Multiple Solutions of the Falkner–Skan Equation for Flow Past a Stretching Boundary

Similarity solutions for pressure gradient driven flow over a stretching boundary may be obtained when the external velocity and the boundary velocity are each proportional to the same power-law of the downstream coordinate. The problem is governed by a two parameter Falkner–Skan equation with β measuring the stretch rate of the moving boundary andλ equal to the ratio of free stream velocity to boundary velocity. Numerical calculations for | β | 1 over a range of positive and negative λ display rich solution behavior. For- 1 β 0 dual solutions (no solution) are found below (above) a critical value λ ₘ ( β ). When λ > 0 one observes triple solutions for0 < β 0.14, unique solutions for 0.14 β 0.5 and dual solutions for 0.5 < β 1. An exact solution is given for β = - 1 and asymptotic analysis is employed to elucidate the solution behavior for β = 0 as λ → 0 and for β = 1 as λ → - 1.