Journal of Fluid Mechanics

Some perturbation solutions in laminar boundary-layer theory

Paul A.  Libby a1 and Herbert  Fox a1
a1 Polytechnic Institute of Brooklyn, Brooklyn, New York

Article author query
libby pa   [Google Scholar] 
fox h   [Google Scholar] 


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.

(Published Online March 28 2006)
(Received May 13 1963)