CONVECTIVE INSTABILITIES AND TRANSPORT PROPERTIES IN HORIZONTAL FLUID LAYERS

Choi CK; Kang KH; Kim MC; Hwang IG

Korean Journal of Chemical Engineering, Vol.15, No.2, 192-198, March, 1998

This paper concerns the analysis of convective instabilities and fully developed transport properties in Benard convection. The onset of convective instabilities driven by surface-tension variations and buoyancy forces is analyzed theoretically by using the propagation theory we have developed. Based on these stability criteria, the subsequent transport correlations of fully developed buoyancy-driven convection in horizontal fluid layers are suggested. It is found that the present predictions are compared favorably with existing experimental results.

Keywords:Benard Convection;Convective Instabilities;Marangoni Number;Nusselt Number;Rayleigh Number

[References]

Busse FH, J. Math. Phys., 46, 140 (1967)
Brian PLT, Ross JR, AIChE J., 18(3), 582 (1972)
Brian PLT, Vivian JE, Mayr ST, Ind. Eng. Chem. Fundam., 10, 75 (1971)
Cheung FB, J. Fluid Mech., 97, 734 (1980)
Cheung FB, Shiah SW, Cho DH, Baker L, J. Heat Transfer, 113, 919 (1991)
Choi CK, Jang CS, Kim MC, Yoon DY, "Buoyancy Effects in a Volumetrically Heated Horizontal Fluid Layer," Heat Transfer (Proc. 1st European Thermal Sci. and 3rd U.K. National Heat Transfer Conf., Birmingham), Vol. 1, Inst. of Chem. Eng., Rugby, 467 (1992)
Choi CK, Kim MC, "Buoyancy Effects in Plane Couette Flow Heated Uniformly from Below," Heat Transfer (Proc. 10th Int. Heat Transfer Conf., Brighton, Edited by Hewitt, G.F.), Vol. 5, Inst. of Chem. Eng., Rugby, 453 (1994)
Choi CK, Lee JD, Hwang ST, Yoo JS, "The Analysis of Thermal Instability and Heat Transfer Prediction in a Horizontal Fluid Layer Heated from Below," Frontiers of Fluid Mechanics (Edited by Yuen, S.), Pergamon Press, Oxford, 1193 (1988)
Foster TD, Phys. Fluids, 12, 2482 (1969)
Goldstein RJ, Volino RJ, J. Heat Transfer, 117, 808 (1995)
Gumerman RT, Homsy GM, J. Fluid Mech., 68, 191 (1975)
Hinkebein TE, Berg JC, Int. J. Heat Mass Transf., 21, 1241 (1978)
Howard LN, "Convection at High Rayleigh Number," Proc. 11th Int. Cong. Appl. Mech., 1109 (1964)
Hwang IG, Choi CK, J. Cryst. Growth, 162, 182 (1996)
Imaishi N, suzuki Y, Hozawa M, Int. Chem. Eng., 22, 659 (1982)
Kang KH, Choi CK, Phys. Fluids, 9, 7 (1997)
Kim MC, "The Onset of Natural Convection and Heat Transfer Correlations in Systems Experiencing Thermal Boundary Layer Characteristics," Ph.D. Thesis, Seoul National Univ., Seoul (1992)
Kim MC, Yoon DY, Choi CK, HWAHAK KONGHAK, 34(4), 455 (1996)
Lee JD, Choi CK, HWAHAK KONGHAK, 31(3), 338 (1993)
Long RR, J. Fluid Mech., 73, 445 (1976)
Nield D, J. Fluid Mech., 19, 341 (1964)
Pearson JRA, J. Fluid Mech., 4, 489 (1958)
Press HM, Teukolsky SA, Vetterling WT, Flannery BP, Numerical Recipes in Fortran, Cambridge Univ. Press, London (1992)
Rayleigh L, Phil. Mag., 32, 529 (1916)
Stuart JT, J. Fluid Mech., 18, 481 (1964)
Vidal A, Acrivos A, Ind. Eng. Chem. Fundam., 7, 53 (1968)
Yoon DY, Choi CK, Korean J. Chem. Eng., 6(2), 144 (1989)
Yoon DY, Choi CK, Lee CG, Kim MC, Choi U, Korean J. Chem. Eng., 13(1), 15 (1996)

[Referenced By]

[1] Busse FH, J. Math. Phys., 46, 140 (1967)

[2] Brian PLT, Ross JR, AIChE J., 18(3), 582 (1972)

[3] Brian PLT, Vivian JE, Mayr ST, Ind. Eng. Chem. Fundam., 10, 75 (1971)

[4] Cheung FB, J. Fluid Mech., 97, 734 (1980)

[5] Cheung FB, Shiah SW, Cho DH, Baker L, J. Heat Transfer, 113, 919 (1991)

[6] Choi CK, Jang CS, Kim MC, Yoon DY, "Buoyancy Effects in a Volumetrically Heated Horizontal Fluid Layer," Heat Transfer (Proc. 1st European Thermal Sci. and 3rd U.K. National Heat Transfer Conf., Birmingham), Vol. 1, Inst. of Chem. Eng., Rugby, 467 (1992)

[7] Choi CK, Kim MC, "Buoyancy Effects in Plane Couette Flow Heated Uniformly from Below," Heat Transfer (Proc. 10th Int. Heat Transfer Conf., Brighton, Edited by Hewitt, G.F.), Vol. 5, Inst. of Chem. Eng., Rugby, 453 (1994)

[8] Choi CK, Lee JD, Hwang ST, Yoo JS, "The Analysis of Thermal Instability and Heat Transfer Prediction in a Horizontal Fluid Layer Heated from Below," Frontiers of Fluid Mechanics (Edited by Yuen, S.), Pergamon Press, Oxford, 1193 (1988)

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

[10] Goldstein RJ, Volino RJ, J. Heat Transfer, 117, 808 (1995)

[11] Gumerman RT, Homsy GM, J. Fluid Mech., 68, 191 (1975)

[12] Hinkebein TE, Berg JC, Int. J. Heat Mass Transf., 21, 1241 (1978)

[13] Howard LN, "Convection at High Rayleigh Number," Proc. 11th Int. Cong. Appl. Mech., 1109 (1964)

[14] Hwang IG, Choi CK, J. Cryst. Growth, 162, 182 (1996)

[15] Imaishi N, suzuki Y, Hozawa M, Int. Chem. Eng., 22, 659 (1982)

[16] Kang KH, Choi CK, Phys. Fluids, 9, 7 (1997)

[17] Kim MC, "The Onset of Natural Convection and Heat Transfer Correlations in Systems Experiencing Thermal Boundary Layer Characteristics," Ph.D. Thesis, Seoul National Univ., Seoul (1992)

[18] Kim MC, Yoon DY, Choi CK, HWAHAK KONGHAK, 34(4), 455 (1996)

[19] Lee JD, Choi CK, HWAHAK KONGHAK, 31(3), 338 (1993)

[20] Long RR, J. Fluid Mech., 73, 445 (1976)

[21] Nield D, J. Fluid Mech., 19, 341 (1964)

[22] Pearson JRA, J. Fluid Mech., 4, 489 (1958)

[23] Press HM, Teukolsky SA, Vetterling WT, Flannery BP, Numerical Recipes in Fortran, Cambridge Univ. Press, London (1992)

[24] Rayleigh L, Phil. Mag., 32, 529 (1916)

[25] Stuart JT, J. Fluid Mech., 18, 481 (1964)

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

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

[28] Yoon DY, Choi CK, Lee CG, Kim MC, Choi U, Korean J. Chem. Eng., 13(1), 15 (1996)