The spatiotemporal instability on mixed convection in porous media

Tae Joon Chung; Min Chan Kim; Chang Kyun Choi

Korean Journal of Chemical Engineering, Vol.26, No.2, 332-338, March, 2009

DOI10.1007/s11814-009-0056-3 Export Citation

The spatiotemporal instability on mixed convection in porous media

Tae Joon Chung^†, Min Chan Kim¹, and Chang Kyun Choi²

R&D center, Samsung Electro-Mechanics, Suwon 443-370, Korea
¹Department of Chemical Engineering, Jeju National University, Jeju 690-756, Korea
²School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea

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The absolute and convective instability on mixed convection in porous media is examined, and the phase transition from the oscillatory wave motion to the stationary vortex one is observed. Based on linear and weakly nonlinear analyses, the critical conditions to mark the onset of traveling transverse rolls are analytically obtained for small Peclet numbers. The flow change from transverse wave to longitudinal vortex is reproduced by numerical simulation. These criteria made good agreement with the available experiment data.

Keywords:Absolute Instability;Convective Instability;Porous Media

[References]

Horton CW, Rogers FT, J. Appl. Phys., 16, 367 (1945)
Lapwood ER, Proc. Camb. Phil. Soc., 44, 518 (1948)
Prats M, J. Geophys. Research, 71, 4835 (1966)
Combarnous MA, Bia P, Soc. Pet. Eng. J., 251, 399 (1971)
Hsu CT, Cheng P, Int. J. Heat Mass Transfer, 23, 798 (1980)
Kim MC, Baik JS, Hwang IG, Yoon DY, Choi CK, Chem. Eng. Sci., 54(5), 619 (1999)
Park JH, Chung TJ, Choi CK, Kim MC, AIChE J., 52(8), 2677 (2006)
Choi CK, Chung TJ, Kim MC, Int. J. Heat Mass Transf., 47(12-13), 2629 (2004)
Lee DH, Yoon DY, Choi CK, Int. J. Heat Mass Transf., 43(16), 2895 (2000)
Chung TJ, Park JH, Choi CK, Yoon DY, Int. J. Heat Mass Transf., 45(14), 3061 (2002)
Combarnous M, Convection naturelle et convection mixte en milieu poreux, Ph.D. thesis, Faculte des sciences de l’univ. de Paris (1970)
Delache A, Ouarzazi MN, Combarnous M, Int. J. Heat Mass Transf., 50(7-8), 1485 (2007)
Dufour F, Neel MC, Phys. Fluids, 10, 2198 (1998)
Muller HW, Lucke M, Kamps M, Phys. Rev. A, 45, 3714 (1992)
Recktenwald A, Lucke M, Muller HW, Phys. Rev. E, 48, 4444 (1993)
Patankar SV, Numerical heat transfer and fluid flow, Taylor and Francis (1980)
Blankenbach B, Busse F, Christensen U, Cserepes L, Gunkel D, Hansen U, Harder H, Jarvis G, Koch M, Marquart G, Moore D, Olson P, Schmeling H,Schanubelt T, Geophys. J. Int., 98, 23 (1989)
Walker KL, Homsy GM, J. Fluid Mech., 87, 449 (1978)
Chen SS, Lavine AS, Int. J. Heat Mass Transf., 39(1), 1 (1996)
Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Thermal Sci., 43, 817 (2004)
Ouazzani MT, Caltagirone JP, Meyer G, Mojtabi A, Int. J. Heat Mass Transfer, 32, 261 (1989)
Joseph DD, Stability of fluid motions I and II, Springer-Verlag, New York (1976)
Gill AE, J. Fluid Mech., 35, 545 (1969)
Huerre P, Propagation in system far from equilibrium, edited by Wesfreid JE, Brand HR, Manneville P, Albinet G, Boccara N, 340 (1988)
Newell AC, Whitehead JA, J. Fluid Mech., 38, 279 (1969)
Segel L, J. Fluid Mech., 38, 203 (1969)

[Referenced By]

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

[2] Lapwood ER, Proc. Camb. Phil. Soc., 44, 518 (1948)

[3] Prats M, J. Geophys. Research, 71, 4835 (1966)

[4] Combarnous MA, Bia P, Soc. Pet. Eng. J., 251, 399 (1971)

[5] Hsu CT, Cheng P, Int. J. Heat Mass Transfer, 23, 798 (1980)

[6] Kim MC, Baik JS, Hwang IG, Yoon DY, Choi CK, Chem. Eng. Sci., 54(5), 619 (1999)

[7] Park JH, Chung TJ, Choi CK, Kim MC, AIChE J., 52(8), 2677 (2006)

[8] Choi CK, Chung TJ, Kim MC, Int. J. Heat Mass Transf., 47(12-13), 2629 (2004)

[9] Lee DH, Yoon DY, Choi CK, Int. J. Heat Mass Transf., 43(16), 2895 (2000)

[10] Chung TJ, Park JH, Choi CK, Yoon DY, Int. J. Heat Mass Transf., 45(14), 3061 (2002)

[11] Combarnous M, Convection naturelle et convection mixte en milieu poreux, Ph.D. thesis, Faculte des sciences de l’univ. de Paris (1970)

[12] Delache A, Ouarzazi MN, Combarnous M, Int. J. Heat Mass Transf., 50(7-8), 1485 (2007)

[13] Dufour F, Neel MC, Phys. Fluids, 10, 2198 (1998)

[14] Muller HW, Lucke M, Kamps M, Phys. Rev. A, 45, 3714 (1992)

[15] Recktenwald A, Lucke M, Muller HW, Phys. Rev. E, 48, 4444 (1993)

[16] Patankar SV, Numerical heat transfer and fluid flow, Taylor and Francis (1980)

[17] Blankenbach B, Busse F, Christensen U, Cserepes L, Gunkel D, Hansen U, Harder H, Jarvis G, Koch M, Marquart G, Moore D, Olson P, Schmeling H,Schanubelt T, Geophys. J. Int., 98, 23 (1989)

[18] Walker KL, Homsy GM, J. Fluid Mech., 87, 449 (1978)

[19] Chen SS, Lavine AS, Int. J. Heat Mass Transf., 39(1), 1 (1996)

[20] Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Thermal Sci., 43, 817 (2004)

[21] Ouazzani MT, Caltagirone JP, Meyer G, Mojtabi A, Int. J. Heat Mass Transfer, 32, 261 (1989)

[22] Joseph DD, Stability of fluid motions I and II, Springer-Verlag, New York (1976)

[23] Gill AE, J. Fluid Mech., 35, 545 (1969)

[24] Huerre P, Propagation in system far from equilibrium, edited by Wesfreid JE, Brand HR, Manneville P, Albinet G, Boccara N, 340 (1988)

[25] Newell AC, Whitehead JA, J. Fluid Mech., 38, 279 (1969)

[26] Segel L, J. Fluid Mech., 38, 203 (1969)