Articles & Issues
- Language
- English
- Conflict of Interest
- In relation to this article, we declare that there is no conflict of interest.
- Publication history
-
Received July 18, 2009
Accepted October 24, 2009
-
This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits
unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © KIChE. All rights reserved.
All issues
Onset of buoyancy-driven convection in isotropic porous media heated from below
Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea
mckim@cheju.ac.kr
Korean Journal of Chemical Engineering, March 2010, 27(3), 741-747(7), 10.1007/s11814-010-0149-z
Download PDF
Abstract
A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, fluid-saturated, horizontal, isotropic porous layer. Darcy’s law is employed to explain characteristics of fluid motion, and Boussinesq approximation is used to consider the density variation. Under the principle of exchange of stabilities, a stability analysis is conducted based on the linear stability analysis and energy method and their modifications. The critical condition of onset of buoyancy-driven convection is obtained as a function of the Darcy-Rayleigh_x000D_
number. The propagation theory and the modified energy method under the self-similar coordinate suggest reasonable stability criteria and support each other. The former one based on the linear stability theory predicts more stable results than the latter based on the energy method. The growth period for disturbances to grow seems to be required until the instabilities are detected experimentally.
References
Ennis-King J, Preston I, Paterson L, Phys. Fluids, 17, 084107 (2005)
Xu X, Chen S, Zhang D, Adv. Water Res., 29, 397 (2006)
Riaz A, Hesse M, Tchelepi HA, Orr Jr. FM, J. Fluid Mech., 548, 87 (2006)
Horton CW, Rogers FT, J. Appl. Phys., 6, 367 (1945)
Lapwood ER, Proc. Camb. 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)
Tan KK, Sam T, Jamaludin H, Int. J. Heat Mass Transf., 46(15), 2857 (2003)
Kaviany M, Int. J. Heat Mass Transfer, 27, 2101 (1984)
Choi CK, Park JH, Kim MC, Heat Mass Transfer, 41, 155 (2004)
Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)
Kim MC, Park JH, Choi CK, Chem. Eng. Sci., 60(19), 5363 (2005)
Chandrasekhar S, Hydrodynamic and hydromagnetic stability, Oxford University Press (1961)
Hwang IG, Choi CK, J. Cryst. Growth, 220(3), 326 (2000)
Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)
Kang KH, Choi CK, Phys. Fluids, 9, 7 (1998)
Kang KH, Choi CK, Hwang IG, AIChE J., 46(1), 15 (2000)
Kim MC, Choi CK, Chem. Eng. Sci., 60(3), 599 (2005)
Kim MC, Kim S, Choi CK, Eur. J. Mech. B: Fluid, 25, 74 (2006)
Shen SF, J. Aerospace Sci., 28, 397 (1961)
Ben Y, Demekhin EA, Chang HC, Phys. Fluids, 14, 999 (2002)
Elder JW, J. Fluid Mech., 27, 609 (1967)
Joseph DD, Arch. Rational Mech. Anal., 22, 163 (1966)
Homsy GM, J. Fluid Mech., 60, 129 (1973)
Elder JW, J. Fluid Mech., 32, 69 (1968)
Foster TD, Phys. Fluids, 12, 2482 (1969)
Straughan B, The Energy Method, Stability, and Nonlinear Convection, Springer-Verlag (1992)
Xu X, Chen S, Zhang D, Adv. Water Res., 29, 397 (2006)
Riaz A, Hesse M, Tchelepi HA, Orr Jr. FM, J. Fluid Mech., 548, 87 (2006)
Horton CW, Rogers FT, J. Appl. Phys., 6, 367 (1945)
Lapwood ER, Proc. Camb. 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)
Tan KK, Sam T, Jamaludin H, Int. J. Heat Mass Transf., 46(15), 2857 (2003)
Kaviany M, Int. J. Heat Mass Transfer, 27, 2101 (1984)
Choi CK, Park JH, Kim MC, Heat Mass Transfer, 41, 155 (2004)
Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)
Kim MC, Park JH, Choi CK, Chem. Eng. Sci., 60(19), 5363 (2005)
Chandrasekhar S, Hydrodynamic and hydromagnetic stability, Oxford University Press (1961)
Hwang IG, Choi CK, J. Cryst. Growth, 220(3), 326 (2000)
Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)
Kang KH, Choi CK, Phys. Fluids, 9, 7 (1998)
Kang KH, Choi CK, Hwang IG, AIChE J., 46(1), 15 (2000)
Kim MC, Choi CK, Chem. Eng. Sci., 60(3), 599 (2005)
Kim MC, Kim S, Choi CK, Eur. J. Mech. B: Fluid, 25, 74 (2006)
Shen SF, J. Aerospace Sci., 28, 397 (1961)
Ben Y, Demekhin EA, Chang HC, Phys. Fluids, 14, 999 (2002)
Elder JW, J. Fluid Mech., 27, 609 (1967)
Joseph DD, Arch. Rational Mech. Anal., 22, 163 (1966)
Homsy GM, J. Fluid Mech., 60, 129 (1973)
Elder JW, J. Fluid Mech., 32, 69 (1968)
Foster TD, Phys. Fluids, 12, 2482 (1969)
Straughan B, The Energy Method, Stability, and Nonlinear Convection, Springer-Verlag (1992)
