Application of a New Method of Approximation in the Solution of Ordinary Differential Equations to the Blasius Equation

[+] Author and Article Information
Ernest D. Kennedy

General Applied Science Laboratories, Inc., Westbury, Long Island, N. Y.

J. Appl. Mech 31(1), 112-114 (Mar 01, 1964) (3 pages) doi:10.1115/1.3629530 History: Received March 13, 1963; Online September 15, 2011


A new method for the approximate solution of ordinary differential equations is applied to the Blasius equation of laminar boundary-layer theory. The Blasius equation is related to a Riccati equation which is, in the first approximation, solved in terms of Airy integrals. The approximation gives a value of the wall shear which is 6 percent below the value calculated by Howarth. In addition to furnishing the wall shear, an explicit expression is derived for the velocity distribution. The new solution is expanded in a convergent series and compared with Blasius’ original series which is known to diverge. The coefficients of only the two lowest order terms agree. Although demonstrated only for the Blasius equation, the method is useful in many problems and is being used to study the Falkner-Skan equation. There is the hope that the analytical expressions for the Blasius function can be used in the many problems where it is the zeroth-order solution and appears as coefficients in the differential equations for the higher order solutions.

Copyright © 1964 by ASME
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