Developing Film Flow on an Inclined Plane With a Critical Point
Author:
Ruschak Kenneth J.1, Weinstein Steven J.1, Ng Kam2
Affiliation:
1. Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14652-3701 2. Research Laboratories, Eastman Kodak Company, Rochester, NY 14650-2142
Abstract
Viscous, laminar, gravitationally-driven flow of a thin film on an inclined plane is analyzed for moderate Reynolds number under critical conditions. A previous analysis of film flow utilized a momentum integral approach with a semiparabolic velocity profile to obtain an ordinary differential equation for the film thickness for flow over a round-crested weir, and the singularity associated with the critical point for a subcritical-to-supercritical transition was removable. For developing flow on a plane with a supercritical-to-subcritical transition, however, the same approach leads to a nonremovable singularity. To eliminate the singularity, the film equations are modified for a velocity profile of changing shape. The resulting predictions compare favorably with those from the two-dimensional boundary-layer equation obtained by finite differences and with those from the Navier-Stokes equation obtained by finite elements.
Publisher
ASME International
Subject
Mechanical Engineering
Reference14 articles.
1. Kistler, S. F., and Schweizer, P. M., eds., 1997, Liquid Film Coating, Chapman & Hall, New York. 2. Schlichting, H., 1979, Boundary-Layer Theory, 7th edition, McGraw-Hill, New York, pp. 157–158. 3. Ruschak, K. J., and Weinstein, S. J., 2000, “Thin-Film Flow at Moderate Reynolds Number,” ASME J. Fluids Eng., 122, pp. 774–778. 4. Alekseenko, S. V., Nakoryakov, V. E., and Pokusaev, B. G., 1994, Wave Flow of Liquid Films, Begell House, Inc., New York. 5. 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.
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