Abstract
The aim of my talk is to give an exposition of a paper presented by Dr. Cercignani and me at the Forth International Symposium on Rarefied Gas Dynamics, held at Toronto, Canada, last july (1),
Time-dependent problems have been scarcely investigated in Ra refied Gas Dynamics for an arbitrary Knudsen number. In fact, only a problem not spatially homogeneous appears to have been considered: the Rayleigh's problem. Also, for this typical problem, only approximate solutions have been given, in the frame of the kinetic theory of gases, by Yang and Lees in 1956 and 1960 (2), and by Gross and Jackson in 1958 (3). Exact solutions have been given in the limiting cases of con tinuum theory (Rayleigh, 1911 (4) ), also with the correction for slip velocity (Schaaf, 1950 (5)).
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References
C. Cercignani and F. Sernagiotto : “ Rayleigh's problem at low Mach numbers according to kinetic theory” (paper presented at the IV Internaz. Symposium on Rarefied Gas Dynamics, Toronto, Canada,july 1964).
H.T.Yang and L. Lees (1956) J. Math. and Phys. 35, 195 ; and in “Rarefied Gas Dynamics” (F.M. Devienne, ed.)p. 201,Pergamon Press, London (1960).
E.P. Gross and E.A. Jackson (1958) Phys. Fluids 1, 318.
Rayleigh, J.W. Strutt, Lord (1911), in “Scientific Papers”, Vol. VI,p. 29, Cambridge University press, Cambridge.
S.A.Schaaf (1950) Univ. of Calif. Inst. of Eng. Research, Rept.NO HE-150–66.
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P.L.Bhatnagar, E.P. Gross, and Krook, Phys.Rev. 94, 511.
K.M.Case, Ann. Phys. (N.Y.) 9, 1,1960.
C. Cercignani, Ann. Phys. (N..Y.) 20, 219, 1962. C. Cercignani, (1964a) “The Kramers problem for a not complete ly diffusing wall ” (to appear in the J. of Math.Anal. and Appl.) C. Cercignani, (1964b) “Plane Couette flow according to the method of elementary solutions” (to appear in the J. of Math, Anal. and Apl.) C. Cercignani, (1964c) “Plane Poiseuille flow according to the me thod of elementary solutions” (to appear in the J. of Math. Anal. and Appl.).
C. Cercignani and F. Sernagiotto (1964) “The method of elementary solutions for time-dependent problems in linearized kinetic theory”. Ann. Phys (N.Y.) 30, 154, 1964.....
S.Albertoni, C. Cercignani, and L. Gotusso, Phys, Fluids 6, 933,1963.
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Sernagiotto, F. (2011). Solution of Rayleigh'S Problem for the Whole Range of Knudsen Numbers. In: Ferrari, C. (eds) Dinamica dei gas rarefatti. C.I.M.E. Summer Schools, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11024-5_8
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