scholarly journals Thin film flow of an Oldroyd 6-constant fluid over a moving belt: an analytic approximate solution

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 44-64 ◽  
Author(s):  
Remus-Daniel Ene ◽  
Vasile Marinca ◽  
Valentin Bogdan Marinca
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Constant Velocity ◽  
Basic Equation ◽  
Film Flow ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Thin Film Flow ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method

AbstractIn this paper the thin film flow of an Oldroyd 6-constant fluid on a vertically moving belt is investigated. The basic equation of a non-Newtonian fluid in a container with a wide moving belt which passes through the container moving vertically upward with constant velocity, is reduced to an ordinary nonlinear differential equation. This equation is solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM). The solutions take into account the behavior of Newtonian and non-Newtonian fluids. Our procedure intended for solving nonlinear problems does not need small parameters in the equation and provides a convenient way to control the convergence of the approximate solutions.

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.

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

2013 ◽  
Vol 19 (4) ◽  
pp. 513-527
Author(s):  
Kamran Alam ◽  
M.T. Rahim ◽  
S. Islam ◽  
A.M. Sidiqqui
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Cylindrical Surface ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Stokes Number ◽  
Velocity Shear ◽  
Thin Film Flow ◽  
Fluid Velocities ◽  
Optimal Homotopy Asymptotic Method

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.

scholarly journals Analytic Approximate Solution for Falkner-Skan Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Bogdan Marinca
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Rapid Convergence ◽  
Boundary Layer Problem ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method ◽  
Good Agreement ◽  
Layer Problem

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

New Models in the Theory of the Hydrodynamic Lubrication of Rough Surfaces

1988 ◽  
Vol 110 (3) ◽  
pp. 402-407 ◽  
Author(s):  
G. Bayada ◽  
M. Chambat
Keyword(s):  
Thin Film ◽  
Qualitative Study ◽  
Stokes System ◽  
Film Flow ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
New Models ◽  
Small Parameters ◽  
The Mean

Recent advances in mathematical analysis of problems described by several small parameters equations are used to revisit the general roughness problem. In this paper, we put forward a new qualitative study of a thin film flow with a rapidly varying gap. Using an asymptotic analysis of the three-dimensional Stokes system we obtain a family of new generalized Reynolds equations. We are led to distinguish three different cases in which the periodic roughness wavelength is on the order of, greater or shorter than the mean thickness of the gap.

Thin film flow of an unsteady Maxwell fluid over a shrinking/stretching sheet with variable fluid properties

2018 ◽  
Vol 28 (7) ◽  
pp. 1596-1612 ◽  
Author(s):  
N. Faraz ◽  
Y. Khan
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Boundary Layer ◽  
Partial Differential Equation ◽  
Stretching Sheet ◽  
Film Flow ◽  
Maxwell Fluid ◽  
Thin Film Flow ◽  
Content Type ◽  
Fluid Properties

Purpose This paper aims to explore the variable properties of a flow inside the thin film of a unsteady Maxwell fluid and to analyze the effects of shrinking and stretching sheet. Design/methodology/approach The governing mathematical model has been developed by considering the boundary layer limitations. As a result of boundary layer assumption, a nonlinear partial differential equation is obtained. Later on, similarity transformations have been adopted to convert partial differential equation into an ordinary differential equation. A well-known homotopy analysis method is implemented to solve the problem. MATHEMATICA software has been used to visualize the flow behavior. Findings It is observed that variable viscosity does not have a significant effect on velocity field and temperature distribution either in shrinking or stretching case. It is noticed that Maxwell parameter has no dramatic effect on the flow of thin liquid fluid. It has been seen that heat flow increases by increasing the conductivity with temperature in both cases (shrinking/stretching). As a result, fluid temperature goes down when than delta = 0.05 than delta = 0.2. Originality/value To the best of authors’ knowledge, nobody has conducted earlier thin film flow of unsteady Maxwell fluid with variable fluid properties and comparison of shrinking and stretching sheet.

scholarly journals A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Mechee ◽  
N. Senu ◽  
F. Ismail ◽  
B. Nikouravan ◽  
Z. Siri
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Film Flow ◽  
New Method ◽  
Kutta Method ◽  
Thin Film Flow ◽  
Third Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

A study of thin film flow of an Oldroyd 8-constant fluid on a moving belt using variational iteration approach

2014 ◽  
Vol 92 (10) ◽  
pp. 1196-1202 ◽  
Author(s):  
A.M. Siddiqui ◽  
A.A. Farooq ◽  
T. Haroon ◽  
M.A. Rana
Keyword(s):  
Thin Film ◽  
Newtonian Fluid ◽  
Film Flow ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Thin Film Flow ◽  
Belt Speed ◽  
Variational Iteration ◽  
Adomian Decomposition

In this paper, we model a steady thin film flow of an Oldroyd 8-constant fluid on a vertically moving belt. The governing nonlinear differential equation is first integrated exactly and then solved by applying the variational iteration method and the Adomian decomposition method. The numerical results obtained by these methods are then compared through graphs and tables 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. Moreover, a reasonable estimation for the belt speed to lift the non-Newtonian fluid is also recorded. This estimation can be used for experimental verification.

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