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The analysis of the flow of a micropolar fluid between two orthogonally moving porous disks with counter rotating directions

100%
Sun Y., Si X., Zheng L., Shen Y., Zhang X.
Open Physics
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2013
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vol. 11
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issue 5
601-614
EN
The present work investigates the unsteady, imcompressible flow of a micropolar fluid between two orthogonally moving porous coaxial disks. The lower and upper disks are rotating with the same angular speed in counter directions. The flows are driven by the contraction and the rotation of the disks. An extension of the Von Kármán type similarity transformation is proposed and is applied to reduce the governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. These differential equations with appropriate boundary conditions are responsible for the flow behavior between large but finite coaxial rotating disks. The analytical solutions are obtained by employing the homotopy analysis method. The effects of some various physical parameters like the expansion ratio, the rotational Reynolds number, the permeability Reynolds number, and micropolar parameters on the velocity fields are observed in graphs and discussed in detail.
2
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Homotopy analysis method for solving Abel differential equation of fractional order

100%
Jafari H., Sayevand K., Tajadodi H., Baleanu D.
Open Physics
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2013
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vol. 11
|
issue 10
1523-1527
EN
In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented.
3
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The flow of a micropolar fluid through a porous channel with expanding or contracting walls

88%
Si X., Zheng L., Zhang X., Chao Y.
Open Physics
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2011
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vol. 9
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issue 3
825-834
EN
The flow of a micropolar fluid in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for the velocity fields and microrotation fields. Graphs are sketched for the effects of some values of parameters, especially the expansion ratio, on the velocity and microrotation fields and associated dynamic characteristics are analyzed in detail.
4
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A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

88%
Dinarvand S.
Open Physics
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2009
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vol. 7
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issue 1
114-122
EN
The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].
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