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.
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September 2001
Technical Briefs
Developing Film Flow on an Inclined Plane With a Critical Point
Kenneth J. Ruschak, Senior Research Associate,
Kenneth J. Ruschak, Senior Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14652-3701
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Steven J. Weinstein, Research Associate,
Steven J. Weinstein, Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14652-3701
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Kam Ng, Research Associate,
Kam Ng, Research Associate,
Research Laboratories, Eastman Kodak Company, Rochester, NY 14650-2142
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Kenneth J. Ruschak, Senior Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14652-3701
Steven J. Weinstein, Research Associate
Manufacturing Research and Engineering Organization, Eastman Kodak Company, Rochester, NY 14652-3701
Kam Ng, Research Associate,
Research Laboratories, Eastman Kodak Company, Rochester, NY 14650-2142
Contributed by the Fluids Engineering Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received by the Fluids Engineering Division July 28, 2000; revised manuscript received April 16, 2001. Associate Editor: F. K. Nasden.
J. Fluids Eng. Sep 2001, 123(3): 698-702 (5 pages)
Published Online: April 16, 2001
Article history
Received:
July 28, 2000
Revised:
April 16, 2001
Citation
Ruschak , K. J., Weinstein , S. J., and Ng , K. (April 16, 2001). "Developing Film Flow on an Inclined Plane With a Critical Point ." ASME. J. Fluids Eng. September 2001; 123(3): 698–702. https://doi.org/10.1115/1.1385516
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