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TECHNICAL BRIEFS

Developing Film Flow on an Inclined Plane With a Critical Point

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

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

Kam Ng

Research Laboratories, Eastman Kodak Company, Rochester, NY 14650-2142

J. Fluids Eng 123(3), 698-702 (Apr 16, 2001) (5 pages) doi:10.1115/1.1385516 History: Received July 28, 2000; Revised April 16, 2001
Copyright © 2001 by ASME
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References

Kistler, S. F., and Schweizer, P. M., eds., 1997, Liquid Film Coating, Chapman & Hall, New York.
Schlichting, H., 1979, Boundary-Layer Theory, 7th edition, McGraw-Hill, New York, pp. 157–158.
Ruschak,  K. J., and Weinstein,  S. J., 2000, “Thin-Film Flow at Moderate Reynolds Number,” ASME J. Fluids Eng., 122, pp. 774–778.
Alekseenko, S. V., Nakoryakov, V. E., and Pokusaev, B. G., 1994, Wave Flow of Liquid Films, Begell House, Inc., New York.
Thomas,  S., Hankey,  W., and Faghri,  A., 1990 “One-Dimensional Analysis of the Hydrodynamic and Thermal Characteristics of Thin Film Flows Including the Hydraulic Jump and Rotation,” ASME J. Heat Transfer, 112, pp. 728–735.
Ruschak,  K. J., and Weinstein,  S. J., 1999, “Viscous Thin-Film Flow Over a Round-Crested Weir,” ASME J. Fluids Eng., 121, pp. 673–677.
Anderson,  H. I., 1984, “On Integral Method Predictions of Laminar Film Flow,” Chem. Eng. Sci., 39, pp. 1005–1010.
Anderson,  H. I., 1987, “The Momentum Integral Approach to Laminar Thin-Film Flow,” Proc. ASME Symposium on Thin Films, Vol. 48, pp. 7–13.
Higuera,  F. J., 1994, “The hydraulic jump in viscous laminar flow,” J. Fluid Mech., 274, pp. 69–92.
Ruyer-Quil,  C., and Manneville,  P., 1998, “Modeling film flows down inclined planes,” The European Physical Journal B, 6, pp. 277–292.
Bruley,  D. F., 1965, “Predicting Vertical Film Flow Characteristics in the Entrance Region,” AIChE J., 11, 945–950.
Cerro,  R. L., and Whitaker,  S., 1971, “Entrance Region Flows With a Free Surface: the Falling Liquid Film,” Chem. Eng. Sci., 26, pp. 785–798.
Rosenhead,  L., 1940, “The Steady Two-Dimensional Radial Flow of Viscous Fluid Between Two Inclined Plane Walls,” Proc. R. Soc. London, Ser. A, 175, pp. 436–467.
Watson,  E. J., 1964, “The Radial Spread of a Liquid Jet Over a Horizontal Plane,” J. Fluid Mech., 20, pp. 481–499.

Figures

Grahic Jump Location
Film profiles for Re=50 and θ=3 deg at four values of ω in Eq. (15). The profiles terminate abruptly because of a zero determinant.
Grahic Jump Location
Photograph showing the standing wave at wall inclinations of 1, 1.5, and 2 degrees. The Reynolds number is 16.
Grahic Jump Location
Film profiles for three values of Re at θ=3 deg from Eqs. (19) and (20) (solid lines) and from the boundary-layer equation (points)
Grahic Jump Location
Film profiles at five angles of inclination for the conditions of the photo. The circles show the location where the coefficient of dH/dχ in Eq. (16) vanishes.
Grahic Jump Location
Film profiles by the finite element method for three values of Re at θ=3 deg. Results for two meshes at Re=15 support a conclusion that the waves are not a numerical artifact.
Grahic Jump Location
Film profiles for Re=50 and θ=3 deg from the solution of the boundary layer equation by the method of residuals, from the solution of the boundary layer equation by the Von Mises transformation, and from the solution of the Navier-Stokes equation by the finite-element method. Also shown is the linear profile for negligible gravity 14.
Grahic Jump Location
Extreme velocity profiles for Re=30 and θ=3 deg from the method of residuals (solid curves) and from the finite element method (points)

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