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  1. 2 Open Physics

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  1. 2 2009

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  1. 2 Dinarvand S.

  2. 1 Doosthoseini A.

  3. 1 Rashidi M.

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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

100%
Dinarvand S.
Open Physics
|
2009
|
vol. 7
|
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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Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

51%
Dinarvand S., Rashidi M., Doosthoseini A.
Open Physics
|
2009
|
vol. 7
|
issue 4
791-799
EN
In this paper, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved analytically by using the homotopy analysis method (HAM). Graphical results are presented to investigate the influence of the nondimensional wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.
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