Abstract
The development with time of the impulsively started laminar flow of a viscous fluid away from a stagnation point is investigated. A series expansion in time is formulated for the shear stress and displacement thickness. This series expansion is obtained from a numerical solution of the full Navier–Stokes equations, and 44 terms are computed for the shear-stress series. The series is analysed and series-improvement techniques are employed to improve its convergence properties. The final series that results converges even for infinite time, and acceptable agreement with the Proudman & Johnson calculations of shear stress for steady-state flow at a stagnation point is obtained. Only 17 terms in the displacement-thickness series are reported, owing to numerical difficulties which are considerably more of an obstacle than in the shear-stress calculation. However, it is observed that the displacement thickness grows exponentially with time. Acceptable agreement with calculations of Proudman & Johnson is obtained for small time. For dimensionless time greater than 2.5, it is concluded that not enough terms are known to extrapolate the displacement-thickness series further.
Published Version
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