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.
Developing Film Flow on an Inclined Plane With a Critical Point
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.
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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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