scholarly journals Approximate analytical solution of the MHD Powell-Eyring fluid flow near accelerated plate

2017 ◽  
Vol 13 (4-1) ◽  
pp. 416-420 ◽  
Author(s):  
Fawzia Mansour Elniel ◽  
Zainal Abdul Aziz ◽  
Faisal Salah ◽  
Shaymaa Mustafa
Keyword(s):  
Magnetic Field ◽  
Sensitivity Analysis ◽  
Shear Stress ◽  
Fluid Flow ◽  
Decomposition Method ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Material Parameters ◽  
Non Linear Equation ◽  
Adomian Decomposition

 In this article, the non-linear equation of unsteady flow of Powell-Eyring fluid is solved by using Adomian Decomposition Method (ADM). The fluid is assumed to be flowing under the effect of magnetic field. The model is developed for the case of constant accelerated plate. Sensitivity analysis is performed to show the effects of material parameters on the velocity profile and shear stress at the wall. The results confirmed the suitability of ADM in solving nonlinear equations. 

ADOMIAN DECOMPOSITION METHOD FOR MAGNETOHYDRODYNAMIC FLOW OF BLOOD INDUCED BY PERISTALTIC WAVES

2017 ◽  
Vol 17 (01) ◽  
pp. 1750007 ◽  
Author(s):  
G. C. SHIT ◽  
N. K. RANJIT ◽  
A. SINHA
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Decomposition Method ◽  
Flow Characteristics ◽  
Adomian Decomposition Method ◽  
Velocity Slip ◽  
Wave Number ◽  
Axial Velocity Component ◽  
Adomian Decomposition ◽  
Small Change

The present investigation deals with the application of Adomian decomposition method (ADM) to blood flow through an asymmetric non-uniform channel induced by peristaltic wave in the presence of magnetic field and the velocity slip at the wall. The ADM is applied with an aim to avoid any simplifications and restrictions, which changes non-linearity of the problem as well as to provide analytical solution. The blood flowing through the vessel is assumed to be Newtonian and incompressible with constant viscosity. The analytical expressions for the axial velocity component, streamlines and wall shear stress are presented. The numerical results of these physical quantities are obtained for different values of the Reynolds number, wave number and Hartmann number. The results obtained for different values of the parameters involved in the problem under consideration show that the flow is appreciably influenced by the presence of slip velocity as well as magnetic field. From this study, we conclude that the assumption of long wavelength and low Reynolds number overestimates the flow characteristics even for a small change in the parameters.

scholarly journals The Adomian Decomposition Method for Solving a Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lazhar Bougoffa
Keyword(s):  
Oxygen Diffusion ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Diffusion Problem ◽  
Moving Boundary Problem ◽  
Resolution Method ◽  
Adomian Decomposition

This paper begins by giving the results obtained by the Crank-Gupta method and Gupta-Banik method for the oxygen diffusion problem in absorbing tissue, and then we propose a new resolution method for this problem by the Adomian decomposition method. An approximate analytical solution is obtained, which is demonstrated to be quite accurate by comparison with the numerical and approximate solutions obtained by Crank and Gupta. The study confirms the accuracy and efficiency of the algorithm for analytic approximate solutions of this problem.

scholarly journals Estimation of the Shear Stress Parameter of a Power-Law Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Samer S. Al-Ashhab ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Decomposition Method ◽  
Positive Curvature ◽  
Adomian Decomposition Method ◽  
Terminal Point ◽  
Stress Parameter ◽  
Adomian Decomposition ◽  
Higher Order Terms ◽  
Numerical Integrators

We apply the Adomian decomposition method to a power-law problem for solutions that do not change the sign of curvature. In particular we consider solutions with positive curvature. The power series obtained via the Adomian decomposition method is used to estimate the shear stress parameter as well as the instant of time where the solution reaches its terminal point of a steady state. We compare our results with estimates obtained via numerical integrators. More importantly we illustrate that the error is predictable and can be reduced without further effort or using higher order terms in the approximating series.

scholarly journals Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1542
Author(s):  
Saima Rashid ◽  
Khadija Tul Kubra ◽  
Juan Luis García Guirao
Keyword(s):  
Analytical Solution ◽  
Acoustic Waves ◽  
Decomposition Method ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Adomian Decomposition ◽  
Actual Solution ◽  
The Laplace Transform

In this paper, the Aboodh transform is utilized to construct an approximate analytical solution for the time-fractional Zakharov–Kuznetsov equation (ZKE) via the Adomian decomposition method. In the context of a uniform magnetic flux, this framework illustrates the action of weakly nonlinear ion acoustic waves in plasma carrying cold ions and hot isothermal electrons. Two compressive and rarefactive potentials (density fraction and obliqueness) are illustrated. With the aid of the Caputo derivative, the essential concepts of fractional derivatives are mentioned. A powerful research method, known as the Aboodh Adomian decomposition method, is employed to construct the solution of ZKEs with success. The Aboodh transform is a refinement of the Laplace transform. This scheme also includes uniqueness and convergence analysis. The solution of the projected method is demonstrated in a series of Adomian components that converge to the actual solution of the assigned task. In addition, the findings of this procedure have established strong ties to the exact solutions to the problems under investigation. The reliability of the present procedure is demonstrated by illustrative examples. The present method is appealing, and the simplistic methodology indicates that it could be straightforwardly protracted to solve various nonlinear fractional-order partial differential equations.

scholarly journals Sumudu Decomposition Method for Solving Fractional Bratu-Type Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 585-605
Author(s):  
N. B. Manjare ◽  
H. T. Dinde
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Type Differential Equation

The purpose of this paper is to introduce Sumudu decomposition method for solving Fractional Bratu-type differential equation. This method is a combination of the Sumudu transform and Adomian decomposition method. The fractional derivative is described in the Caputo sense. The Sumudu decomposition method is applied to obtain approximate analytical solution of non-linear Fractional Bratu-type differential equation. A novel combination of Sumudu transform and Adomian decomposition provides approximate solution in the form of infinite convergent series solution. The behavior of approximate analytical solutions and exact solutions for different values of α are plotted graphically. The results acquired from Sumudu decomposition method indicates that the proposed method is very well founded, suitable and effective. Finally, some numerical examples are given to illustrate the efficiency and applicability of our method.

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