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

The Falkner-Skan flows past stretching boundaries are revisited in this paper. The usual assumption U (w) (x) = lambda 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 < lambda < + 1 dual solutions describing either opposing (lambda < 0) or aiding (lambda > 0) flow regimes were found. In the range lambda > 1 unique solutions occur, while below the critical value lambda (c) = - 2 no solutions exist at all. The mechanical features of these solutions are discussed in some detail.