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Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received June 25, 2019
Accepted July 22, 2019

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.

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Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Layer Bounded by Semi-infinite Coaxial Cylinders

Min Chan Kim^†

Department of Chemical Engineering, Jeju National University, 102, Jejudaehak-ro, Jeju-si, Jeju-do, 63243, Korea

mckim@cheju.ac.kr

Korean Chemical Engineering Research, October 2019, 57(5), 723-729(7), 10.9713/kcer.2019.57.5.723 Epub 20 September 2019

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Abstract

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy’s law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

Keywords

Stability Porous medium Buoyancy-driven convection Coaxial cylinder

References

Horton CW, Rogers FT, J. Appl. Phys., 16(6), 367 (1945)
Lapwood ER, Proc. Camb. Phil. Soc., 44(4), 508 (1948)
Wooding RA, Proc. Roy. Soc. London A, 252(1268), 120 (1959)
Beck JL, Phys. Fluids, 15(8), 1377 (1972)
Zebib A, Phys. Fluids, 21(4), 699 (1978)
Bau HH, Torrance KE, Phys. Fluids, 24(3), 382 (1981)
Haugen KB, Tyvand PA, Phys. Fluids, 15(9), 2661 (2003)
Rees DA, Tyvand PA, J. Eng. Math., 49(2), 181 (2004)
Bringedal C, Berre I, Nordbotten JM, Rees DAS, Phys. Fluids, 23(9), 094109 (2011)
Barletta A, Storesletten L, Phys. Fluids, 25(4), 044101 (2013)
Ennis-King J, Preston I, Paterson L, Phys. Fluids, 17, 084107 (2005)
Riaz A, Hesse M, Tchelepi HA, Orr FM, J. Fluid Mech., 548, 87 (2006)
Kim MC, Choi CK, Phys. Fluids, 24(4), 044102 (2012)
Kim MC, Trans. Porous Med., 97(3), 395 (2013)
Myint PC, Firoozabadi A, Phys. Fluids, 25(4), 044105 (2013)
Nield DA, Bejan A, Convection in porous media. 3rd ed. Springer(2016).
Wessel-Berg D, SIAM J Appl. Math., 70(4), 1219 (2009)
Robinson JL, Phys Fluids, 19(6), 778 (1976)
Ryoo WS, Kim MC, Korean J. Chem. Eng., 35(6), 1247 (2018)
Kim MC, Korean Chem. Eng. Res., 57(1), 142 (2019)
Southard MZ, Dias LJ, Himmelstein KJ, Stella VJ, Pharmaceutical Res., 8(12), 1489 (1991)