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Received March 16, 2003
Accepted July 15, 2003
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The Temporal Evolution of Thermal Instability in Fluid Layers Isothermally Heated from Below
School of Chemical Engineering, Seoul National University, Seoul 151-744, Korea 1Department of Chemical Engineering, Cheju National University, Cheju 690-756, Korea
ckchoi@snu.ac.kr
Korean Journal of Chemical Engineering, January 2004, 21(1), 41-47(7), 10.1007/BF02705379
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Abstract
The temporal development of thermal disturbances in the fluid layer heated isothermally from below is investigated, based on propagation theory. This theory is examined by using scaling. To examine the behavior of thermal instability the mean-field approximation is employed and resulting equations are solved by Galerkin method. The stability criteria to mark the onset of convective instability are newly suggested as the intersection point of the growth rate of averaged temperature with that of its fluctuation. The resulting critical time is close to that derived from_x000D_
propagation theory. By considering the nonlinear effects, the characteristic times to represent the detection time of manifest convection and also to exhibit the minimum Nusselt number are discussed.
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Foster TD, Phys. Fluids, 8, 1249 (1965)
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Gresho PM, Sani RL, Int. J. Heat Mass Transf., 14, 207 (1971)
Herring JR, J. Atmos. Sci., 20, 325 (1963)
Herring JR, J. Atmos. Sci., 21, 277 (1964)
Hohenberg PC, Swift JB, Phys. Rev., A, 46, 4773 (1992)
Inoue Y, Akutagawa S, Saeki S, Ito R, Kag. Kog. Ronbunshu, 9, 359 (1983)
Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)
Kang KH, Choi CK, Hwang IG, AIChE J., 46(1), 15 (2000)
Kim MC, Park HK, Choi CK, Theor. Comput. Fluid Dynamics, 16, 49 (2002)
Koschmieder EL, Pallas SG, Int. J. Heat Mass Transf., 17, 991 (1974)
Mahler EG, Schechter RS, Wissler EH, Phys. Fluids, 11, 1901 (1968)
Morton BR, J. Mech. Appl. Math., 10, 433 (1957)
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Rayleigh L, Phil. Mag., 32, 529 (1916)
Soberman RK, Phys. Fluids, 2, 131 (1959)
Yang DJ, Choi CK, Phys. Fluids, 14, 930 (2002)
