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Natural convection in porous media

Published online by Cambridge University Press:  20 April 2006

V. Prasad ,
F. A. Kulacki  and
M. Keyhani
V. Prasad
Affiliation:
Department of Mechanical Engineering, Columbia University, New York, NY 10027
F. A. Kulacki
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, DE 19716
M. Keyhani
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, DE 19716
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Abstract

Experimental results on free convection in a vertical annulus filled with a saturated porous medium are reported for height-to-gap ratios of 1.46, 1 and 0.545, and radius ratio of 5.338. In these experiments, the inner and outer walls are maintained at constant temperatures. The use of several fluid–solid combinations indicates a divergence in the Nusselt-number–Rayleigh-number relation, as also reported by previous investigators for horizontal layers and vertical cavities. The reason for this divergence is the use of the stagnant thermal conductivity of the fluid-filled solid matrix. A simple model is presented to obtain an effective thermal conductivity as a function of the convective state, and thereby eliminate the aforementioned divergence. A reasonable agreement between experimentally and theoretically determined Nusselt numbers is then achieved for the present and previous experimental results. It is thus concluded that a unique relationship exists between the Nusselt and Rayleigh numbers unless Darcy's law is inapplicable. The factors that influence the breakdown of Darcian behaviour are characterized and their effects on heat-transfer rates are explained. It is observed that, once the relation between the Nusselt and Rayleigh numbers branches out from that obtained via the mathematical formulation based on Darcy's law, its slope approaches that for a fluid-filled enclosure of the same geometry when the Rayleigh number is large enough. An iterative scheme is also presented for estimation of effective thermal conductivity of a saturated porous medium by using the existing results for overall heat transfer.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 89 - 119
Copyright
© 1985 Cambridge University Press

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References

Bear J.1972 Dynamics of Fluids in Porous Media. Elsevier.
Bories, S. A. & Combarnous M. A.1973 J. Fluid Mech. 57, 63.
Brinkman H. C.1949 Appl. Sci. Res. Suppl. 2–4, 190.
Buretta R. J.1972 Thermal convection in a fluid filled porous layer with uniform internal heat sources. Ph.D. dissertation, Department of Aeronautical Engineering, University of Minnesota.
Buretta, R. J. & Berman A. S.1976 Trans. ASME E: J. Appl. Mech. 48, 249.
Catton I.1984 In Proc. NATO Advanced Study Institute on Natural Convection: Fundamentals and Applications. (Ed. W. Aung, S. Kakac & R. Viskanta). Hemisphere.
Chan B. K. C., Ivey, C. M. & Barry J. M.1970 Trans. ASME C: J. Heat Transfer 2, 21.
Cheng P.1978 Adv. Heat Transfer 14, 1.
Combarnous M.1970a Convection naturelle et convection mixte en milieu poreux. Ph.D. thesis, University of Paris.
Combarnous M.1970b Rev. Gen. Therm. 9, 1355.
Combarnous M.1972 C.R. Acad. Sci., Paris A 275, 1375.
Combarnous, M. & Bories S. A.1974 Intl J. Heat Mass Transfer 17, 505.
Combarnous, M. & Bories S. A.1975 Adv. Hydrosci. 10, 231.
Elder J. W.1967 J. Fluid Mech. 27, 29.
Graebel W. P.1981 Intl J. Heat Mass Transfer 24, 125.
Gupta, V. P. & Joseph D. D.1973 J. Fluid Mech. 64, 51.
Havstad, M. A. & Burns P. J.1982 Intl J. Heat Mass Transfer 11, 1755.
Hickox, C. E. & Gartling D. K.1982 ASME Paper 82-HT-68.
Horton, C. W. & Rogers F. T.1945 J. Appl. Phys. 16, 360.
Kaneko T., Mohtadi, M. F. & Aziz K.1974 Intl J. Heat Mass Transfer 17, 485.
Katto, Y. & Masuoka T.1967 Intl J. Heat Mass Transfer 10, 297.
Keyhani, M. & Kulacki F. A.1984 In preparation.
Klarsfeld S.1970 Rev. Gen. Therm. 9, 1403.
Kubair, V. G. & Simha C. R. V.1982 Intl J. Heat Mass Transfer 25, 399.
Kulkarni A. V.1983 Experimental studies on convective heat transfer in a vertical porous annulus with constant heat flux on the inner wall. M.S. thesis, Department of Mechanical and Aerospace Engineering, University of Delaware.
Kunii, D. & Smith J. M.1960 AIChE J. 49, 71.
Lapwood E. R.1948 Proc. Camb. Phil. Soc. 44, 508.
Mcgregor, R. K. & Emery A. F.1969 Trans. ASME C: J. Heat Transfer 91, 391.
Prasad V.1983 Natural convection in porous media—an experimental and numerical study for vertical annular and rectangular enclosures. Ph.D. dissertation, Department of Mechanical and Aerospace Engineering, University of Delaware.
Prasad, V. & Kulacki F. A.1982 Heat Transfer in Porous Media. ASME LTD, vol. 22, p. 35. [Also Trans. ASME C: J. Heat. Transfer 106 (1984), 152.]
Prasad, V. & Kulacki F. A.1983 ASME Paper 83-HT-66. [Also Trans. ASME C: J. Heat Transfer 106 (1984), 158.]
Prasad, V. & Kulacki F. A.1984a Intl J. Heat Mass Transfer 27, 207.
Prasad, V. & Kulacki F. A.1984b Trans. ASME C: J. Heat Transfer (in Press). [Also ASME Paper 84-HT-76. 22nd ASME/AIChE Natl Heat Transfer Conf., Niagara Falls, 1984.]
Prasad, V. & Kulacki F. A.1984c Submitted to Trans. ASME C: J. Heat Transfer.Google Scholar
Raithby, G. D. & Wong H. H.1981 Num. Heat Transfer 4, 447.
Reda D. C.1983 Trans. ASME C: J. Heat Transfer 105, 795.
Seki N., Fukusako, S. & Inaba H.1978 Intl J. Heat Mass Transfer 21, 985.
Schneider K. J.1963 In Proc. 11th Intl Congr. on Refr., vol. II-4, p. 247. Pergamon.
Sheriff N.1966 In Proc. 3rd Intl Heat Transfer Conf., vol. 2, p. 132.
Thomas, R. W. & de Vahl Davis G.1970 In Proc. 4th Intl Heat Transfer Conf., vol. 4, NC 24, Elsevier.
Vafai, K. & Tien C. L.1981 Intl J. Heat Mass Transfer 24, 195.
Walker, K. L. & Homsy G. M.1978 J. Fluid Mech. 97, 449.
Weber J. E.1975 Intl J. Heat Mass Transfer 18, 569.
Wooding R. A.1957 J. Fluid Mech. 2, 273.
Yagi S., Kunii, D. & Wakao N.1961 In Intl Developments Heat Transfer, p. 742. ASME.
Yen Y. C.1974 Intl J. Heat Mass Transfer 17, 1349.