Closure to “Discussion of ‘On Laminar Thin-Film Flow Along a Vertical Wall’” (1985, ASME J. Appl. Mech., 52, p. 499)

1985 ◽  
Vol 52 (2) ◽  
pp. 499-499 ◽  
Author(s):  
T. R. Roy
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Vertical Wall ◽  
Thin Film Flow

Thin-Film Flow at Moderate Reynolds Number

2000 ◽  
Vol 122 (4) ◽  
pp. 774-778 ◽  
Author(s):  
Kenneth J. Ruschak ◽  
Steven J. Weinstein
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Free Surface ◽  
Film Flow ◽  
Previous Analysis ◽  
Vertical Wall ◽  
Integral Approach ◽  
Internal Boundary ◽  
Thin Film Flow ◽  
Moderate Reynolds Number

Viscous, laminar, gravitationally-driven flow of a thin film over a round-crested weir is analyzed for moderate Reynolds numbers. A previous analysis of this flow utilized a momentum integral approach with a semiparabolic velocity profile to obtain an equation for the film thickness (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). In this work, a viscous boundary layer is introduced in the manner of Haugen (Haugen, R., 1968, “Laminar Flow Around a Vertical Wall,” ASME J. Appl. Mech. 35, pp. 631–633). As in the previous analysis of Ruschak and Weinstein, the approximate equations have a critical point that provides an internal boundary condition for a bounded solution. The complication of a boundary layer is found to have little effect on the thickness profile while introducing a weak singularity at its beginning. The thickness of the boundary layer grows rapidly, and there is little cumulative effect of the increased wall friction. Regardless of whether a boundary layer is incorporated, the approximate free-surface profiles are close to profiles from finite-element solutions of the Navier-Stokes equation. Similar results are obtained for the related problem of developing flow on a vertical wall (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). Less accurate results are obtained for decelerating flow on a horizontal wall (Watson, E. J., 1964, “The Radial Spread of a Liquid Jet Over a Horizontal Plane,” J. Fluid Mech. 20, pp. 481–499) where the flow is not gravitationally driven. [S0098-2202(00)01904-0]

Influence of Upstream Conditions and Gravity on Highly Inertial Thin-Film Flow

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Roger E. Khayat
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Flow Field ◽  
Film Flow ◽  
Flow Direction ◽  
Vertical Wall ◽  
Galerkin Projection ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Horizontal Wall

Steady two-dimensional thin-film flow of a Newtonian fluid is examined in this theoretical study. The influence of exit conditions and gravity is examined in detail. The considered flow is of moderately high inertia. The flow is dictated by the thin-film equations of boundary layer type, which are solved by expanding the flow field in orthonormal modes in the transverse direction and using Galerkin projection method, combined with integration along the flow direction. Three types of exit conditions are investigated, namely, parabolic, semiparabolic, and uniform flow. It is found that the type of exit conditions has a significant effect on the development of the free surface and flow field near the exit. While for the parabolic velocity profile at the exit, the free surface exhibits a local depression, for semiparabolic and uniform velocity profiles, the height of the film increases monotonically with streamwise position. In order to examine the influence of gravity, the flow is studied down a vertical wall as well as over a horizontal wall. The role of gravity is different for the two types of wall orientation. It is found that for the horizontal wall, a hydraulic-jump-like structure is formed and the flow further downstream exhibits a shock. The influence of exit conditions on shock formation is examined in detail.

On Laminar Thin-Film Flow Along a Vertical Wall

1984 ◽  
Vol 51 (3) ◽  
pp. 691-692 ◽  
Author(s):  
T. R. Roy
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Velocity Profile ◽  
Film Flow ◽  
Vertical Wall ◽  
Thin Film Flow ◽  
Runge Kutta Method ◽  
Parabolic Velocity Profile ◽  
Cubic Polynomial ◽  
Momentum Integral

An accelerating laminar thin-film flow along a vertical wall is investigated in this paper. Using a cubic polynomial for the velocity profile inside the boundary layer the momentum integral equation is solved by a Runge-Kutta method to determine the boundary layer thickness. The corresponding film-thickness is then calculated for the entrance region. These results are compared with the existing results obtained by using a parabolic velocity profile.

Similarity solutions for laminar thin-film flow along a vertical wall

1993 ◽  
Vol 26 (6) ◽  
pp. 928-932 ◽  
Author(s):  
P S Lawrence ◽  
B Nageswara Rao
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Vertical Wall ◽  
Similarity Solutions ◽  
Thin Film Flow

Studies on laminar thin film flow along a vertical wall

1991 ◽  
Vol 89 (1-4) ◽  
pp. 21-31 ◽  
Author(s):  
P. Sam Lawrence ◽  
B. Nageswara Rao
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Vertical Wall ◽  
Thin Film Flow

Thin film flow of magnetohydrodynamic (MHD) pseudo-plastic fluid on vertical wall

2014 ◽  
Vol 245 ◽  
pp. 544-556 ◽  
Author(s):  
M.K. Alam ◽  
A.M. Siddiqui ◽  
M.T. Rahim ◽  
S. Islam ◽  
E.J. Avital ◽  
...  
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Vertical Wall ◽  
Thin Film Flow ◽  
Plastic Fluid

Effects of heat generation/absorption on thin film flow of an unsteady Casson fluid over a penetrable flat plate

2020 ◽  
Author(s):  
Jagadish V. Tawade ◽  
Deena Sunil Sharanappa ◽  
M.B Veena ◽  
S.P. Pallavi
Keyword(s):  
Thin Film ◽  
Flat Plate ◽  
Heat Generation ◽  
Film Flow ◽  
Casson Fluid ◽  
Thin Film Flow
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