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Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. (English) Zbl 1211.76042
Summary: Unsteady two-dimensional stagnation point flow of an incompressible viscous fluid over a flat deformable sheet is studied when the flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. After a similarity transformation, the unsteady boundary layer equation is solved numerically using the Keller-box method for the whole transient from $\tau =0$ to the steady state $\tau \rightarrow \infty $. Also, a complete analysis is made of the governing equation at $\tau =0$, the initial unsteady flow, at large times $\tau =\infty $, the steady state flow, and a series solution valid at small times $\tau\ll 1$). It is found that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state flow (large time solution).

MSC:
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
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References:
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