Abstract
In this paper, we propose a reliable treatment for the Falkner-Skan equation, which can be described as the non-dimensional velocity distribution in the laminar boundary layer over a flat plate. We propose an algorithm of two steps that will introduce an exact solution to the equation, followed by a correction to that solution. Three different special cases: Hiemenz flow (beta = 1), Homann flow (beta = 1/2), and Blasius problem (beta = 0) have been considered. When the pressure gradient parameter beta takes sufficiently large values, we use a transformation of variable that reduces the Falkner-Skan equation into an equivalent boundary value problem in a finite domain, and we solve this problem by a different technique that allows us to find f '' (0) : Also, various exact solutions can be obtained in a straightforward manner by using a direct method when beta = -1 : The new technique, as presented in this paper, has been shown to be very efficient for solving the Falkner-Skan equation.