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 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 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 An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

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 Solution of the Fractional Form of Unsteady Squeezing Flow through Porous Medium

2017 ◽  
Vol 2017 ◽  
pp. 1-16
Author(s):  
A. A. Hemeda ◽  
E. E. Eladdad ◽  
I. A. Lairje
Keyword(s):  
Porous Medium ◽  
Fractional Order ◽  
Axisymmetric Flow ◽  
Analytical Techniques ◽  
Approximate Solutions ◽  
Nonlinear Ordinary Differential Equation ◽  
Squeezing Flow ◽  
Normal Velocity ◽  
Adomian Decomposition ◽  
Comparison Of The Results

We propose two friendly analytical techniques called Adomian decomposition and Picard methods to analyze an unsteady axisymmetric flow of nonconducting, Newtonian fluid. This fluid is assumed to be squeezed between two circular plates passing through porous medium channel with slip and no-slip boundary conditions. A single fractional order nonlinear ordinary differential equation is obtained by means of similarity transformation with the help of the fractional calculus definitions. The resulting fractional boundary value problems are solved by the proposed methods. Convergence of the two methods’ solutions is confirmed by obtaining various approximate solutions and various absolute residuals for different values of the fractional order. Comparison of the results of the two methods for different values of the fractional order confirms that the proposed methods are in a well agreement and therefore they can be used in a simple manner for solving this kind of problems. Finally, graphical study for the longitudinal and normal velocity profiles is obtained for various values of some dimensionless parameters and fractional orders.

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 Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 791 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Dian Chen Lu ◽  
Marjan Goodarzi
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transformation ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Integral Transform Method

This study is about the lubrication of a long porous slider in which the fluid is injected into the porous bottom. The similarity transformation reduces the Navier-Stokes equations to couple nonlinear, ordinary differential equations, which are solved by a new algorithm. The proposed technique is based on integral transformation. Apparently, there is great symmetry between proposed method and variation iteration method, Adomian decomposition method but in integral transform method all the boundary conditions are applied, then a recursive scheme is used for the analytical solutions, which is unlike the Variational Iteration Method, Adomian Decomposition Method, and other existing analytical methods. Solutions are obtained for much larger Reynolds numbers, and they are compared with analytical and numerical methods. Effects of Reynolds number on velocity components are presented.

Flow instabilities between two parallel planes semi-obstructed by an easily penetrable porous medium

2011 ◽  
Vol 689 ◽  
pp. 417-433 ◽  
Author(s):  
N. Silin ◽  
J. Converti ◽  
D. Dalponte ◽  
A. Clausse
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Stability Margin ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
The Stability ◽  
Cross Section Profile ◽  
Planar Flows

AbstractA study of instabilities in planar flows produced by the presence of a parallel penetrable porous obstruction is presented. The case considered is a flow between parallel plates partially obstructed by a porous medium. The most unstable perturbation modes are obtained solving numerically the eigenvalue problem derived from the linear stability analysis of the two-dimensional Navier–Stokes equations applied to the geometry of interest. The analysis leads to an extended Orr–Sommerfeld equation including a porous term. It was found that the ratios of the permeability and depth of the obstruction with respect to the free flow layer depth are the relevant parameters influencing the stability margin and the structure of the most unstable modes. To validate the conclusions of the theoretical analysis, an experiment with air flowing through a channel semi-obstructed by a regular array of cylindrical wires was performed. The critical Reynolds number, which was determined by measuring the amplitude of velocity fluctuations at the interface of the porous medium, agrees with the theoretical predictions. The dominant instability mode was characterized by the cross-section profile of the root mean square of the velocity perturbations, which matches reasonable well with the eigenfunction of the most unstable eigenvalue. Also, the wavenumber was determined by correlating the velocity measurements in two sequential locations along the channel, which compares well with the theoretical value.

The Squeezing of a Fluid Between Two Plates

1976 ◽  
Vol 43 (4) ◽  
pp. 579-583 ◽  
Author(s):  
C.-Y. Wang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Nonlinear Ordinary Differential Equation ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Normal Velocity ◽  
Parallel Plates ◽  
Navier Stokes Equations

A viscous fluid lies between two parallel plates which are being squeezed or separated. If the normal velocity is proportional to (1 − αt)−1/2 the unsteady Navier-Stokes equations admit similarity solutions. The resulting nonlinear ordinary differential equation is governed by a parameter S which characterizes unsteadiness. Asymptotic solutions for small S and for large positive S are found which compare well with those obtained by numerical integration. It is found that the resistance is proportional to (1 − αt)−2 but is not necessarily opposite to the direction of motion.

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