Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-16T09:24:11.200Z Has data issue: false hasContentIssue false
  • English
  • Français

On Blasius's equation governing flow in the boundary layer on a flat plate

Published online by Cambridge University Press:  24 October 2008

S. Richardson
S. Richardson
Affiliation:
Applied Mathematics, University of Edinburgh
Get access Rights & Permissions [Opens in a new window]

Abstract

The original approach of Blasius to the solution of the differential equation now associated with his name was to develop the unknown function as a power series. Unfortunately, this series has a limited radius of convergence, so that such a representation is not valid over the whole range of interest. It is shown here that, if we work instead with a particular inverse function, this can be expanded as a power series which converges for all relevant values of the independent variable. Moreover, the number associated with the solution which is of principal physical interest can be expressed in terms of the asymptotic properties of the coefficients of this series. Exploiting this relationship, we find upper and lower bounds for this number in terms of the zeros of two particular families of polynomials.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 179 - 184
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Blasius, H.Z. Math. Phys. 56 (1908), 1.Google Scholar
(2)Goldstein, S.Modern developments in fluid dynamics (Oxford, 1938).Google Scholar
(3)Hille, E.Analytic Function Theory, vol. 1 (Blaisdell, 1959).Google Scholar
(4)Meksyn, D.C.R. Acad. Sci., Paris. 248 (1959), 2286.Google Scholar
(5)Meksyn, D.New methods in laminar boundary-layer theory (Pergamon, 1961).Google Scholar
(6)Punnis, B.Arch. Math. 7 (1956), 165.CrossRefGoogle Scholar
(7)Töpfer, C.Z. Math. Phys. 60 (1912), 397.Google Scholar
(8)Weyl, H.Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 578.CrossRefGoogle Scholar
(9)Weyl, H.Ann. of Math. 43 (1942), 381.CrossRefGoogle Scholar