| Popis: |
The problem of the free streamline solutions of the Falkner–Skan equation is revisited in this paper. Until now, such solutions were found for negative values of the pressure gradient parameter β only. All of them are associated with slip velocities − 1 f ′ 0 ∞ and emerge from the trivial solution f = η of the problem. The present paper shows, however, that in the positive range 1 β ∞ , just below the interval − 1 f ′ 0 ∞ , a further branch of free streamline solutions of slip velocities − 2 ≤ f ′ 0 − 1 exists. These new solutions emerge from an exact solution of the Falkner–Skan equation which describes the flow in a converging channel with moving boundaries at the saddle–node bifurcation point f ′ 0 = − 2 , f ′ ′ 0 = 0 . For the large- β asymptotics of this solution branch a new algorithm is presented. The occurrence of further free streamline solutions in the range β 0 , as well as the existence of free streamlines of vanishing slip velocities, f ′ ′ 0 = f ′ 0 = 0 , both for positive and negative values of β is also addressed in the paper. The flow inside a cone is also considered shortly and the occurrence of free streamline solutions is pointed out also in this case. |
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