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Received September 8, 2003
Accepted September 26, 2003
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Onset of Buoyancy-Driven Convection in the Horizontal Fluid Layer Heated from Below with Time-Dependent Manner
Department of Chemical Engineering, Cheju National University, Cheju 690-756, Korea 1School of Chemical Engineering, Seoul National University, Seoul 151-744, Korea
mckim@cheju.ac.kr
Korean Journal of Chemical Engineering, January 2004, 21(1), 69-74(6), 10.1007/BF02705382
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Abstract
The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with time-dependent manner is analyzed by using propagation theory. Here the dimensionless critical time τc to mark the onset of convective instability is presented as a function of the Rayleigh number Raφ and the Prandtl number Pr. The present stability analysis predicts that τc decreases with increasing Pr for a given Raφ. The present predictions compare reasonably well with existing experimental results. It is found that in deep-pool systems the deviation of temperature profiles from conduction state occurs starting from a certain time τ=(2~4)τc.
References
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Kim MC, Chung TJ, Choi CK, Int. J. Heat Mass Transf., 46(14), 2629 (2003)
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Lee DH, Yoon DY, Choi CK, Int. J. Heat Mass Transf., 43(16), 2895 (2000)
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Tan KK, Thorpe RB, Chem. Eng. Sci., 54(2), 225 (1999)
Yang DJ, Choi CK, Phys. Fluids, 14, 930 (2002)
Choi CK, Kang KH, Kim MC, Hwang IG, Korean J. Chem. Eng., 15(2), 192 (1998)
Choi CK, Kim MC, "Buoyancy Effects in Plane Couette Flow Heated Uniformly from Below," Proc. 10th Int. Heat Transfer Conf., 5, 453 (1994)
Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, "Temporal Evoluation of Thermal Convection in an Initially, Stably Stratified Fluid," Proc. Int. Symposium on Transient Convective Heat and Mass Transfer in Single and Two-Phase Flows (Extended Abstracts), Cesme, pp. 63-66 (2003)
Chung TJ, Park JH, Choi CK, Yoon DY, Int. J. Heat Mass Transf., 45(14), 3061 (2002)
Davaille A, Jaupart C, J. Fluid Mech., 253, 141 (1993)
Davenport IF, King CJ, "The Initiation of Natural Convection Caused by Time-Dependent Profiles," Lawrence Berkeley Laboratory Report No. LBL-660 (1972)
Davenport IF, King CJ, Int. J. Heat Mass Transf., 17, 69 (1974)
Foster TD, Phys. Fluids, 8, 1249 (1965)
Foster TD, Phys. Fluids, 12, 2482 (1969)
Hwang IG, Choi CK, J. Cryst. Growth, 162, 182 (1996)
Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)
Kang KH, Choi CK, Hwang IG, AIChE J., 46(1), 15 (2000)
Kim MC, Baik JS, Hwang IG, Yoon DY, Choi CK, Chem. Eng. Sci., 54(5), 619 (1999)
Kim MC, Chung TJ, Choi CK, Int. J. Heat Mass Transf., 46(14), 2629 (2003)
Kim MC, Park HK, Choi CK, Theoret. Comput. Fluid Dynamics, 16, 49 (2002)
Lee DH, Yoon DY, Choi CK, Int. J. Heat Mass Transf., 43(16), 2895 (2000)
Morton BR, J. Mech. Appl. Math., 10, 433 (1957)
Tan KK, Thorpe RB, Chem. Eng. Sci., 54(2), 225 (1999)
Yang DJ, Choi CK, Phys. Fluids, 14, 930 (2002)
