Thin-film flow of magnetohydrodynamic (MHD) Johnson–Segalman fluid on vertical surfaces using the Adomian decomposition method

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.

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

Canadian Journal of Physics ◽

10.1139/cjp-2012-0335 ◽

2014 ◽

Vol 92 (10) ◽

pp. 1196-1202 ◽

Cited By ~ 2

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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MHD and Slip Effect on Two-immiscible Third Grade Fluid on Thin Film Flow over a Vertical Moving Belt

Open Physics ◽

10.1515/phys-2019-0059 ◽

2019 ◽

Vol 17 (1) ◽

pp. 575-586 ◽

Cited By ~ 4

Author(s):

Zeeshan Khan ◽

Nasser Tairan ◽

Wali Khan Mashwani ◽

Haroon Ur Rasheed ◽

Habib Shah ◽

...

Keyword(s):

Thin Film ◽

Adomian Decomposition Method ◽

Single Layer ◽

Immiscible Fluids ◽

Third Grade ◽

Model Parameters ◽

Thin Film Flow ◽

Coupled Equations ◽

Adomian Decomposition ◽

Layer Flow

Abstract The present paper related to thin film flows of two immiscible third grade fluids past a vertical moving belt with slip conditions in the presence of uniform magnetic field. Immiscible fluids we mean superposed fluids of different densities and viscosities. The basic governing equations of continuity, momentum and energy are incorporated. The modeled coupled equations are solved analytically by using Adomian Decomposition Method (ADM) along with Homotopy Analysis Method (HAM). The residual errors show the authentication of the present work. For comparison, numerical method (ND-Solve) is also applied and good agreement is found. The effects of model parameters on velocity, skin friction and temperature variation have been studied. At the end, the present study is also compared with single layer flow and revealed in close agreement with the result available in the literature.

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Numerical Investigation of Thin Film Flow of a Third-Grade Fluid on a Moving Belt Using Evolutionary Algorithm-Based Heuristic Technique

Journal of Circuits System and Computers ◽

10.1142/s0218126622500116 ◽

2021 ◽

pp. 2250011

Author(s):

Fazal Subhan ◽

Suheel Abdullah Malik ◽

Muhammad Asghar Khan ◽

Muhammad Adnan Aziz ◽

M. Irfan Uddin ◽

...

Keyword(s):

Thin Film ◽

Film Flow ◽

Fitness Function ◽

Third Grade ◽

Third Grade Fluid ◽

Thin Film Flow ◽

Adomian Decomposition ◽

Grade Fluid ◽

The Impact ◽

The Given

This paper presents a stochastic heuristic approach to solve numerically nonlinear differential equation (NLDE) governing the thin film flow of a third-grade fluid (TFF-TGF) on a moving belt. Moreover, the impact on velocity profile due to fluid attribute is also investigated. The estimate solution of the given NLDE is achieved by using the linear combination of Bernstein polynomials with unknown constants. A fitness function is deduced to convert the given NLDE along with its boundary conditions into an optimization problem. Genetic algorithm (GA) is employed to optimize the values of unknown constants. The proposed approach provided results in good agreement with numerical values taken by Runge–Kutta and more accurate than two popular classical methods including Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The error is minimized 10[Formula: see text] times to 10[Formula: see text] times.

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Temperature Dependent Viscosity of a Third Order Thin Film Fluid Layer on a Lubricating Vertical Belt

Abstract and Applied Analysis ◽

10.1155/2015/386759 ◽

2015 ◽

Vol 2015 ◽

pp. 1-13

Author(s):

T. Gul ◽

S. Islam ◽

R. A. Shah ◽

I. Khan ◽

L. C. C. Dennis

Keyword(s):

Thin Film ◽

Variable Viscosity ◽

Fluid Layer ◽

Adomian Decomposition Method ◽

Slip Boundary Condition ◽

Thin Film Flow ◽

Third Order ◽

Temperature Dependent Viscosity ◽

Approximate Analytical Solutions ◽

Adomian Decomposition

This paper aims to study the influence of heat transfer on thin film flow of a reactive third order fluid with variable viscosity and slip boundary condition. The problem is formulated in the form of coupled nonlinear equations governing the flow together with appropriate boundary conditions. Approximate analytical solutions for velocity and temperature are obtained using Adomian Decomposition Method (ADM). Such solutions are also obtained by using Optimal Homotopy Asymptotic Method (OHAM) and are compared with ADM solutions. Both of these solutions are found identical as shown in graphs and tables. The graphical results for embedded flow parameters are also shown.

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