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Received December 1, 2014
Accepted February 9, 2015
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Some theoretical aspects on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated impulsively from below
Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea 1School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea
mckim@jejunu.ac.kr
Korean Journal of Chemical Engineering, December 2015, 32(12), 2400-2405(6), 10.1007/s11814-015-0035-9
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Abstract
Some theoretical aspects of the onset of buoyancy-driven instability in an initially quiescent, isotropic fluidsaturated porous layer are considered. Darcy’s law is employed to examine characteristics of fluid motion under the Boussinesq approximation. Using linear theory, we derive stability equations and transform them in the similarity domain. Based on linear stability equations in the similarity domain, we prove the principle of exchange of stabilities and show that the stability parameter is stationary. The temperature disturbance field is expressed as a series of orthonormal functions and the vertical velocity one is obtained in simple recursive form. The validity of the quasi-steady state approximation (QSSA) is also proved by comparing the stability characteristics under the QSSA with those obtained from the eigenanalysis without the QSSA.
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References
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Lapwood ER, Proc. Camb. Philos. Soc., 44, 508 (1948)
Chandrasekhar S, Hydrodynamic and Hydromagnetic Stability, Oxford University Press (1961).
Caltagirone JP, Quart. J. Mech. Appl. Math., 33, 47 (1980)
YOON DY, CHOI CK, Korean J. Chem. Eng., 6(2), 144 (1989)
Ennis-King J, Preston I, Paterson L, Phys. Fluids, 17, 084107 (2005)
Xu X, Chen S, Zhang D, Adv. Water Res., 29, 397 (2006)
Hassanzadeh H, Pooladi-Darvish M, Keith DW, Transp. Porous Media, 65(2), 193 (2006)
Riaz A, Hesse M, Tchelepi HA, Orr FM, J. Fluid Mech., 548, 87 (2006)
Selim A, Rees DAS, J. Porous Media, 10, 1 (2007)
Wessel-Berg D, SIAM J. Appl. Math., 70, 1219 (2009)
Kim MC, Choi CK, Phys. Fluids, 24, 044102 (2012)
Ben Y, Demekhin EA, Chang HC, Phys. Fluids, 14, 999 (2002)
Pritchard D, Eur. J. Mech. B/Fluids, 28, 564 (2009)
Amundson NR, Mathematical Methods in Chemical Engineering, Prentice Hall (1966).
Kim MC, Korean J. Chem. Eng., 30(6), 1207 (2013)
