On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder

2007 ◽  
Vol 361 (4-5) ◽  
pp. 316-322 ◽  
Author(s):  
T. Hayat ◽  
M. Sajid
Keyword(s):  
Thin Film ◽  
Analytic Solution ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Fourth Grade ◽  
Thin Film Flow ◽  
Grade Fluid ◽  
Fourth Grade Fluid

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 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

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.

scholarly journals On Modified Algorithm for Fourth-Grade Fluid

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Farah Jabeen Awan ◽  
Asif Mehmood ◽  
Syed Tauseef Mohyud-Din ◽  
Saleh M. Hassan
Keyword(s):  
Homotopy Perturbation Method ◽  
Vertical Cylinder ◽  
Fourth Grade ◽  
Outer Side ◽  
Rational Homotopy ◽  
Thin Film Flow ◽  
Homotopy Perturbation ◽  
Grade Fluid ◽  
Fourth Grade Fluid ◽  
Method Analysis

This paper shows the analysis of the thin film flow of fourth-grade fluid on the outer side of a vertical cylinder. Solution of the governing nonlinear equation is obtained by Rational Homotopy Perturbation Method (RHPM); comparison with exact solution reflects the reliability of the method. Analysis shows that this method is reliable for even high nonlinearity. Graphs and tables strengthen the idea.

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.

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