Series solution to the Falkner–Skan equation with stretching boundary

Abstract

A new analytical method, namely homotopy analysis method (HAM), is applied to solve the nonlinear Falkner–Skan equation with stretching boundary and a series solution is given in this paper. The comparisons are also made among the results of the present work, Riley and Weidman’s and numerical method by fourth-order Runge–Kutta method combined with Newton–Raphson technique. It shows that the analytical approximate solution agrees well with numerical method for Falkner–Skan wedge flow ( β > 0) when γ ⩾ 0 and also satisfy the conclusion of Riley and Weidman that there is unique solution in this case, which shows the validity of the present work in this condition. For the case of γ < 0 with a range of values of β, the analytical approximate solution gives upper solution branch of the multiple solutions of the Falkner–Skan equation with stretching boundary by numerical methods of both Riley and Weidman’s and the author’s, and the possible reasons are further analyzed.