BUOYANCY-DRIVEN CONVECTION IN A HORIZONTAL FLUID LAYER UNDER UNIFORM VOLUMETRIC HEAT SOURCES

Kim MC; Yoon DY; Choi CK

Korean Journal of Chemical Engineering, Vol.13, No.2, 165-171, March, 1996

Buoyancy effect in an internally heated horizontal fluid layer is considered under the linear stability analysis. The horizontal fluid layer is confined between a rigid adiabatic lower boundary and a rigid isothermal upper boundary. The onset of thermal convection is analyzed by using the propagation theory which transforms partial disturbance equations into ordinary ones similarly under the principle of exchanges of stabilities. The eigenvalue problem is solved by the method of rapidly converging power series. In addition, the convection of stability condition to the fully developed heat transport is investigated. Results show that the critical time to mark cellular convection has increased with a decrease in the Prandtl number. Based on the present stability criteria, a new correlation of the Nusselt number is produced as a function of both the Rayleigh number and the Prandtl number. It is shown that the present correlation on thermal convection compares reasonably with existing experimental data of wa-ter.

Keywords:Buoyancy Effects;Propagation Theory;Nusselt Number;Prandtl Number;Rayleigh Number

[References]

Arpaci VS, "Microscales of Turbulence Heat Transfer Correlations," Proc. 10th Int. Transfer Conf., Brighton, U.K., 1, 129 (1994)
Benard H, Annu. Chem. Phys., 23, 62 (1901)
Berg JC, Acrivos A, Boudart M, Adv. Chem. Eng., 6, 61 (1974)
Carslaw HS, Jaeger JC, "Conduction of Heat in Solids," Oxford Univ. Press, England (1959)
Chandrasekhar S, "Hydrodynamic and Hydromagnetic Stability," Oxford Univ. Press, London (1961)
Cheung FB, J. Fluid Mech., 97, 734 (1980)
Choi CK, Kim MC, "Convective Instability in the Thermal Entrance Region of Plane Couette Flow Heated Uniformly from Below," Proc. 9th Int. Heat Transfer Conf., Jerusalem, 2, 519 (1990)
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 Mech. (ed. by Shen Yuen), Pergamon Press, Oxford, 1193 (1988)
Choi CK, Shin CB, Hwang ST, "Thermal Instability in Thermal Entrance Region of Plane Couette Flow Heated Uniformly from Below," Proc. 8th Int. Heat Transfer Conf., San Francisco, 3, 1389 (1984)
Chun YH, Choi CK, HWAHAK KONGHAK, 29(3), 381 (1991)
Eckert ERG, Robert MD, "Analysis of Heat and Mass Transfer," McGraw-Hill, New York (1972)
Fidler H, Wille R, "Warmetransport bie Fier Konvection in Einer Horizontalen Fludssigkeitsschicht mit Volumenheizung," Teil 1, Rep. Deutsch Forschungs Varsuchsantsalt Luft-Raumfahrt, Inst. Turbulenzfenschung, Berlin (1971)
Foster TD, Phys. Fluids, 8, 1249 (1965)
Foster TD, Phys. Fluids, 12, 2482 (1969)
Howard LN, "Convection at High Rayleigh Number," Proc. 11th Int. Congress Appl. Mech., Munich, 1109 (1964)
Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)
Kikuchi Y, Kawasaki T, Shioyama T, Int. J. Heat Mass Transf., 25, 363 (1978)
Kim MC, Choi CK, Davis EJ, Int. J. Eng. Fluid Mech., 3, 71 (1990)
Kim MC, Choi CK, "Buoyancy Effects in Thermally Developing Plane Poiseuille Flow," Proc. 5th Asian Cong. Fluid Mech., Taejon, 1, 310 (1992)
Kulack FA, Emara AA, J. Fluid Mech., 83, 375 (1977)
Kulacki FA, Goldstein RJ, Appl. Sci. Res., 13, 81 (1975)
Kulacki FA, Nagle ME, J. Heat Transfer, 97, 204 (1975)
Long RR, J. Fluid Mech., 73, 445 (1976)
Rayleigh L, Philos. Mag., 32, 529 (1916)
Mathews J, Walker RL, "Mathermatical Method of Physics," Benjamin, California (1973)
Roberts PH, J. Fluid Mech., 30, 30 (1967)
Sparrow EM, Goldstein RJ, Jonsson VK, J. Fluid Mech., 18, 513 (1964)
Stuart JT, J. Fluid Mech., 18, 481 (1964)
Wankat PC, Homsy GM, Phys. Fluids, 20, 1200 (1977)
Yoon DY, Choi CK, Korean J. Chem. Eng., 6(2), 144 (1989)

[Referenced By]

[1] Arpaci VS, "Microscales of Turbulence Heat Transfer Correlations," Proc. 10th Int. Transfer Conf., Brighton, U.K., 1, 129 (1994)

[2] Benard H, Annu. Chem. Phys., 23, 62 (1901)

[3] Berg JC, Acrivos A, Boudart M, Adv. Chem. Eng., 6, 61 (1974)

[4] Carslaw HS, Jaeger JC, "Conduction of Heat in Solids," Oxford Univ. Press, England (1959)

[5] Chandrasekhar S, "Hydrodynamic and Hydromagnetic Stability," Oxford Univ. Press, London (1961)

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

[7] Choi CK, Kim MC, "Convective Instability in the Thermal Entrance Region of Plane Couette Flow Heated Uniformly from Below," Proc. 9th Int. Heat Transfer Conf., Jerusalem, 2, 519 (1990)

[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 Mech. (ed. by Shen Yuen), Pergamon Press, Oxford, 1193 (1988)

[9] Choi CK, Shin CB, Hwang ST, "Thermal Instability in Thermal Entrance Region of Plane Couette Flow Heated Uniformly from Below," Proc. 8th Int. Heat Transfer Conf., San Francisco, 3, 1389 (1984)

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

[11] Eckert ERG, Robert MD, "Analysis of Heat and Mass Transfer," McGraw-Hill, New York (1972)

[12] Fidler H, Wille R, "Warmetransport bie Fier Konvection in Einer Horizontalen Fludssigkeitsschicht mit Volumenheizung," Teil 1, Rep. Deutsch Forschungs Varsuchsantsalt Luft-Raumfahrt, Inst. Turbulenzfenschung, Berlin (1971)

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

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

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

[16] Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)

[17] Kikuchi Y, Kawasaki T, Shioyama T, Int. J. Heat Mass Transf., 25, 363 (1978)

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

[19] Kim MC, Choi CK, "Buoyancy Effects in Thermally Developing Plane Poiseuille Flow," Proc. 5th Asian Cong. Fluid Mech., Taejon, 1, 310 (1992)

[20] Kulack FA, Emara AA, J. Fluid Mech., 83, 375 (1977)

[21] Kulacki FA, Goldstein RJ, Appl. Sci. Res., 13, 81 (1975)

[22] Kulacki FA, Nagle ME, J. Heat Transfer, 97, 204 (1975)

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

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

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

[26] Roberts PH, J. Fluid Mech., 30, 30 (1967)

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

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

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

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