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Received January 26, 2009
Accepted March 1, 2009
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Network numerical simulation of two-dimensional nonlinear micropolar hydrodynamics in a Darcian porous medium
ETS Ingenieros Industriales Campus Muralla del Mar, Departamento de Ingenieria T´ermica y de Fluidos, Universidad Polit´ecnica de Cartegna, Cartagena, Spain 1Energy Systems, Magnetohydrodynamics and Heat Transfer Research,Mechanical Engineering Subject Group, Department of Engineering and Mathematics,Sheaf Building, Sheffield Hallam University, Sheffield, S1 1WB, England, UK 2Fluid Dynamics and Heat Transfer Research, Department of Mechanical Engineering, Southern Taiwan University, 1 Nai-Tai Street, YungKang City, Tainan County, Taiwan
O.Beg@shu.ac.uk
Korean Journal of Chemical Engineering, September 2009, 26(5), 1226-1234(9), 10.1007/s11814-009-0213-8
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Abstract
The two-dimensional steady-state boundary layer flow of an incompressible micropolar fluid in a Darcian porous medium is studied theoretically and computationally. The governing parabolic partial differential equations are reduced to dimensionless form by using a set of transformations, under appropriate boundary conditions. A network simulation method (NSM) solution is presented. Translational velocities (U, V) are found to increase with a rise in Darcy number_x000D_
(Da) and to increase and decrease, respectively, with a rise in micropolar parameter (Er), i.e., Eringen number (ratio of micropolar vortex viscosity to Newtonian viscosity). Micro-rotation is increased with increasing Er and Da values. Translational velocity gradient, ∂U/∂Y and micro-rotation gradient, ∂Ω/∂Y both increase with Darcy number; however, they are both found to decrease with increasing micropolar parameter, Er. The present study finds applications in polymer flows in filtration systems, chemical engineering, biorheology of porous tissue and plastic sheet processing.
Keywords
References
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Nagel LW, SPICE, Computer Program to Simulate Semiconductor Circuits, Memorandum UCB/ERL M520, University of California, Berkeley, USA (1975)
Schlichting H, Boundary-layer theory, McGraw-Hill, New York, 6th edition (1979)
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Khan T, Park JK, Kwon JH, Korean J. Chem. Eng., 24(5), 816 (2007)
Kim YD, Klingenberg DJ, Korean J. Chem. Eng., 14(1), 30 (1997)
Kang SY, Sangani AA, Korean J. Chem. Eng., 19(3), 363 (2002)
Han MS, Jung HC, Park JH, Hyun JC, Kim WN, Korean J. Chem. Eng., 19(2), 337 (2002)
Amanifard N, Khodaparast Haghi A, Korean J. Chem. Eng., 25(2), 191 (2008)
Kim KH, Chung CH, Korean J. Chem. Eng., 18(6), 796 (2001)
Kim DS, Cho ES, Choi CK, Korean J. Chem. Eng., 11(3), 190 (1994)
Jeong GT, Lee GY, Cha JM, Park DH, Korean J. Chem. Eng., 25(1), 118 (2008)
Yim SS, Kwon YD, Kim HI, Korean J. Chem. Eng., 18(5), 741 (2001)
CHUN MS, PARK OO, KIM JK, Korean J. Chem. Eng., 7(2), 126 (1990)
Lee HJ, Suda H, Haraya K, Korean J. Chem. Eng., 22(5), 721 (2005)
Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)
Savins JG, Ind. Eng. Chem., 61, 18 (1969)
Kozicki W, Encyclopedia of Fluid Mechanics, 6, 965 (1986)
Christopher RH, Middleman S, I & EC Fundamentals, 4, 422 (1965)
Kemblowski Z, Michniewicz M, Rheologica Acta., 18, 730 (1979)
Dharmadikhari RV, Kale DD, Chem. Eng. Sci., 40, 527 (1985)
Pascal H, Int. J. Eng. Sci., 21, 199 (1983)
Al-Farris T, Pinder KL, Canadian J. Chem. Eng., 65, 391 (1987)
Bhargava R, Takhar HS, Rawat S, Beg TA, Beg OA, Nonlinear Analysis: Modeling and Control J., 12, 317 (2007)
Yoon DY, Kim MC, Choi CK, Korean J. Chem. Eng., 20(1), 27 (2003)
Takhar HS, Bhargava R, Rawat S, Beg TA, Beg OA, Int. J. Appl. Mech. and Eng., 12, 215 (2007)
Beg OA, Takhar HS, Bharagava R, Rawat S, Prasad VR, Physica Scripta: Proc. Royal Swedish Academy of Sciences, 77, 1 (2008)
So JH, Oh WK, Yang SM, Korean J. Chem. Eng., 21(5), 921 (2004)
Lim YT, Park OO, Korean J. Chem. Eng., 18(1), 21 (2001)
Koo SK, Korean J. Chem. Eng., 23(2), 176 (2006)
Eringen AC, J. Mathematics and Mechanics, 16, 1 (1966)
Stokes VK, Theories of fluids with microstructure: An introduction, Springer, New York/Berlin (1984)
Migun NP, J. Engineering Physics (USSR), 41, 832 (1981)
Peddieson J, McNitt PR, Boundary-layer theory for a micropolar fluid, recent advances in engineering science, Editor: Eringen AC, 5, 1, 405-426, Gordon and Breach, New York (1968)
Gorla RSR, Int. J. Eng. Sci., 25, 759 (1987)
Soundalgekar VM, Takhar HS, Int. J. Eng. Sci., 21, 961 (1983)
Annapurna N, Ramaniah G, Japan J. Appl. Physics, 15, 2441 (1976)
Bernardy T, Vodohospod. Cas., 28, 319 (1980)
Beg OA, Bhargava R, Rawat S, Takhar HS, Beg TA, Nonlinear Analysis: Modeling and Control J., 12, 157 (2007)
Beg OA, Beg TA, Takhar HS, Bharagava R, Hung TK, Int. J. Fluid Mechanics Research, 34, 403 (2007)
Beg OA, Bhargava R, Rawat S, Halim K, Takhar HS, Meccanica, 43, 391 (2008)
Beg OA, Bhargava R, Rawat S, Kahya E, Emirates J. Eng. Res., 13, 51 (2008)
Eringen AC, Mechanics of Micromorphic Continua, Mechanics of Generalized Continua, Kroner E (Editor), Springer-Verlag, Berlin, 18-35 (1968)
Eringen AC, Int. J. Eng. Sci., 2, 205 (1964)
Nath G, Rheologica Acta, 14, 850 (1975)
Ahmadi G, Int. J. Eng. Sci., 14, 639 (1976)
Beg OA, Zueco J, Takhar HS, Beg TA, Nonlinear Analysis: Modelling and Control J., 13, 281 (2008)
Beg OA, Zueco J, Takhar HS, Int. Communications Heat Mass Transfer, 35, 810 (2008)
Beg OA, Takhar HS, Zueco J, Sajid A, Bhargava R, Acta Mechanica, 200, 129 (2008)
Beg OA, Zueco J, Takhar HS, Communications in Nonlinear Science Numerical Simulation, 14, 1082 (2009)
Beg OA, Zueco J, Beg TA, Takhar HS, Acta Mechanica, 202, 181 (2009)
Beg OA, Zueco J, Bhargava R, Takhar HS, Int. J. Thermal Sciences, 48, 913 (2009)
Zueco J, Beg OA, Beg TA, Takhar HS, J. Porous Media, 12, 519 (2008)
Zueco J, Beg OA, Takhar HS, Prasad VR, Applied Thermal Engineering, 29, 2808 (2009)
Pspice 6.0. Irvine, California 92718. Microsim Corporation, 20 Fairbanks (1994)
Nagel LW, SPICE, Computer Program to Simulate Semiconductor Circuits, Memorandum UCB/ERL M520, University of California, Berkeley, USA (1975)
Schlichting H, Boundary-layer theory, McGraw-Hill, New York, 6th edition (1979)
Bear J, Dynamics of fluids in porous media, Dover, New York (1988)
