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Series solutions of unsteady boundary-layer flows over a stretching flat plate. (English) Zbl 1145.76352
Summary: An analytic technique, namely, the homotopy analysis method, is applied to give series solution of the unsteady boundary-layer flows over an impermeable stretching plate. Different from all previous perturbation solutions, our series solutions are convergent in the whole time region \(0 \leq \tau < +\infty \). To the best of our knowledge, such kind of series solution has never been reported for this problem. Besides, two kinds of new similarity transformations about dimensionless time are proposed. Using these two different similarity transformations, we obtain the same convergent solution valid in the whole time region \(0 \leq \tau < +\infty \). Furthermore, it is shown that a nonlinear initial/boundary-value problem can be replaced by an infinite number of linear boundary-value subproblems.

MSC:
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
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