A new exact solution for boundary layer flow over a stretching plate

In this paper, we give an exact analytical solution of the Falkner-Skan equation for all values of beta. Generalized similarity transformations are used to convert the Prandtl's boundary layer equations into a non-linear ordinary differential equation which accounts two important flow parameters: the pressure gradient parameter beta and velocity ratio parameter epsilon. Our exact solution method embeds a known closed-form solution for beta=-1 as a special case. We also give the Dirichlet's series solution to the problem for epsilon = 0, which is particularly useful when the derivative boundary condition at infinity is zero. We compare the results of both methods with that of direct numerical solution, and found that there is a good agreement between both the results. The results are presented in the form of velocity profiles and skin friction coefficient. Finally, the physical significance of the flow parameters is discussed in detail. (C) 2012 Elsevier Ltd. All rights reserved.