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Comput Methods Biomech Biomed Engin. 2011 Oct;14(10):853-62. doi: 10.1080/10255842.2010.497490. Epub 2011 May 24.

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels.

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Islamic Azad University, Central Tehran Branch, Young Researchers Club, Tehran, Iran.


In this article, 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 investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.

[Indexed for MEDLINE]

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