Creeping flow past and within a permeable spheroid

Numerical simulation on steady flow around and through a porous sphere

“…Vainshtein et al (2002) applied the Stokes and Darcy equations to the fluid motions outside and within the spheroid, respectively. Expressions for the hydrodynamic resistance experienced by spheroids are derived, which showed that the resistance varies significantly with the aspect ratio and permeability.…”

Flow past a porous approximate spherical shell

“…[10]. They have examined the flow past permeable circular disk and elongated rods as limiting casesThe aim of the present paper is to study the flow of incompressible viscous fluid past and within a porous approximate spherical shell.…”

A numerical model of fibrous filters containing deposit

“…Approximating the partial derivatives using finite differences and using equation (19), equations (30) and (31) are written in terms of the unknowns ψ p , ψ' f and ω f on AB, ψ' f and ω' f on BCDA and the knowns ψ f and ω f on BCDA . Hence equations (28), (30) and (31) give 2N f +N p equations in the 2N f +N p unknowns: ψ p , ψ' f and ω f on AB ψ' p on BFEA ψ' f and ω' f on BCDA These were solved and then the complete boundary information on AB obtained, using equation (19) to obtain ψ f , equation (26) to obtain ψ' p , and equation (22) to obtain ω' f .…”

“…Due to the formation of the boundary layer equation (2) is only applicable to high permeability materials. An alternative method is to solve equation (1) in the porous region with additional assumptions on the interface boundary, Vainshtein et al 31 . One of these is a linear relationship between the slip velocity in the free flow and its derivative normal to the surface, Beavers and Joseph 32 .…”