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The Navier-Stokes solution for laminar flow past a semi-infinite flat plate

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Summary

A numerical solution joining Carrier and Lin's solution near the leading edge to the boundary layer solution at large distance of the leading edge is presented. The solution is valid for any Reynolds number. Results are given for the skin friction, the integrated skin friction, the displacement thickness, the pressure along the plate and the velocity ahead of the plate. The asymptotic value of the integrated skin friction agrees very well with the exact value. The displacement thickness is already different from zero for small distances ahead of the plate.

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References

  1. G. F. Carrier and C. C. Lin, On the nature of the boundary layer near the leading edge of a flat plate,Quart. Appl. Math., 6, pp. 63–68 (1948).

    Google Scholar 

  2. R. T. Davis, Laminar incompressible flow past a semi-infinite flat plate,J. Fluid Meck., 27, pp. 691–704, (1967).

    Google Scholar 

  3. W. R. Dean, On the steady motion of viscous liquid past a flat plate,Mathematika 1, pp. 143–156 (1954).

    Google Scholar 

  4. M. D. van Dyke,Perturbation methods in fluid mechanics, Academic Press, New York (1964).

    Google Scholar 

  5. S. Goldstein, On some methods of approximation in fluid mechanics,Proc. Int. Congress Math., 1954, North-Holland Publ., Amsterdam (1957).

    Google Scholar 

  6. S. Goldstein,Lectures on Fluid Mechanics, Wiley (Interscience), New York (1960).

    Google Scholar 

  7. I. Imai, Second approximation to the laminar boundary layer flow over a flat plate.J. Aeronaut. Sci., 24, pp. 155–156, (1957).

    Google Scholar 

  8. S. Kaplun, The role of coordinate systems in boundary layer theory.Z. Angew. Math. Phys., 5, pp. 111–135 (1954).

    Google Scholar 

  9. P. A. Lagerstrom, Laminar flow theory,Theory of laminar flows, F. K. Moore ed. University Press, Princeton (1964).

    Google Scholar 

  10. J. A. Lewis and G. F. Carrier, Some remarks on the flat plate boundary layer,Quart. Appl. Math., 7, pp. 228–234, (1949).

    Google Scholar 

  11. J. D. Murray, Incompressible viscous flow past a semi-infinite flat plate,J. Fluid Mech., 21, pp. 337–344 (1965).

    Google Scholar 

  12. K. Stewartson, On asymptotic expansions in the theory of boundary layers,J. Math. and Phys., 36, pp. 173–191, (1957).

    Google Scholar 

  13. A. Thom and C. J. Apelt,Field computations in Engineering and Physics, Van Nostrand Comp., London (1961).

    Google Scholar 

  14. D. Dijkstra, The Navier-Stokes solution for laminar flow past a semi-infinite flat plate (addendum).Report TW-72, Math. Department, University of Groningen (1969).

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Authors and Affiliations

  1. Dept. of Mathematics, University of Groningen, The Netherlands

    A. I. Van De Vooren & D. Dijkstra

Authors
  1. A. I. Van De Vooren
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  2. D. Dijkstra
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Van De Vooren, A.I., Dijkstra, D. The Navier-Stokes solution for laminar flow past a semi-infinite flat plate. J Eng Math 4, 9–27 (1970). https://doi.org/10.1007/BF01535176

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  • DOI: https://doi.org/10.1007/BF01535176

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