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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 0τ<+. 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 0τ<+. Furthermore, it is shown that a nonlinear initial/boundary-value problem can be replaced by an infinite number of linear boundary-value subproblems.
MSC:
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
76M55Dimensional analysis and similarity (fluid mechanics)