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The downstream solution for steady viscous flow past a paraboloid

Published online by Cambridge University Press:  24 October 2008

D. R. Miller
Affiliation:
Department of Industrial and Systems EngineeringUniversity of Florida

Extract

The flow of a viscous incompressible fluid past a paraboloid of revolution is described by matching a series of boundary-layer approximations valid far downstream to a series of potential flow solutions valid far from the solid surface. The development parallels that of Goldstein (3) and Murray (10) for the flat plate, becoming identical for infinitely large Reynolds number; it is found that logarithmic terms must be introduced at the third stage of the matching, and that these produce constants in the downstream solution which remain indeterminate. These terms result from interaction between inner and outer solutions, rather than from appearance of a complementary function of the inner equation.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

1Erdélyi, A. et al. Higher transcendental functions. 3 Volumes, McGraw-Hill, New York, 1953.Google Scholar
2Goldstein, S.Flow of an incompressible viscous fluid along a semi-infinite flat plate. Inst. Engrg. Res., Univ. Calif., Tech. Rep. HE-150-144, 1956.Google Scholar
3Goldstein, S.Lectures on fluid mechanics (Interscience, New York, 1960).Google Scholar
4Imai, Isao.Second approximation to the laminar boundary-layer flow over a flat plate. J. Aero. Sci. 24 (1957), 155156.Google Scholar
5Lee, L. L.Boundary layer over a thin needle. Phys. Fluids 10 (1967), 820822.Google Scholar
6Libby, P. A. and Fox, H.Some perturbation solutions in laminar boundary-layer theory. J. Fluid Mech. 17 (1963), 433449.CrossRefGoogle Scholar
7Mark, R. M.Laminar boundary layers on slender bodies of revolution in axial flow. Galcit hypersonic memo, No. 21, 06 30, 1954.Google Scholar
8Mather, D. J.The motion of viscous liquid past a paraboloid. Quart. J. Mech. Appl. Math. 14 (1961), 423429.CrossRefGoogle Scholar
9Miller, D. R.The boundary layer on a paraboloid of revolution. Proc. Cambridge Philos. Soc. 65 (1969), 285299.Google Scholar
10Murray, J. D.Incompressible viscous flow past a semi-infinit flat plate. J. Fluid Mech. 21 (1965), 337344.Google Scholar
11Murray, J. D.A simple method for determining asymptotic forms of Navier–Stokes solutions for a class of large Reynolds number flows. J. Math. and Phys. 46 (1967), 120.Google Scholar
12Pillow, A. F.Diffusion of heat and circulation in potential flow convection. J. Math. Mech. 13 (1964), 521545.Google Scholar
13Stewartson, K.On asymptotic expansions in the theory of boundary layers. J. Math. and Phys. 36 (1957), 173191.Google Scholar
14Ting, L.Asymptotic solutions of wakes and boundary layers. J. Eng. Math. 2 (1968), 2328.CrossRefGoogle Scholar