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Falkner–Skan flows past moving boundaries: an exactly solvable case

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Abstract

The Falkner–Skan flows past stretching boundaries are revisited in this paper. The usual assumption U w (x) = λ U(x), i.e. the proportionality of the stretching velocity U w (x) and the free stream velocity U(x) is adopted. For the special case of a converging channel (wedge nozzle), U(x) ~ − 1/x, exact analytical solutions in terms of elementary hyperbolic functions are reported. In the range − 2 < λ < + 1 dual solutions describing either opposing (λ < 0) or aiding (λ > 0) flow regimes were found. In the range λ > 1 unique solutions occur, while below the critical value λ c  = − 2 no solutions exist at all. The mechanical features of these solutions are discussed in some detail.

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  1. Institute of Building Technology, ETH Zürich, Wolfgang-Pauli-Str.1, 8093, Zürich, Switzerland

    E. Magyari

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Magyari, E. Falkner–Skan flows past moving boundaries: an exactly solvable case. Acta Mech 203, 13–21 (2009). https://doi.org/10.1007/s00707-008-0031-9

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