On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers

The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examine in detail new exact solutions, called Pseudo-shnilarity, where the external velocity varies inversely-linear with the distance along the surface (u(e)(x) = u(infinity)x(-1)). The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties of solutions depend on the suction parameter. Furthermore, making use of the fourth-order Runge-Kutta scheme together with the shooting method, numerical solutions are obtained. (c) 2005 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.