IJPAM: Volume 78, No. 3 (2012)
A NATURALLY PERMEABLE CHANNEL
Department of Mathematics and Statistics
University of the West Indies
St. Augustine, TRINIDAD
Abstract. Laminar flows of two immiscible, incompressible fluids past permeable channels were studied, motivated by works done by Beavers and Joseph [#!boundaryconditions!#] and Bhatt [#!bhatt!#]. These works were based on the observations that flow past permeable membranes were more pronounced than flows past solid membranes, and in this study we treat Plane Couette, Generalized Couette and Poiseuille Flow. Flows in the free channel were modelled by Navier-Stokes equations, and in the porous layer the two layered Brinkman-Darcy configuration used by Hill and Straughan [#!hillstraughan2008!#] was employed. After calculating velocity profiles in all channels, mass flow rates for each of the two fluids were computed. Graphs showing fractional increase in mass flow rates past porous as opposed to non-porous membranes were plotted, and these graphs corresponded well with those done by Beavers and Joseph [#!boundaryconditions!#] and Bhatt [#!bhatt!#].
Received: April 3, 2012
AMS Subject Classification: 76S99
Key Words and Phrases: Porous media, Beaver's Joseph condition, fluids
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395