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

Abstract

This paper 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 {\it Pseudo-similarity}, where the external velocity varies inversely-linear with the distance in the $x$-direction along the surface ($U_e(x) = U_\infty x^{-1}). $ The analysis shows that solutions exist only for a lateral suction. Here it is assumed that the flow is induced by a continuous permeable surface with the stretching velocity $ U_wx^{-1}.$ 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.