scholarly journals Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hamid Khan ◽  
S. Islam ◽  
Javed Ali ◽  
Inayat Ali Shah
Keyword(s):  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
First Grade ◽  
Analytic Solutions ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Transform Method ◽  
Slip Boundary ◽  
Adomian Decomposition ◽  
Grade Fluid

We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functionsur(r,z,t)=(1/r)(∂ψ/∂z)anduz(r,z,t)=−(1/r)(∂ψ/∂r)and a transformationψ(r,z)=r2F(z). The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.

scholarly journals Analytic Comparison of MHD Squeezing Flow in Porous Medium with Slip Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Transform Method ◽  
Slip Boundary ◽  
Adomian Decomposition

The aim of this paper is to compare the efficiency of various techniques for squeezing flow of an incompressible viscous fluid in a porous medium under the influence of a uniform magnetic field squeezed between two large parallel plates having slip boundary. Fourth-order nonlinear ordinary differential equation is obtained by transforming the Navier-Stokes equations. Resulting boundary value problem is solved using Differential Transform Method (DTM), Daftardar Jafari Method (DJM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Optimal Homotopy Asymptotic Method (OHAM). The problem is also solved numerically using Mathematica solver NDSolve. The residuals of the problem are used to compare and analyze the efficiency and consistency of the abovementioned schemes.

scholarly journals Application of Daftardar Jafari Method to First Grade MHD Squeezing Fluid Flow in a Porous Medium with Slip Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Velocity Profile ◽  
Nonlinear Boundary ◽  
Slip Boundary Condition ◽  
First Grade ◽  
Squeezing Flow ◽  
Parallel Plates ◽  
Governing Equations ◽  
Slip Boundary

In the present work, in the presence of magnetic field and with slip boundary condition, squeezing flow of a Newtonian fluid in a porous medium between two large parallel plates is investigated. The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. By using residual of the problem, the validity of solution is established. The velocity profile is argued through graphs for various values of parameters.

scholarly journals Study of Fuzzified Boundary Value Problems for MHD Couette and Poiseuille Flow of a Differential Type Fluid

2021 ◽  
Author(s):  
Muhammad Nadeem ◽  
Imran Siddique ◽  
Raja Noshad Jamil ◽  
Ali Akgül
Keyword(s):  
Adomian Decomposition Method ◽  
Mhd Flow ◽  
Parallel Plates ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Environment ◽  
Adomian Decomposition ◽  
Grade Fluid ◽  
Differential Type ◽  
Engineering Parameters ◽  
Fuzzy Parameter

Abstract In this work, discuss the magneto-hydro-dynamics (MHD) flow in three fundamental flaws of the third-grade fluid between two parallel plates in a fuzzy environment by the fuzzy Adomian decomposition method (ADM). We extend the work of Kamran and Siddique [19], using fuzzy differential equations (FDEs) and explain our approach with the help of membership function of triangular fuzzy numbers (TFNs). In the end, the effect of the fuzzy parameter (\(\alpha \in [0,\,1]\)), and other engineering parameters on fuzzy velocity profiles are investigating in graphically and tabular representation.

scholarly journals A COMPARISON OF THE ADOMIAN AND HOMOTOPY PERTURBATION METHODS IN SOLVING THE PROBLEM OF SQUEEZING FLOW BETWEEN TWO CIRCULAR PLATES

2010 ◽  
Vol 15 (4) ◽  
pp. 491-504 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Tahira Haroon ◽  
Saira Bhatti ◽  
Ali R. Ansari
Keyword(s):  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Computational Effort ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Circular Plates ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The objective of this paper is to compare two methods employed for solving nonlinear problems, namely the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). To this effect we solve the Navier‐Stokes equations for the unsteady flow between two circular plates approaching each other symmetrically. The comparison between HPM and ADM is bench‐marked against a numerical solution. The results show that the ADM is more reliable and efficient than HPM from a computational viewpoint. The ADM requires slightly more computational effort than the HPM, but it yields more accurate results than the HPM.

scholarly journals SPLINES SOLUTIONS OF HIGHER-ORDER BVPs THAT ARISE IN CONSISTENT MAGNETIZED FORCE FIELD

Fractals ◽  
2021 ◽  
Author(s):  
AASMA KHALID ◽  
AKMAL REHAN ◽  
KOTTAKKARAN SOOPPY NISAR ◽  
ABDEL-HALEEM ABDEL-ATY ◽  
MOHAMMED ZAKARYA
Keyword(s):  
Force Field ◽  
Gravitational Force ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Nonlinear Boundary Value Problems ◽  
Transform Method ◽  
B Spline ◽  
Adomian Decomposition ◽  
Differential Transform ◽  
Cubic Polynomial

In this paper, cubic polynomial and nonpolynomial splines are developed to solve solutions of 10th- and 12th-order nonlinear boundary value problems (BVPs). Such types of BVPs occur when a consistent magnetized force field is applied crosswise the fluid in the substance of gravitational force. We will amend our problem into such a form that converts the system of [Formula: see text]th- [Formula: see text] [Formula: see text]th-order BVPs into a new system of [Formula: see text]nd-order BVPs. The appropriate outcomes by using CP Spline and CNP Spline are compared with the exact root. To show the efficiency of our results, absolute errors calculated by using CP Spline and CNP Spline have been compared with other methods like differential transform method, Adomian decomposition method, variational iteration method, cubic B-spline, homotopy perturbation method, [Formula: see text]th- and [Formula: see text]th-order B-spline and our results are very encouraging. Graphs and tables are also presented in the numerical section of this paper.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

scholarly journals An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

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