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Some perturbation solutions in laminar boundary-layer theory

  • Paul A. Libby (a1) and Herbert Fox (a1)

The velocity fields associated with a variety of flows which may be described by perturbations of the Blasius solution are considered. These are flows which, for example, because of localized mass transfer, involve the initial-value problem of boundary-layer theory, or which involve a variable ratio of the viscosity-density product, or finally which involve mass transfer. The perturbation solutions are presented so that in accord with the usual linearization procedures further applications for the determination of first-order effects can be readily made. In addition, each of these perturbations involves a common differential operator whose eigenfunctions form a complete orthogonal set. Accordingly, a procedure for systematically improving each perturbation solution to obtain higher-order effects by quadrature is presented. The results of applications in several cases are given and are compared to more accurate solutions where available.

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Kramer, R. F. & Lieberstein, H. M.1959Numerical solution of the boundary layer equations without similarity assumption. J. Aero. Sci.26, 508.

Lees, L.1956Laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds. Jet Propulsion, 26, 259.

Pallone, A.1961Non-similar solution of the compressible-laminar-boundary-layer equations with application to the upstream-transpiration cooling problem. J. Aero. Sci.28, 449.

Stewartson, K.1957On asymptotic expansion in the theory of boundary layer. J. Math. Phys.36, 173.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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