Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method

In this article, the self-similar wall jet over an impermeable, resting plane surface (the Glauert-jet) is considered. Through an analytic technique to solve nonlinear problems namely the homotopy analysis method, we obtain an explicit series solution for the Glauert-jet problem. This series solution converges efficiently to the closed-form solution found by Glauert in the whole region 0 ⩽ ξ < +∞. In the frame of the homotopy analysis method, it is shown that the convergence region of the explicit series solution may be adjusted to obtain more accurate results.