Laminar Flow Along a Vertical Wall

1968 ◽  
Vol 35 (4) ◽  
pp. 631-633 ◽  
Author(s):  
R. Haugen
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Film Thickness ◽  
Closed Form ◽  
Analytical Study ◽  
Vertical Wall ◽  
Mathematical Solution ◽  
Dimensionless Variables ◽  
Accelerating Flow

An analytical study is presented which describes the laminar accelerating flow of a thin film falling along a vertical wall. The approximate mathematical solution is given with emphasis on the growth and decrease of the boundary layer and film thickness, respectively. These resultant solutions are given in closed form and are found dependent upon two-dimensionless variables: φ2=3U0νgh02 and ζ2=1+2gh0x¯U02.

Effect of a Suction Upon Laminar Flow Along a Vertical Wall

1969 ◽  
Vol 36 (4) ◽  
pp. 877-878 ◽  
Author(s):  
M. A. A. Khan
Keyword(s):  
Thin Film ◽  
Approximate Solution ◽  
Laminar Flow ◽  
Film Thickness ◽  
Vertical Wall

The laminar flow of a thin film past a vertical wall subjected to suction is studied. An approximate solution for small porosity is obtained in the accelerated region. A relation between film thickness and distance traveled is presented.

A Numerical Study of the Laminar Flow of Non-Newtonian Fluids Along a Vertical Wall

1973 ◽  
Vol 40 (1) ◽  
pp. 290-292 ◽  
Author(s):  
T. M. T. Yang ◽  
D. W. Yarbrough
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Laminar Flow ◽  
Power Law ◽  
Analytical Solutions ◽  
Numerical Study ◽  
Vertical Wall ◽  
Newtonian Fluids ◽  
Momentum Integral ◽  
Accelerating Flow

The momentum integral technique is used to describe the steady-state, laminar, accelerating flow of a power-law liquid film along a vertical wall. Values for film thicknesses and boundary-layer thicknesses are obtained numerically and compared with existing analytical solutions for Newtonian fluids.

Laminar Flow Along a Porous Vertical Wall

1982 ◽  
Vol 49 (1) ◽  
pp. 250-253 ◽  
Author(s):  
P. D. Verma ◽  
K. C. Sarangi ◽  
P. D. Ariel
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Laminar Flow ◽  
Film Thickness ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Dimensionless Parameter ◽  
Vertical Wall ◽  
Suction Parameter ◽  
Steady Laminar

The behavior of boundary layer thickness, film thickness is investigated for steady laminar flow along a porous vertical wall. Using a sixth-degree velocity profile the resulting equation from the Von Karman integral equation has been integrated numerically. The boundary layer thickness, film thickness are shown graphically for different values of suction parameter λ1 = v0h0/ν and a dimensionless parameter φ=3νu0gh021/2.

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]

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.

Laminar Flow Along a Vertical Wall

1967 ◽  
Vol 34 (3) ◽  
pp. 535-537 ◽  
Author(s):  
Nabil A. Hassan
Keyword(s):  
Surface Tension ◽  
Laminar Flow ◽  
Vertical Wall ◽  
Universal Curve ◽  
Fluid Films ◽  
Mathematical Solution ◽  
Thin Fluid

The problem of laminar flow of thin fluid films is investigated theoretically. An appropriate mathematical solution is given, where surface tension is neglected. The result is one universal curve.

Organic thin film thickness-dependent photocurrents polarity in graphene heterojunction phototransistor

Carbon ◽  
2021 ◽  
Vol 178 ◽  
pp. 506-514
Author(s):  
Meiyu He ◽  
Jiayue Han ◽  
Xingwei Han ◽  
Jun Gou ◽  
Ming Yang ◽  
...  
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Organic Thin Film ◽  
Thin Film Thickness

scholarly journals Experimental Study on the Thickness-Dependent Hardness of SiO2 Thin Films Using Nanoindentation

Coatings ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Weiguang Zhang ◽  
Jijun Li ◽  
Yongming Xing ◽  
Xiaomeng Nie ◽  
Fengchao Lang ◽  
...  
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Grain Size ◽  
Integrated Circuits ◽  
Film Thickness ◽  
Depth Range ◽  
Micro Electro Mechanical Systems ◽  
Si Substrates ◽  
Sio2 Thin Film ◽  
Average Grain Size

SiO2 thin films are widely used in micro-electro-mechanical systems, integrated circuits and optical thin film devices. Tremendous efforts have been devoted to studying the preparation technology and optical properties of SiO2 thin films, but little attention has been paid to their mechanical properties. Herein, the surface morphology of the 500-nm-thick, 1000-nm-thick and 2000-nm-thick SiO2 thin films on the Si substrates was observed by atomic force microscopy. The hardnesses of the three SiO2 thin films with different thicknesses were investigated by nanoindentation technique, and the dependence of the hardness of the SiO2 thin film with its thickness was analyzed. The results showed that the average grain size of SiO2 thin film increased with increasing film thickness. For the three SiO2 thin films with different thicknesses, the same relative penetration depth range of ~0.4–0.5 existed, above which the intrinsic hardness without substrate influence can be determined. The average intrinsic hardness of the SiO2 thin film decreased with the increasing film thickness and average grain size, which showed the similar trend with the Hall-Petch type relationship.

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