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Further solutions of the Falkner-Skan equation

  • K. Stewartson (a1)
Abstract

In an attempt to understand the mechanism governing separation the possibility of there being further solutions to the Falkner-Skan equation f′′′ + ff″ + β(1 − f′2) = 0, in addition to those found by Hartree, is investigated.

It is found that when β < − 0·1988 there are no solutions satisfying |f′| ⩽ 1 for all η, and that if 0>β> − 0·1988 there are two acceptable solutions, one with f″(0) < 0. The new ones are computed to three places of decimals for various values of β and tabulated. In addition, it is shown that if − 0·5 < β < 0 there is a family of solutions corresponding to boundary layers bounded on one side by free streamlines. These are also computed and graphs of f(0) and δ1 are displayed. The impact of these solutions on the theory of separation is discussed.

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References
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(1)Falkner, V. M. and Skan, S. W.Phil Mag. (7) 12 (1931), 865.
(2)Fox, L.Proo. Camb. phil. Soc. 46 (1950), 50.
(3)Hartree, D. R.Proc. Camb. phil. Soc. 33 (1937), 223.
(4)Stewartson, K.Proc. Camb. phil. Soc. 49 (1953), 561.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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