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Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

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Dinarvand S., Rashidi M., Doosthoseini A.
Open Physics
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2009
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vol. 7
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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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The flow of a micropolar fluid through a porous channel with expanding or contracting walls

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Si X., Zheng L., Zhang X., Chao Y.
Open Physics
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2011
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vol. 9
|
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.
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