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TECHNICAL PAPERS

Laminar, Gravitationally Driven Flow of a Thin Film on a Curved Wall

[+] Author and Article Information
Kenneth J. Ruschak, Steven J. Weinstein

Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14652-3701

J. Fluids Eng 125(1), 10-17 (Jan 22, 2003) (8 pages) doi:10.1115/1.1522412 History: Received June 29, 2001; Revised June 20, 2002; Online January 22, 2003
Copyright © 2003 by ASME
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References

Figures

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Photograph of the standing wave marking the transition from supercritical to subcritical flow on a curved wall; the view is downward toward the standing wave from the side. Label 1, vertical wall; 2, curved wall; 3, standing wave with slope shadowed by the lighting; 4, wall inclined at 2 deg; 5, sidewalls. Areas beyond the sidewalls of the flow have been blackened to eliminate distractions in the surroundings. The computed film thickness profile for these conditions is plotted in Fig. 9.
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Film thickness profiles for Re=20 and δ=0.0147 from the film equation with varying velocity profile and the Navier-Stokes equation on a downwardly curving wall. Only the position of the critical point from the Nusselt film equation is indicated because the profile is indistinguishable. The initially subcritical flow becomes supercritical as wall inclination increases.
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Plot of the velocity profile parameter A for the conditions of Fig. 3. Upstream and downstream, A→0 as the velocity profile becomes fully developed.
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The range of velocity profiles for the conditions of Fig. 3 from the film equation with varying velocity profile and from the Navier-Stokes equation. The two profiles from the film equation correspond to the extreme values of A. The range of velocity at each of 11 nodes is shown for the Navier-Stokes equation.
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Film profiles for Re=20 and δ=0.0093 from the film equation with varying velocity profile and the Navier-Stokes equation on an upwardly curving wall. The initially supercritical flow becomes subcritical as wall inclination decreases.
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An expanded view of film profiles for the conditions of Fig. 6 in the vicinity of the standing wave. The Nusselt film equation gives two sections that are discontinuous at the critical point; the section upstream of the critical point is indistinguishable and not shown
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The range of velocity profiles for the conditions of Fig. 6 from the film equation with varying velocity profile and from the Navier-Stokes equation. The two profiles from the film equation correspond to the extreme values of A. The range of velocity at each of 11 nodes is shown for the Navier-Stokes equation.
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Film profiles from the film equation with varying velocity profile and from the Navier-Stokes equation for flow on an upwardly curving wall. For the middle curves, Re=12,δ=0.021, and Bo=600, the conditions of Fig. 1; for the highest curves, Re=0.1; and for the lowest curves, Re=25.
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Film thickness profile for Re=50 and δ=0.05 from the film equation with varying velocity profile for flow on a downwardly curving wall that is horizontal upstream and vertical downstream. The initially supercritical flow becomes subcritical as film thickness increases due to drag; the flow becomes supercritical again where the wall steepens.
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Flow on a wall inclined at 20 deg from horizontal into a pool at Re=20 with and without surface tension

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