime is called the slip regime because the gas slips upon the boundary with a velocity Us and, at the boundary, has a temperature 40 Part I - Chapter 2. Perturbation Methods for the Boltzmann Equation different from the temperature of the boundary itself. 4) where ( is the slip coefficient. A similar formula holds for the temperature jump. Maxwell computed ( to be approximately equal to (y7r /2)>' (for complete diffusion of the molecules at the wall; see Eq.
28] K. Barwinkel and S. Schippers, in Rarefied Gas Dynamics: Space-Related Studies E. P. Muntz, D. P. Weaver and D. H. , 487-501, AlAA, Washington (1989). [29] J. C. Maxwell, Phil. Trans. Royal Soc. 170, 231-256, Appendix (1879). [30] S. Nocilla, in Rarefied Gas Dynamics, L. , 169, Academic Press, New York (1961) [31] F. Hurlbut and F. S. Sherman, Phys. Fluids 11,486-496 (1968). [32] M. N. Kogan, Rarefied Gas Dynamics, Plenum Press, New York (1969). [33] I. KU8cer, J. Mozina and F. , Vol. l, 97-108, Editrice Tecnico-Scientifica, Pisa ( (1974).
All these models contain pure diffusion according to a nondrifting Maxwellian as a limiting case (Eq. 20) with Q = 1. The use of this particular model is justified for low-velocity flows over technical surfaces, but is inaccurate for flows with orbital velocity. In fact, the elaboration of the measurements of lift-to-drag ratio for the Shuttle Orbiter in the free-molecular regime38 implies a significant departure from diffuse, fully-equilibrated re-emission of molecules at the wall. It is remarkable that, for any scattering kernel satisfying the three properties of normalization, positivity and preservation of equilibrium, a simple inequality holds.