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The laminar unsteady flow of a viscous fluid away from a plane stagnation point

Published online by Cambridge University Press:  20 April 2006

Mark J. Hommel
Mark J. Hommel
Affiliation:
Department of Mechanical Engineering, Stanford University Present address: F. G. Bercha and Associates, Houston, Texas.
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 407 - 416
Copyright
© 1983 Cambridge University Press

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