Analysis of Thin Film Flows Using a Flux Vector Splitting1

2003 ◽  
Vol 125 (2) ◽  
pp. 365-374 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega
Keyword(s):  
Thin Film ◽  
Shallow Water ◽  
Radial Flow ◽  
Computational Domain ◽  
Flux Vector ◽  
Thin Film Flow ◽  
Flow Problems ◽  
Shallow Water Approximation ◽  
Flux Vector Splitting ◽  
Film Flows

We propose a flux vector splitting (FVS) for the solution of film flows radially spreading on a flat surface created by an impinging jet using the shallow-water approximation. The governing equations along with the boundary conditions are transformed from the physical to the computational domain and solved in a rectangular grid. A first-order upwind finite difference scheme is used at the point of the shock while a second-order upwind differentiation is applied elsewhere. Higher-order spatial accuracy is achieved by introducing a MUSCL approach. Three thin film flow problems (1) one-dimensional dam break problem, (2) radial flow without jump, and (3) radial flow with jump, are investigated with emphasis in the prediction of hydraulic jumps. Results demonstrate that the method is useful and accurate in solving the shallow water equations for several flow conditions.

A Flux Vector Splitting Technique for Shallow Water Equations

2003 ◽  
Author(s):  
Arturo Pacheco-Vega ◽  
J. Rafael Pacheco ◽  
Tamara Rodic´
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Hydraulic Jump ◽  
Computational Domain ◽  
Flux Vector ◽  
Governing Equations ◽  
Splitting Technique ◽  
Flux Vector Splitting ◽  
Film Flows ◽  
Upwind Finite Difference

We present a flux vector splitting (FVS) for the solution of the shallow water equations with emphasis in their application to film flows for which a hydraulic jump may exist. The governing equations and boundary conditions are transformed from the physical to the computational domain and solved in a rectangular grid. A first-order upwind finite difference scheme is used at the point of the shock while a second-order upwind differentiation is applied elsewhere. Higher-order spatial accuracy is achieved by using a MUSCL approach. Two problems, (a) one-dimensional dam break problem and (b) radial flow with jump, are investigated to show the usefulness and accuracy of the method. Results demonstrate that the method is able to predict accuratelly the hydraulic jump using shallow water theory.

A kinetic flux vector splitting scheme for shallow water flows

2003 ◽  
Vol 26 (6) ◽  
pp. 635-647 ◽  
Author(s):  
S.Q. Zhang ◽  
M.S. Ghidaoui ◽  
W.G. Gray ◽  
N.Z. Li
Keyword(s):  
Shallow Water ◽  
Splitting Scheme ◽  
Flux Vector ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Flux Vector Splitting

scholarly journals Three-dimensional magnetohydrodynamic nanofluid thin-film flow with heat and mass transfer over an inclined porous rotating disk

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401986975 ◽  
Author(s):  
Muhammad Jawad ◽  
Zahir Shah ◽  
Aurangzeb Khan ◽  
Saeed Islam ◽  
Hakeem Ullah
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Liquid System ◽  
Thin Film Flow ◽  
Homotopy Analysis ◽  
Injection Effect ◽  
Film Flows

In the present study, the three-dimensional Darcy–Forchheimer magnetohydrodynamic thin-film nanofluid containing flow over an inclined steady rotating plane is observed. Nanofluid thin-film flows are taken thermally radiated and suction/injection effect is also considered. By similarity variables, the partial differential equations are transformed into a set of first-ordinary differential equations (ODES). By Homotopy Analysis Method, the required ODES is solved. The boundary layer over an inclined steady rotating plane is plotted and observed in detail for the velocity, [Formula: see text], and [Formula: see text] profiles. The influence of various embedded parameters such as variable thickness, [Formula: see text]Pr, and thermophoretic parameter on velocity, [Formula: see text], and [Formula: see text] profile. The influence of many parameters is explained by graphs for the velocity, [Formula: see text], and [Formula: see text]. The crucial terms of Nusselt number and Sherwood number have also been observed numerically and physically for [Formula: see text] and [Formula: see text]. Radiation phenomena is the cause of energy to the liquid system. For more rotation parameters, the thermal boundary-layer thickness is reduced.

Micro-Inertia Effects in Laminar Thin-Film Flow Past a Sinusoidal Boundary

1997 ◽  
Vol 119 (1) ◽  
pp. 211-216 ◽  
Author(s):  
Jin Hu ◽  
Hans J. Leutheusser
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Hydrodynamic Lubrication ◽  
Dynamic Properties ◽  
Navier Stokes ◽  
Thin Film Flow ◽  
Navier Stokes Equation ◽  
Inertia Effects ◽  
Experimental Findings ◽  
Film Flows

Micro-inertia effects of surface roughness on hydrodynamic lubrication are analyzed in the light of similitude principles, viz. a newly conceived reduced Reynolds number and the classical parameter of relative roughness. In particular, the dynamic properties of laminar sheet flow in a two-dimensional channel between a sinusoidal wall and a flat wall are studied. FEM solutions of the Navier-Stokes equation are compared with corresponding experimental findings. The latter are gathered in an especially designed laminar-flow wind tunnel. Conclusions are drawn concerning the roughness sensitivity of laminar thin-film flows.

A Continuum Model for Dense Third Body Thin Film Flow: Interactions With Discrete Simulations

2007 ◽  
Author(s):  
John Tichy ◽  
Yves Bertier ◽  
Ivan Iordanoff
Keyword(s):  
Thin Film ◽  
Continuum Theory ◽  
Solid Lubrication ◽  
Thin Film Flow ◽  
Dynamics Model ◽  
Third Body ◽  
Flow Interactions ◽  
Film Flows ◽  
The Continuum ◽  
Lubrication Mechanisms

The present paper applies a recent continuum theory due to Aranson and Tsimring [1] for dense granular flows to thin film flows. Such third body granular flow may apply to solid lubrication mechanisms. The continuum theory is unique in that it addresses solid-like behavior and the transition to fully fluidized behavior. The continuum studies are complemented by a discrete particle dynamics model of Iordanoff et al. [2].

An optimal homotopy asymptotic method applied to the nonlinear thin film flow problems

2018 ◽  
Vol 28 (12) ◽  
pp. 2816-2841 ◽  
Author(s):  
Jalil Manafian ◽  
Cevat Teymuri sindi
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Homotopy Perturbation Method ◽  
Film Flow ◽  
Nonlinear Problems ◽  
Thin Film Flow ◽  
Content Type ◽  
Flow Problems ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method

PurposeThis paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems.Design/methodology/approachThis approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary.FindingsThe obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering.Originality/valueThe proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.

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