Solution of the Magnetohydrodynamics Jeffery-Hamel Flow Equations by the Modified Adomian Decomposition Method

2015 ◽  
Vol 7 (5) ◽  
pp. 675-686 ◽  
Author(s):  
Lei Lu ◽  
Junsheng Duan ◽  
Longzhen Fan
Keyword(s):  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Hartmann Number ◽  
Adomian Decomposition Method ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Equations ◽  
Analytical Approximations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

AbstractIn this paper, the nonlinear boundary value problem (BVP) for the Jeffery-Hamel flow equations taking into consideration the magnetohydrodynamics (MHD) effects is solved by using the modified Adomian decomposition method. We first transform the original two-dimensional MHD Jeffery-Hamel problem into an equivalent third-order BVP, then solve by the modified Adomian decomposition method for analytical approximations. Ultimately, the effects of Reynolds number and Hartmann number are discussed.

scholarly journals EXACT AND APPROXIMATE ANALYTIC SOLUTIONS OF THE JEFFERY-HAMEL FLOW PROBLEM BY THE DUAN-RACH MODIFIED ADOMIAN DECOMPOSITION METHOD

2016 ◽  
Vol 21 (2) ◽  
pp. 174-187 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Samy Mziou ◽  
Randolph C. Rach
Keyword(s):  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Boundary ◽  
Flow Problem ◽  
Adomian Decomposition Method ◽  
Analytic Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).

scholarly journals Solution of Two-Point Linear and Nonlinear Boundary Value Problems with Neumann Boundary Conditions Using a New Modified Adomian Decomposition Method

2020 ◽  
pp. 49-60
Author(s):  
Justina Mulenga ◽  
Patrick Azere Phiri
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Value Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

In this paper, we present the New Modified Adomian Decomposition Method which is a modification of the Modified Adomian Decomposition Method. The new method incorporates the inverse linear operator theorem into the modified Adomian decomposition method for the calculation of u0. Six linear and nonlinear boundary value problems with Neumann conditions are solved in order to test the method. The results show that the method is effective.

scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

MHD Natural Convection Slip Flow through Vertical Porous Plates with Time-Periodic Boundary Conditions

2018 ◽  
Vol 388 ◽  
pp. 135-145
Author(s):  
Samuel Olumide Adesanya ◽  
L. Rundora ◽  
R.S. Lebelo ◽  
K.C. Moloi
Keyword(s):  
Convective Flow ◽  
Decomposition Method ◽  
Hartmann Number ◽  
Slip Flow ◽  
Adomian Decomposition Method ◽  
Periodic Boundary Conditions ◽  
Temperature Profiles ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Time Periodic

In this work, the convective flow of heat generating hydromagnetic fluid through a leaky channel is investigated. Due to channel porosity, the asymmetrical slip conditions are imposed on both walls. The coupled dimensionless partial differential equations are reduced to a system of second-order boundary-value problems based on some flow assumptions and solved by Adomian decomposition method (ADM). Variations in velocity and temperature profiles are presented and discussed in detail. The result of the analysis revealed that increasing Hartmann number decreases the flow velocity while the slip parameters enhance the flow.

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