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

Publication history: Received February 8, 2009
Accepted March 15, 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.

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Thermal instability of a fluid layer when cooled isothermally from above

Joo Hyung Moon Kyung Hyun Ahn^† Chang Kyun Choi Min Chan Kim¹

School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea ¹Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea

ahnnet@snu.ac.kr

Korean Journal of Chemical Engineering, November 2009, 26(6), 1441-1446(6), 10.1007/s11814-009-0230-7

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Abstract

The onset of buoyancy-driven convection in an initially motionless isothermal fluid layer is analyzed numerically. The infinite horizontal fluid layer is suddenly cooled from above to relatively low temperature. The rigid lower boundary remains at the initial temperature. In the present transient system, when the Rayleigh number Ra exceeds 1101, thermal convection sets in due to buoyancy force. To trace the temporal growth rates of the mean temperature and its fluctuations we solve the Boussinesq equation by using the finite volume method. We suggest that the system begins to be unstable when the growth rate of temperature disturbances becomes equal to that of the conduction field. Three different characteristic times are classified to interpret numerical results clearly: the onset time of intrinsic instability, the detection time of manifest convection and the undershoot time in a plot of the cooling rate versus time. The present scenario is that the thermal instability sets in at the critical time, then grows super-exponentially up to near the undershoot time, and between these two times the first visible motion is detected. Numerical results are compared with available experimental data. It is found that the above scenario looks promising and the critical time increases with decreasing the Prandtl number Pr and also the Rayleigh number Ra.

Keywords

Buoyancy-driven Convection Growth Rate Thermal Instability Rayleigh Number

References

Morton BR, Q. J. Mech. App. Math., 10, 433 (1957)
Choi CK, Park JH, Kim MC, Heat Mass Trans., 41, 155 (2004)
Choi CK, Kang KH, Phys. Fluids, 9, 7 (1997)
Foster TD, Phys. Fluids, 8, 1249 (1965)
Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)
Tan KK, Thorpe RB, Chem. Eng. Sci., 51(17), 4127 (1996)
Spangenberg WG, Rowland WR, Phys. Fluids, 4, 743 (1961)
Foster TD, Phys. Fluids, 8, 1770 (1965)
Plevan RE, Quinn JA, AIChE J., 12, 894 (1965)
Blair LM, Quinn JA, J. Fluid Mech., 36, 385 (1969)
Mahler EG, Schechter RS, Chem. Eng. Sci., 25, 955 (1970)
Tan KK, Thorpe RB, Chem. Eng. Sci., 47, 3565 (1992)
Chung TJ, Kim MC, Choi CK, Korean J. Chem. Eng., 21(1), 41 (2004)
Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Thermal Sci., 43, 817 (2004)
Park JH, Chung TJ, Choi CK, Kim MC, AIChE J., 52(8), 2677 (2006)
Park JH, Kim MC, Moon JH, Park SH, Choi CK, IASME Transactions, 2, 1674 (2005)
Patankar SV, Numerical heat transfer and fluid flow, Taylor & Francis, New York (1980)