A series solution of the Falkner–Skan equation using the crocco–wang transformation

Abstract

A direct series solution for the Falkner–Skan equation is obtained by first transforming the problem using the Crocco–Wang transformation. The transformation converts the third-order problem to a second-order two-point boundary value problem. The method first constructs a series involving the unknown skin-friction coefficient [Formula: see text]. Then, [Formula: see text] is determined by using the secant method or Newton’s method. The derivative needed for Newton’s method is also computed using a series derived from the transformed differential equation. The method is validated by solving the Falkner–Skan equation for several cases reported previously in the literature.