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Received January 7, 2013
Accepted March 3, 2013
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Analysis of onset of buoyancy-driven convection in a fluid layer saturated in anisotropic porous media by the relaxed energy method
Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea
mckim@cheju.ac.kr
Korean Journal of Chemical Engineering, June 2013, 30(6), 1207-1212(6), 10.1007/s11814-013-0039-2
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Abstract
A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law is used to explain characteristics of fluid motion, and the anisotropy of permeability is considered. Under the Boussinesq approximation, the energy stability equations are derived following the energy formulation. The stability equations are analyzed numerically under the relaxed energy stability concept. For the various anisotropic ratios, the critical times are predicted as a function of the Darcy-Rayleigh number, and the critical Darcy-Rayleigh number is also obtained. The present predictions are compared with existing theoretical ones.
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Kneafsey TJ, Pruess K, Transp. Porous Media, 82(1), 123 (2010)
Ennis-King J, Paterson L, SPE J., 84344-PA (2005)
Riaz A, Hesse M, Tchelepi HA, Orr FM, J. Fluid Mech., 548, 87 (2006)
Hassanzadeh H, Pooladi-Darvish M, Keith DW, Transp. Porous Media, 65(2), 193 (2006)
Xu X, Chen S, Zhang Z, Adv. Water Res., 29, 397 (2006)
Rapaka S, Pawar RJ, Stauffer PH, Zhang D, Chen S, J. Fluid Mech., 641, 227 (2009)
Hidalgo J, Carrera J, J. Fluid Mech., 640, 441 (2009)
Slim AC, Ramakrishnan TS, Phys. Fluids., 22, 124103 (2010)
Kim MC, Choi CK, Phys. Fluids., 24, 044102 (2012)
Elenius MT, Nordbotten JM, Kalisch H, IMA J. Appl. Math., 77, 771 (2012)
Horton CW, Rogers FT, J. Appl. Phys., 6, 367 (1945)
Lapwood ER, Proc. Cambridge Phil. Soc., 44, 508 (1948)
Caltagirone JP, Q. J. Mech. Appl. Math., 33, 47 (1980)
YOON DY, CHOI CK, Korean J. Chem. Eng., 6(2), 144 (1989)
Selim A, Rees DAS, J. Porous Media., 10, 1 (2007)
Hassanzadeh H, Pooladi-Darvish M, Keith DW, AIChE J., 53(5), 1121 (2007)
Kim MC, Choi CK, Phys. Fluids., 19, 088103 (2007)
Nield DA, Bejan A, Convection in Porous Media, 4th Ed., Springer (2013)
Hong JS, Kim MC, Transp. Porous Media, 72(2), 241 (2008)
REES DAS, STORESLETTEN L, Transp. Porous Media, 19(1), 79 (1995)
Kim MC, Korean J. Chem. Eng., 30(4), 831 (2013)
Kim MC, Korean J. Chem. Eng., 29(12), 1688 (2012)
Kneafsey TJ, Pruess K, Transp. Porous Media, 82(1), 123 (2010)
