Optimal homotopy asymptotic method with application to thin film flow

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herişanu ◽  
Iacob Nemeş
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Thin Film Flow ◽  
Analytical Technique ◽  
Grade Fluid ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear Problems ◽  
Fourth Grade Fluid

AbstractA new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.

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 Comparison of Optimal Homotopy Asymptotic and Adomian Decomposition Methods for a Thin Film Flow of a Third Grade Fluid on a Moving Belt

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Fazle Mabood ◽  
Nopparat Pochai
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Thin Film Flow ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Grade Fluid

We have investigated a thin film flow of a third grade fluid on a moving belt using a powerful and relatively new approximate analytical technique known as optimal homotopy asymptotic method (OHAM). The variation of velocity profile for different parameters is compared with the numerical values obtained byRunge-Kutta Fehlberg fourth-fifth ordermethod and with Adomian Decomposition Method (ADM). An interesting result of the analysis is that the three terms OHAM solution is more accurate than five terms of the ADM solution and this thus confirms the feasibility of the proposed method.

Numerical study of a thin film flow of fourth grade fluid

2015 ◽  
Vol 25 (4) ◽  
pp. 929-940 ◽  
Author(s):  
Amer Rasheed ◽  
Rab Nawaz ◽  
Sohail Ahmed Khan ◽  
Hanifa Hanif ◽  
Abdul Wahab
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Approximate Solution ◽  
Flow Velocity ◽  
Film Flow ◽  
Thin Film Flow ◽  
Content Type ◽  
Flow Parameters ◽  
Grade Fluid ◽  
Fourth Grade Fluid

Purpose – The purpose of this paper is to study the thin film flow of a fourth grade fluid subject to slip conditions in order to understand its velocity profile. Design/methodology/approach – An exact expression for flow velocity is derived in terms of hyperbolic sine functions. The practical usage of the exact flow velocity is restrictive as it involves very complicated integrals. Therefore, an approximate solution is also derived using a Galerkin finite element method and numerical error analysis is performed. Findings – The behavior of fluid velocity with respect to various flow parameters is discussed. The results are not restrictive to small values of flow parameters unlike those obtained earlier using homotopy analysis method and homotopy perturbation method. Originality/value – An approximate solution based on finite element technique is derived.

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 Unsteady thin film flow of a fourth grade fluid over a vertical moving and oscillating belt

2016 ◽  
Vol 5 (3) ◽  
pp. 223-235 ◽  
Author(s):  
Taza Gul ◽  
Fazle Ghani ◽  
S. Islam ◽  
R.A. Shah ◽  
I. Khan ◽  
...  
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Fourth Grade ◽  
Thin Film Flow ◽  
Grade Fluid ◽  
Fourth Grade Fluid
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