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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508
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BRINKMAN FLOW THROUGH A POROUS CYLINDER EMBEDDED IN ANOTHER UNBOUNDED POROUS MEDIUM
ABSTRAKT
This work concerns the study of steady incompressible viscous fluid flow through a porous cylinder embedded in another infinite porous medium. Brinkman equations for the flow inside and outside porous cylinder in their stream function formulations are used. A closed form exact solution is obtained for the governing equations. Explicit expressions for stream functions, velocity profiles, stresses and pressures are obtained. A new result for drag force experienced by the porous cylinder is investigated. The dependence of the drag coefficient, shear stress, streamlines patterns and velocity profiles for various values of parameters are presented graphically and discussed.
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Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, New York: Dover, 1972.
-
Beavers, G.S. and Joseph, D.D., Boundary Conditions at aNaturally Permeable Wall, J. FluidMech, vol. 30, no. 1, pp. 197-207, 1967.
-
Brinkman, H.C., A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles, Appl. Sci. Res, vol. A1, pp. 27-34, 1947.
-
Deo, S., Stokes Flow past a Swarm of Porous Circular Cylinders with Happel and Kuwabara Boundary Conditions, Sadhana, vol. 29, no. 4, pp. 381-387, 2004.
-
Deo, S., Yadav, P.K., and Tiwari, A., Slow Viscous Flow through a Membrane Built Up from Porous Cylindrical Particles with an Impermeable Core, App. Math. Mod., vol. 34, pp. 1329-1343,2010.
-
Deo, S. and Gupta, B.R., Drag on a Porous Sphere Embedded in Another Porous Medium, J. Porous Media, vol. 13, no. 11, pp. 1009-1016, 2010.
-
Deo, S., Filippov, A., Tiwari, A., Vasin, S., and Starov, V., Hydrodynamic Permeability of Aggregates of Porous Particles with an Impermeable Core, Adv. Coll. Inter. Sci., vol. 164, pp. 21-37,2011.
-
Grosan, T., Postelnicu, A., and Pop, I., Brinkman Flow of a Viscous Fluid through a Spherical Porous Medium Embedded in Another Porous Medium, Trans. Porous Med., vol. 81, pp. 89-103, 2010.
-
Hackborn, W.W., An Analysis of Stokes Flow in an Annular Region, Canad. Appl. Math. Quart., vol. 8, no. 2, pp. 171-182,2000.
-
Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Dordrecht: Kluwer, 1991.
-
Kuwabara, S., The Forces Experienced by Randomly Distributed Parallel Circular Cylinders or Spheres in a Viscous Flow at Small Reynolds Number, J. Phys. Soc. Jpn., vol. 14, pp. 527-532, 1959.
-
Nield, D.A. and Bejan, A., Convection in Porous Media, 3rd ed., New York: Springer, 2006.
-
Pop, I. and Cheng, P., Flow past a Circular Cylinder Embedded in a Porous Medium based on the Brinkman Model, Int. J. Eng. Sci., vol. 30, pp. 257-262, 1992.
-
Rajashekhar, G.P. and Sano, O., Two Dimensional Viscous Flow past a Slightly Deformed Circular Cavity in a Porous Medium, FluidDyn. Res, vol. 28, pp. 281-293,2001.
-
Yadav, P.K. and Deo, S., Stokes Flow past a Porous Spheroid Embedded in Another Porous Medium, Meccanica, vol. 47, pp. 1499-1516, 2012.
-
Yadav, P.K., Tiwari, A., Deo, S., Yadav, M.K., Filippov, A., Vasin, S., and Sherysheva, E., Hydrodynamic Permeability of Biporous Membrane, Colloid J, vol. 75, no. 4, pp. 473-482, 2013.