Journal
TRANSPORT IN POROUS MEDIA
Volume 81, Issue 1, Pages 89-103Publisher
SPRINGER
DOI: 10.1007/s11242-009-9389-y
Keywords
Permeable sphere; Porous media; Brinkman model; Analytical solution
Categories
Funding
- [CEEX ET90 2006-2008]
- [PN-II-ID525/2007]
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An analytical investigation for a two-dimensional steady, viscous, and incompressible flow past a permeable sphere embedded in another porous medium is presented using the Brinkman model, assuming a uniform shear flow far away from the sphere. Semi-analytical solutions of the problem are derived and relevant quantities such as velocities and shearing stresses on the surface of the sphere are obtained. The streamlines inside and outside the sphere and the radial velocity are shown in several graphs for different values of the porous parameters sigma(1) = (mu/(mu) over bar)(a/root K-1) and sigma(2) = (mu/(mu) over bar)(a/root K-2), where a is the radius of the sphere, mu is the dynamic viscosity of the fluid, (mu) over bar is an effective or Brinkman viscosity, while K-1 and K-2 are the permeabilities of the two porous media. It is shown that the dimensionless shearing stress on the sphere is periodic in nature and its absolute value increases with an increase of both porous parameters sigma(1) and sigma(2).
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