Film Flow Of Fluid Research Articles

Unsteady Drainage of Electrically Conducting Power Law Fluid

In this paper, the thin film flow of a power law MHD fluid on a vertical cylinder f or a drainage problem has been studied. The nonlinear differential equation has been derived from the momentum equation by Jeffrey's approach. Series solutions have been obtained for velocity, flow rate and thickness of the fluid film by Perturbation method. The graphical results for velocity profile and thickness of the film are discussed and examined for different parame ters of interest. Without MHD our problem reduces to well known Newtonian and power law problem.

Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV–KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar–Nepomnyashchy and Johnson–Noble–Rodrigues–Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.

Analysis of Unsteady MHD Thin Film Flow of a Third Grade Fluid with Heat Transfer down an Inclined Plane

An investigation is made for unsteady MHD thin film flow of a third grade fluid down an inclined plane with no slip boundary condition. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved using method of separation of variable and eigen functions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the magnetic field parameter and gravitational parameter depends on time.

Laplace Transform Method for Unsteady Thin Film Flow of a Second Grade Fluid through a Porous Medium

In this article, we have effectively used the Numerical Inversion of Laplace transform to study the time-dependent thin film flow of a second grade fluid flowing down an inclined plane through a porous medium. The solution to the governing equation is obtained by using the standard Laplace transform. However, to transform the obtained solutions from Laplace space back to the original space, we have used the Numerical Inversion of Laplace transform. Graphical results have been presented to show the effects of different parameters involved and to show how the fluid flow evolves with time.

Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface

Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

Variational iteration and Adomian decomposition methods for the nonlinear thin film flow of a Jeffrey-six constant fluid on a vertically moving belt

In this paper, we investigate a thin film flow problem that arises in the lifting of a Jeffrey-six constant fluid on a vertically moving belt. The governing nonlinear differential equation is first integrated analytically and then solved by applying both He's variational iteration method (VIM) and Adomian's decomposition method (ADM). The numerical results obtained by these methods are compared through graphs and no visible difference is observed. This study highlights the significant features of the proposed methods and their ability for solving nonlinear problems arising in non-Newtonian fluid mechanics.

The Drainage of Thin Liquid Films on an Inclined Solid Surface

In this paper, we consider the thinning process of an inclined thin liquid film over a solid boundary with an inclination angle to the horizontal in gravity driven flow. Throughout this work, we assumed that the fluid thickness is constant far behind the front and we neglect the thickness of the film at the beginning of the motion. The equation of the film thickness is obtained analytically, using the similarity method by which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only. The solution of the governing equations of the film thickness is obtained numerically by the Rung-Kutta method with the aid of Mat lab(ode45). We present here some of the theoretical aspects of the instability development in an inclined thin liquid films on a solid surface in two dimensional coordinate system with an inclination angle to the horizontal . There are different types of phenomena that can occur, such as drainage, details of rupture, non-Newtonian surface properties in moving contract lines in thin liquid films (1). These phenomena can help to describe the physical processes that occur in our real world. (2,3) have studied the case of contact line instabilities of thin liquid films but with constant flux configuration and also they considered some global models of a moving contact lines. (4) studied the thin liquid films flowing down the inverted substrate in three dimensional flow. (5) investigated the dynamics of an inclined thin liquid films of variable thickness in steady and unsteady cases and when the film is stationary and uniform. (6) considered the stability of thin liquid films and sessile droplets. The stability of the contact line of thin fluid film flows with constant flux configuration is considered by (7). (8) considered the spreading of thin liquid films with small surface tension in the case when the flow is unsteady. The Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field was considered by (9). In this paper we investigate the drainage of the inclined thin liquid films where the gravity and other forces such as viscous and surface tension forces have a significant effect on the flow of the film. We use the similarity method by which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only. The solution of the governing equations of the liquid film thickness is obtained numerically.

Falling film flow of a viscoelastic fluid along a wall

In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non‐dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear‐thinning and shear‐thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain. Copyright © 2013 John Wiley & Sons, Ltd.

A novel in vitro loading system to produce supraphysiologic oscillatory fluid shear stress

A multi-well fluid loading (MFL) system was developed to deliver oscillatory subphysiologic to supraphysiologic fluid shear stresses to cell monolayers in vitro using standard multi-well culture plates. Computational fluid dynamics modeling with fluid-structure interactions was used to quantify the squeeze film fluid flow between an axially displaced piston and the well plate surface. Adjusting the cone angle of the piston base modulated the fluid pressure, velocity, and shear stress magnitudes. Modeling results showed that there was near uniform fluid shear stress across the well with a linear drop in pressure across the radius of the well. Using the MFL system, RAW 264.7 osteoclastic cells were exposed to oscillatory fluid shear stresses of 0, 0.5, 1.5, 4, 6, and 17Pa. Cells were loaded 1h per day at 1Hz for two days. Compared to sub-physiologic and physiologic levels, supraphysiologic oscillatory fluid shear induced upregulation of osteoclastic activity as measured by tartrate-resistant acid phosphatase activity and formation of mineral resorption pits. Cell number remained constant across all treatment groups.

Stability of two-layer shear-thinning film flows

The stability of a two-layer film flow of non-Newtonian fluids is studied with a linear temporal approach. Shear-thinning fluids are considered, which follow the four-parameter inelastic Carreau model. A modified Orr-Sommerfeld equation system is obtained, which is solved by using a spectral Tau collocation method based on Chebyshev polynomials. The effects of density and viscosity stratification are considered, as well as the influence of the shear-thinning properties of the fluid. It is found that, when the viscosity is stronger in the upper layer, the base flow and the stability properties are almost not influenced by the change of the shear-thinning properties in this upper layer. In the other situations, the shear-thinning properties have an influence on the different instabilities, the long-wave surface instability and the short- and long-wave interface instabilities.

Comparison of optimal homotopy asymptotic method and homotopy perturbation method for strongly non-linear equation

In this paper, we employ an approximate analytical method, namely the optimal homotopy asymptotic method (OHAM), to investigate a thin film flow of a third grade fluid down an inclined plane and provided accurate solution unlike other erroneous results available in the literature. The variation of the velocity field for different parameters is compared with the numerical values obtained by the Runge–Kutta Fehlberg fourth–fifth order numerical method and with the homotopy perturbation method (HPM). Finally, it was found that for all values of parameters OHAM agrees well with the numerical disparate HPM.

Hydrodynamics of nonlinear viscoplastic fluid in cylindrical hydrocyclone

A flow of non-linear viscoplastic fluid film in a cylindrical hydrocyclone was simulated. The distribution of the velocity component and also a dependence of a fluid film thickness on an axial coordinate were determined by numerical solution of a set of rheodynamic model equations for various rheological properties of the liquid and dimensionless quantities. An influence of plastic properties of the liquid on damping of the circumferential component of the velocity was examined. The results were physically substantiated.

English

An investigation is made for unsteady magnetohydrodynamic (MHD) thin film flow of a third grade fluid down an inclined plane. The non-linear partial differential equation governing the flow and heat transfer are reduced to a system of non-linear algebraic equations using implicit finite difference approximation to obtain velocity and temperature profile. The effect of various physical parameter on both velocity and temperature profile obtained are studied through several graphs. It is noticed that the velocity and temperature profile decreases due to increase in third grade parameter and magnetic parameter.   Key word: Non-Newtonian fluid, magnetohydrodynamic (MHD) flow, third grade fluid, implicit finite difference approximation, heat transfer.

Numerical studies for flow and heat transfer of the Powell-Eyring fluid thin film over an unsteady stretching sheet with internal heat generation using the chebyshev finite difference method

An analysis is carried out to study the unsteady two-dimensional Powell-Eyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of a similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of nonlinear ordinary differential equations. A numerical solution of the resulting nonlinear differential equations is found by using an efficient Chebyshev finite difference method. A comparison of numerical results is made with the earlier published results for limiting cases. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.

A numerical study of thin film flow of a non-Newtonian fluid on a vertically moving belt using variational iteration approach

This paper provides an investigation regarding the modeling and analysis of a thin film flow of an Oldroyd 8-constant fluid on a vertically moving belt. The governing nonlinear problem is solved by using Variational Iteration Method (VIM). The results of the present method are then compared with those obtained by Adomian Decomposition Method (ADM) and an excellent agreement is observed. This comparison reveals that VIM may be considered as an efficient alternative method for solving nonlinear problems arising in non-Newtonian fluid mechanics. Expressions for some important physical quantities such as volume flux, average velocity, the belt speed for the lifting of the non-Newtonian fluid are also derived.

Effects of variable fluid properties on the thin film flow of Ostwald-de Waele fluid over a stretching surface

We investigate, in this paper, the effects of thermo-physical properties on the flow and heat transfer in a thin film of a power-law liquid over a horizontal stretching surface in the presence of a viscous dissipation. The fluid properties, namely the fluid viscosity and the fluid thermal conductivity, are assumed to vary with temperature. Using a similarity transformation, the governing partial differential equations with a time dependent boundary are converted into coupled non-linear Ordinary Differential Equations (ODEs) with variable coefficients. Numerical solutions of the coupled ODEs are obtained by a finite difference scheme known as the Keller-box method. Results for the velocity and temperature distributions are presented graphically for different values of the pertinent parameters. The effects of unsteady parameter on the skin friction, the wall temperature gradient and the film thickness are presented and analyzed for zero and non-zero values of the temperature-dependent thermo-physical properties. The results obtained reveal many interesting features that warrant further study on the non-Newtonian thin film fluid flow phenomena, especially the shear-thinning phenomena.

Solution of the steady thin film flow of non-Newtonian fluid on vertical cylinder using Adomian Decomposition Method

In this paper, the steady thin film flow on the outer surface of long vertical cylinder of non-Newtonian Johnson–Segalman fluid for lifting and drainage problems have been investigated. Adomian decomposition (ADM) and numerical methods are applied for the solutions of the non-linear problems. Expressions for the velocity field and average velocity have been derived for both the problems, respectively. For Weissenberg number We=0, we retrieve Newtonian cases for both the problems. We also obtain the results for Maxwell fluid by taking slip parameter a=1. We also discussed the effect of the Stokes number St, the Weissenberg number We, the ratio of viscosities ϕ and the slip parameter a on the fluid flows.

Optimal Homotopy Asymptotic Method for a thin film flow of a pseudo plastic fluid draining down or lifting up on a cylindrical surface

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter ?=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter ? and the thickness ? of the fluid film on the fluid velocities.

Exact solutions for thin film flows of a PTT fluid down an inclined plane and on a vertically moving belt

This paper investigates the exact solutions for the thin film flow of PTT fluid having zero solvent viscosity, in two cases: (i) down an inclined plane and (ii) on a vertically moving belt. The problems are solved taking into consideration both the linear and exponential PTT models. Expressions for important physical quantities such as velocity, volume flow rate and average velocity are also reported.

Two analytical methods applied to study thin film flow of an Eyring-Powell fluid on a vertically moving belt

Two analytical methods applied to study thin film flow of an Eyring-Powell fluid on a vertically moving belt