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The Effect of Permeability on the Drag of a Porous Sphere in a Uniform Stream
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.19710510103
Subject(s) - drag , porosity , reynolds number , permeability (electromagnetism) , mechanics , stokes flow , drag coefficient , darcy's law , stokes' law , porous medium , radius , parasitic drag , mathematics , physics , flow (mathematics) , materials science , mathematical analysis , geometry , classical mechanics , chemistry , turbulence , computer science , composite material , biochemistry , membrane , computer security
The present investigation is concerned with the problem of studying the effect of permeability on drag coefficient for the flow past a porous sphere placed in an otherwise uniform incident stream at low Reynolds number. The problem is formulated using the full Navier‐Stokes equations describing the flow outside the sphere while Darcy's law governs the flow inside the sphere. The solution is, then, sought by the method of matched asymptotic expansions involving three simultaneous expansions up to an order Re. It is found that the effect of porosity on the drag is that it reduces the effective radius a of the sphere by a factor (1 + k'/2a 2 ) −1 , where k' is the permeability.