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The Flow of a Viscous Fluid Past an Inhomogeneous Porous Cylinder
Author(s) -
Singh M. P.,
Gupta J. L.
Publication year - 1971
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19710510102
Subject(s) - potential flow around a circular cylinder , drag , cylinder , mechanics , radius , stokes flow , darcy's law , viscous liquid , permeability (electromagnetism) , physics , stokes' law , drag coefficient , flow (mathematics) , asymptotic expansion , classical mechanics , mathematics , porous medium , porosity , geometry , mathematical analysis , open channel flow , geology , chemistry , geotechnical engineering , biochemistry , computer security , membrane , computer science
The slow stationary motion of a uniformly flowing viscous fluid past a circular porous inhomogeneous cylinder of radius (a + b) is considered. The problem is fully described by the Darcy law, which holds good in the region inside the body, the Navier‐Stokes equations, describing the flow field outside the body, the continuity conditions and the suitable boundary conditions. The solution to the system of equations is obtained by the construction and suitable matching of four simultaneous asymptotic expansions: inner‐most expansion valid in the region 0 ≦ r' ≦ a, interior expansion valid in the region a ≦ r' ≦ (a + b) and the usual inner (Stokes) and outer (Oseen) expansions. The drag formula is expressed in terms of an equivalent permeability. The effect of permeability on the drag is that it reduces the effective radius of the cylinder by a factor exp [–∽KT'/(a + b) 2 ]. Several special cases have been considered.