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 ββ. 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 ββ and velocity ratio parameter ϵϵ. Our exact solution method embeds a known closed-form solution for β=−1β=−1 as a special case. We also give the Dirichlet's series solution to the problem for ϵ=0ϵ=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.

► A new exact analytical solution to the Falkner–Skan equation for all values of pressure gradient ββ and velocity ratio ϵϵ parameters. ► A closed-form solution is obtained for β=−1β=−1 in terms of error and exponential functions. ► This solution is rewritten in convenient form and used to generalize for any value of ββ. ► The Dirichlet series which is particularly useful when f′(∞)=0f′(∞)=0 is also given in ϵ=0ϵ=0. ► Many interesting physical parameters are discussed.