증발이 일어나는 액체층에서 부력 및 표면장력의 변화에 의한 자연대류의 발생

김민찬; 윤도영; 최창균

HWAHAK KONGHAK, Vol.34, No.4, 455-461, August, 1996

Export Citation

증발이 일어나는 액체층에서 부력 및 표면장력의 변화에 의한 자연대류의 발생

The Onset of Natural Convection Driven by Buoyanccy-Forces and Surface-Tension Gradients During Liquid Evaporation

김민찬, 윤도영, 최창균

초록

자유 경계면이 윗면이 증발에 의해 급격히 냉각되는 수평 유체층에서 부력 및 표면장력의 변화에 의하여 유발되는 자연대류의 발생시점을 이론적으로 해석하였다. 시간에 따른 교란의 변화와 기본 온도 분포의 시간 의존형의 비선형성을 고려하는 전파이론을 적용하여 안정성 해석을 수행하였다. 자연대류 발생 시점은 부력효과를 나타내는 Rayleigh수와 표면장력의 변화를 나타내는 Marangoni수에 의하여 결정되었으며, 부력과 표면장력의 효과는 자연대류를 일으키는데 상승작용을함을 알 수 있었다. 본 연구의 해석결과는 프로판올에 대한 실험결과를 합리적으로 설명하였다.

The onset time of natural convection driven by buoyancy forces and surface tension gradients is analysed theoretically in the initially quiescent horizontal fluid layers. The fluid layers experience the rapid evaporative cooling at the upper free surfacce. For this system, the stability analysis is conducted on the basis of the propagation theory that considers the time-dependent properties of disturbances and the nonlinear base temperature profiles. The onset time of natural convection has been governed by the Rayleigh number and the Maragoni number which represent the buoyancy-force and surface-tension effects, respecti- vely. The buoyancy forces and surface-tension gradients reinforce eaach other to induce na- tural convection. The results of the present analysis explain the experimental data of propanolreasonably.

Keywords:Onset Time;Natural Convection;Rayleigh Number;Marangoni Number;Propagation Theory

[References]

Benard H, Ann. Chem. Phys., 23, 14 (1901)
Lord R, Philos. Mag., 32, 529 (1916)
Person JRA, J. Fluid Mech., 4, 489 (1958)
Zierep J, Ortel H, "Convective Transport and Instability Phenomena," G. Braun, Karlsruhe (1982)
Seriven LE, Sternling CV, J. Fluid Mech., 19, 321 (1964)
Nield DA, J. Fluid Mech., 19, 341 (1964)
Lee GJ, Kim MC, Choi CK, Proc. 1st Int. Conf. Transport Phenomena in Processing, 774 (1993)
Foster TD, Phys. Fluids, 8, 1249 (1965)
Wankat PC, Homsy GM, Phys. Fluids, 20, 1200 (1977)
Jhavary BS, Homsy GM, AAPG Bull., 114, 251 (1982)
Choi CK, Shin CB, Hwang ST, Proc. 8th Int. Heat Transfer Conf., 3, 1389 (1984)
Yoon DY, Choi CK, Korean J. Chem. Eng., 6(2), 144 (1989)
Kim MC, Choi CK, Davis EJ, Int. J. Eng. Fluid Mech., 3, 71 (1990)
Chun YH, Choi CK, HWAHAK KONGHAK, 29(3), 381 (1991)
Vidal A, Acrivos A, Ind. Eng. Chem. Fundam., 7, 53 (1968)
Gummerman RJ, Homsy GM, J. Fluid Mech., 68, 191 (1975)
Osizik MN, "Heat Conduction," John-Wiley, New York (1980)
Carslaw HS, Jaeger JC, "Conductionof Heat in Solids," Oxford Univ. Press, England (1959)
Davis EJ, Choi CK, J. Fluid Mech., 81, 565 (1977)
Sparow EM, Goldstein RJ, Jonsson VK, J. Fluid Mech., 18, 513 (1964)
Mathews J, Walker RL, "Mathematical Method of Physics," Benjamin, California (1973)
Foster TD, Phys. Fluids, 12, 2482 (1969)
Lee JD, Choi CK, Shin CB, Int. Chem. Eng., 30, 761 (1990)

[Referenced By]

[1] Benard H, Ann. Chem. Phys., 23, 14 (1901)

[2] Lord R, Philos. Mag., 32, 529 (1916)

[3] Person JRA, J. Fluid Mech., 4, 489 (1958)

[4] Zierep J, Ortel H, "Convective Transport and Instability Phenomena," G. Braun, Karlsruhe (1982)

[5] Seriven LE, Sternling CV, J. Fluid Mech., 19, 321 (1964)

[6] Nield DA, J. Fluid Mech., 19, 341 (1964)

[7] Lee GJ, Kim MC, Choi CK, Proc. 1st Int. Conf. Transport Phenomena in Processing, 774 (1993)

[8] Foster TD, Phys. Fluids, 8, 1249 (1965)

[9] Wankat PC, Homsy GM, Phys. Fluids, 20, 1200 (1977)

[10] Jhavary BS, Homsy GM, AAPG Bull., 114, 251 (1982)

[11] Choi CK, Shin CB, Hwang ST, Proc. 8th Int. Heat Transfer Conf., 3, 1389 (1984)

[12] Yoon DY, Choi CK, Korean J. Chem. Eng., 6(2), 144 (1989)

[13] Kim MC, Choi CK, Davis EJ, Int. J. Eng. Fluid Mech., 3, 71 (1990)

[14] Chun YH, Choi CK, HWAHAK KONGHAK, 29(3), 381 (1991)

[15] Vidal A, Acrivos A, Ind. Eng. Chem. Fundam., 7, 53 (1968)

[16] Gummerman RJ, Homsy GM, J. Fluid Mech., 68, 191 (1975)

[17] Osizik MN, "Heat Conduction," John-Wiley, New York (1980)

[18] Carslaw HS, Jaeger JC, "Conductionof Heat in Solids," Oxford Univ. Press, England (1959)

[19] Davis EJ, Choi CK, J. Fluid Mech., 81, 565 (1977)

[20] Sparow EM, Goldstein RJ, Jonsson VK, J. Fluid Mech., 18, 513 (1964)

[21] Mathews J, Walker RL, "Mathematical Method of Physics," Benjamin, California (1973)

[22] Foster TD, Phys. Fluids, 12, 2482 (1969)

[23] Lee JD, Choi CK, Shin CB, Int. Chem. Eng., 30, 761 (1990)