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Dispersion effects on thermal convection in porous media

Published online by Cambridge University Press:  19 April 2006

Oddmund Kvernvold
Affiliation:
Department of Mechanics, University of Oslo, Norway Present address: Det norske Veritas, 1322 Hovik, Norway.
Peder A. Tyvand
Affiliation:
Department of Mechanics, University of Oslo, Norway

Abstract

The influence of hydrodynamic dispersion on thermal convection in porous media is studied theoretically. The fluid-saturated porous layer is homogeneous, isotropic and bounded by two infinite horizontal planes kept at constant temperatures. The supercritical, steady two-dimensional motion, the heat transport and the stability of the motion are investigated. The dispersion effects depend strongly on the Rayleigh number and on the ratio of grain diameter to layer depth. The present results provide new and closer approximations to experimental data of the heat transport.

Type
Research Article
Copyright
© 1980 Cambridge University Press

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References

Bear, J. 1969 Hydrodynamic dispersion. In Flow Through Porous Media (ed. R. De Wiest), pp. 109199. Academic.
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.
Buretta, R. 1972 Thermal convection in a fluid-filled porous layer with uniform internal heat sources. Ph.D. dissertation, University of Minnesota.
Cheng, P. 1978 Heat transfer in geothermal systems. Adv. Heat Transfer 14, 1105.Google Scholar
Combarnous, M. 1970 Convection naturelle et convection mixte en milieu poreux. Thèse Dr.Sc.Phys., Université de Paris.
Combarnous, M. A. & Bories, S. A. 1975 Hydro-thermal convection in saturated porous media. Adv. Hydrosci. 10, 231307.Google Scholar
Elder, J. W. 1967 Steady free convection in a porous medium heated from below. J. Fluid Mech. 27, 2948.Google Scholar
Fried, J. J. 1975 Groundwater Pollution. Elsevier.
Fried, J. J. & Combarnous, M. A. 1971 Dispersion in porous media. Adv. Hydrosci. 7, 169282.Google Scholar
Horton, C. W. & Rogers, F. T. 1945 Convection currents in a porous medium. J. Appl. Phys. 16, 367370.Google Scholar
Katto, Y. & Masuoka, T. 1967 Criterion for the onset of convective flow in a fluid in a porous medium. Int. J. Heat Mass Transfer 10, 297309.Google Scholar
Kuo, H. L. 1961 Solution of the non-linear equations of cellular convection and heat transport. J. Fluid Mech. 10, 611634.Google Scholar
Kvernvold, O. 1975 Non-linear convection in a porous medium. Univ. Oslo Preprint Ser. no. 1.Google Scholar
Neischloss, H. & Dagan, G. 1975 Convective currents in a porous layer heated from below: the influence of hydrodynamic dispersion. Phys. Fluids 18, 757761.CrossRefGoogle Scholar
Palm, E., Weber, J. E. & Kvernvold, O. 1972 On steady convection in a porous medium. J. Fluid Mech. 54, 153161.Google Scholar
Pfannkuch, H. O. 1963 Contribution à l’étude des déplacements dans un milieu poreux. Rev. Inst. Fr. Pétr. 18, 215270.Google Scholar
Poreh, M. 1965 The dispersivity tensor in isotropic and axisymmetric mediums. J. Geophys. Res. 70, 39093913.Google Scholar
Rubin, H. 1974 Heat dispersion effect on thermal convection in a porous medium layer. J. Hydrol. 21, 173185.Google Scholar
Saffman, P. G. 1959 A theory of dispersion in a porous medium. J. Fluid Mech. 6, 321349.Google Scholar
Saffman, P. G. 1960 Dispersion due to molecular diffusion and macroscopic mixing in flow through a network of capillaries. J. Fluid Mech. 7, 194208.Google Scholar
Scheüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129144.Google Scholar
Schneider, K. J. 1963 Investigation of the influence of free thermal convection on heat transfer through granular materials. 11th Int. Cong. of Refrigeration, Munich, paper no. 11-4.
Straus, J. M. 1974 Large amplitude convection in porous media. J. Fluid Mech. 64, 5163.Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Roy. Soc. A 219, 186203.Google Scholar
Tyvand, P. A. 1977 Heat dispersion effect on thermal convection in anisotropic porous media. J. Hydrol. 34, 335342.Google Scholar
Weber, J. E. 1975 Dispersion effect on buoyancy-driven convection in stratified flows through porous media. J. Hydrol. 25, 5970.Google Scholar