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

Abstract

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-similarity, where the external velocity varies inversely—linear with the distance along the surface ( u e ( x ) = u ∞ 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.