하부면이 일정열속으로 가열되는 수평 다공질 유체층의 자연대류 유발에 관한 해석

윤도형; 최창균

HWAHAK KONGHAK, Vol.29, No.5, 622-629, October, 1991

Export Citation

하부면이 일정열속으로 가열되는 수평 다공질 유체층의 자연대류 유발에 관한 해석

The Analysis on the Onset of Natural Convection in a Horizontal Porous Layer Uniformly Heated from Below

윤도형, 최창균

초록

유체로 포화되어 있는 초기 정지상태의 수평 다공질 유체층의 하부면이 일정열속으로 가열될 때, 시간의존성이 비선형 온도분포하에서 자연대류 임계시점을 이론적으로 예측하였다. 안정성해석은 선형이론과 안정성교환의 원리하에서 열침투깊이가 길이척도인자로 사용되는 전파이론에 근거하였다. 교란의 시간의존성 변화를 고려하기 위하여 유사변환을 통한 교란방정식의 해를 수치적으로 구하여, 정규적인 세포 형태의 교란이 발생될 임계시점을 Rayleigh 수, Prandtl 수 그리고 Darcy 수의 함수로 구성되는 상관식을 유도하였다. Prandtl 수, Darcy 수가 작아질수록 같은 가열조건에 대하여 자연대류는 늦게 발생되는 것으로 보여진다.

When an initially quiescent, horizontal porous layer saturated with fluid experiences uniform heating from below, the time of the onset of natural convection in time-dependent, nonlinear temperature fields is predicted theoretically. The stability analysis is conducted on the basis of the propagation theory in which the thermal penetration depth is used as a length scaling factor under linear theory with the principle of exchange of stabilities. The solution for disturbance equations of similar transform considering time-de-pendent variations of disturbances is obtained numerically. The resulting correlations of the critical time to mark the onset of regular cells are derived as a function of the Rayleigh number, Prandtl number, and Darcy number. It is seen that natural convection sets in later as the Prandtl number and the Darcy number become smaller.

[References]

Horton CW, Rogers FT, Appl. Phys., 16, 367 (1945)
Lapwood ER, Proc. Camb. Phil. Soc., 44, 508 (1948)
Rudraiah N, Veerappa B, Rao SB, J. Heat Transfer, 102, 254 (1980)
Walker K, Homsy GM, J. Heat Transfer, 99, 338 (1977)
Katto Y, Masuoka T, Int. J. Heat Mass Transf., 10, 297 (1967)
Foster TD, Phys. Fluids, 8, 1249 (1965)
Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)
Wankat PC, Homsy GM, Phys. Fluids, 20, 1200 (1977)
Choi CK, Shin CB, Hwang ST, Proc. 8th Int. Heat Transfer Conf., San Francisco, 3, 1389 (1986)
Yoo JS, Choi CK, Korean J. Chem. Eng., 4(2), 128 (1987)
Lee JD, Choi CK, Shin CB, Int. Chem. Eng., 30, 761 (1988)
Yoo JY, Park P, Choi CK, Ro ST, Int. J. Heat Mass Transf., 30, 927 (1987)
Kim MC, Choi CK, Davis EJ, Int. J. Eng. Fluid Mech., 3, 71 (1990)
Yoon DY, Choi CK, Korean J. Chem. Eng., 6(2), 144 (1989)
Yoon DY, Choi CK, HWAHAK KONGHAK, 27(3), 348 (1989)
Slattery JC, Momentum, Energy, and Mass Transfer in Continua, McGraw-Hill, New York (1972)
Ozisik MN, Heat Conduction, John-Wiley, New York (1980)
Forsythe GE, Malcolm MA, Moler CB, Computer Methods for Mathematical Computations, Prentice-Hall, New Jersey (1977)
Nielsen RC, Sabersky RH, Int. J. Heat Mass Transf., 17, 69 (1974)
Chen K, Chen MM, Sohn CW, J. Fluid Mech., 132, 49 (1983)

[1] Horton CW, Rogers FT, Appl. Phys., 16, 367 (1945)

[2] Lapwood ER, Proc. Camb. Phil. Soc., 44, 508 (1948)

[3] Rudraiah N, Veerappa B, Rao SB, J. Heat Transfer, 102, 254 (1980)

[4] Walker K, Homsy GM, J. Heat Transfer, 99, 338 (1977)

[5] Katto Y, Masuoka T, Int. J. Heat Mass Transf., 10, 297 (1967)

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

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

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

[9] Choi CK, Shin CB, Hwang ST, Proc. 8th Int. Heat Transfer Conf., San Francisco, 3, 1389 (1986)

[10] Yoo JS, Choi CK, Korean J. Chem. Eng., 4(2), 128 (1987)

[11] Lee JD, Choi CK, Shin CB, Int. Chem. Eng., 30, 761 (1988)

[12] Yoo JY, Park P, Choi CK, Ro ST, Int. J. Heat Mass Transf., 30, 927 (1987)

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

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

[15] Yoon DY, Choi CK, HWAHAK KONGHAK, 27(3), 348 (1989)

[16] Slattery JC, Momentum, Energy, and Mass Transfer in Continua, McGraw-Hill, New York (1972)

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

[18] Forsythe GE, Malcolm MA, Moler CB, Computer Methods for Mathematical Computations, Prentice-Hall, New Jersey (1977)

[19] Nielsen RC, Sabersky RH, Int. J. Heat Mass Transf., 17, 69 (1974)

[20] Chen K, Chen MM, Sohn CW, J. Fluid Mech., 132, 49 (1983)