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Rayleigh Problem in a Radiating Compressible Gas I. Plate Mach Number Finite
1.H. Schlichtmg, in Boundary Layer Theory, translated by J. Kestin (McGraw‐Hill Book Company, Inc., New York, 1960), 4th ed., p. 72. Schlichting points out that the credit for solving this problem is actually due to Stokes.
2.H. Lamb, Hydrodynamics (Dover Publications, Inc., New York, 1945), 6th ed., p. 590.
3.C. R. Illingworth, Proc. Cambridge Phil. Soc. 46, 603 (1950).
4.M. D. Van Dyke, Z. Angew. Math. Phys. 3, 343 (1952).
5.K. Stewartson, Proc. Cambridge Phil. Soc. 51, 202 (1955).
6.A. Solan and I. M. Cohen, Phys. Fluids (to be published).
7.R. Goulard, in The High Temperature Aspects of Hypersonic Flow, W. C. Nelson, Ed. (The Macmillan Company, London, 1964).
8.W. G. Vincenti and C. H. Kruger, Jr., Introduction to Physical Gas Dynamics (John Wiley & Sons, Inc., New York, 1965).
9.R. Goulard and M. Goulard, Intern. J. Heat Mass Transfer 1, 81 (1960).
10.V. Kourganoff, Basic Methods in Transfer Problems (Dover Publications, Inc., New York, 1963).
11.R. Goulard, in High Temperatures in Aeronautics, C. Ferrari, Ed. (Pergamon Press, Inc., Oxford, England, 1964).
12.W. D. Hayes and R. F. Probstein, Hypersonic Flow Theory (Academic Press Inc., New York, 1959).
13.We use the notation etc., to denote equalities or inequalities of order of magnitude. Thus means and and means [possibly ] in the standard O‐o notation. This notation, proposed by F. E. Bisshopp, is particularly effective in compound asymptotic orderings, such as, e.g.,
14.M. D. Kruskal, in Mathematical Models in Physical Sciences, S. Drodot, Ed. (Prentice‐Hall, Inc., Englewood Cliffs, New Jersey, 1963). In particular, we base our treatment on Kruskal’s “Principle of Maximal Complication (or Minimal Simplification).”
15.M. D. Van Dyke, Perturbation Methods in Fluid Mechanics (Academic Press Inc., New York, 1964). Most of the ideas of Ref. 14 can be found also here, but in a less crystallized form.
16.A. Solan and I. M. Cohen, Brown University Report Nonr 562(35)/10 (1966). The present paper is condensed from this report.
17.From here on we define the scale factors by exact, rather than asymptotic, equalities. This allows us to keep track of the numerical factors in the equations.
18.The scaling in terms of Bo when is introduced not for asymptotics but for similarity.
19.J. B. Serrin (to be published).
20.This simplification is obtained also in the case when if t is replaced by the new independent variable as in Ref. 5.
21.W. J. Lick, J. Fluid Mech. 18, 274 (1964).
22.B. S. Baldwin, Jr., NASA Technical Report R‐138 1962).
23.J. Douglas, Jr., in Advances in Computers, F. L. Alt, Ed. (Academic Press Inc., New York, 1961), Vol. 2.
24.A. Solan and I. M. Cohen, Phys. Fluids 9, 2365 (1966).
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