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Boundary layer development on a semi-infinite suddenly heated vertical plate

Published online by Cambridge University Press:  06 March 2002

JOHN C. PATTERSON
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811 Australia
TASMAN GRAHAM
Affiliation:
Department of Environmental Engineering, University of WA, Nedlands, WA 6907 Australia Present address: Maunsell McIntyre, P.O. Box 1823, Milton, QLD 4064, Australia.
WOLFGANG SCHÖPF
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811 Australia Present address: Experimentalphysik V, Universitaet Bayreuth, 95440 Bayreuth, Germany.
S. W. ARMFIELD
Affiliation:
Department of Mechanical and Mechatronic Engineering, University of Sydney, Sydney NSW 2006 Australia

Abstract

The flow resulting from suddenly heating a semi-infinite, vertical wall immersed in a stationary fluid has been described in the following way: at any fixed position on the plate, the flow is initially described as one-dimensional and unsteady, as though the plate is doubly infinite; at some later time, which depends on the position, a transition occurs in the flow, known as the leading-edge effect (LEE), and the flow becomes two-dimensional and steady. The transition is characterized by the presence of oscillatory behaviour in the flow parameters, and moves with a speed greater than the maximum fluid velocities present in the boundary layer. A stability analysis of the one-dimensional boundary layer flow performed by Armfield & Patterson (1992) showed that the arrival times of the LEE determined by numerical experiment were predicted well by the speed of the fastest travelling waves arising from a perturbation of the initial one-dimensional flow. In this paper, we describe an experimental investigation of the transient behaviour of the boundary layer on a suddenly heated semi-infinite plate for a range of Rayleigh and Prandtl numbers. The experimental results confirm that the arrival times of the LEE at specific locations along the plate, relatively close to the leading edge, are predicted well by the Armfield & Patterson theory. Further, the periods of the oscillations observed following the LEE are consistent with the period of the maximally amplified waves calculated from the stability result. The experiments also confirm the presence of an alternative mechanism for the transition from one-dimensional to two-dimensional flow, which occurs in advance of the arrival of the LEE at positions further from the leading edge.

Type
Research Article
Copyright
© 2002 Cambridge University Press

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