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Natural Convection in Porous Media

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Advances in Transport Phenomena in Porous Media

Part of the book series: NATO ASI Series ((NSSE,volume 128))

Abstract

When the temperature of the saturating fluid phase in a porous medium is not uniform, some flows induced by buoyancy effects may occur. Commonly called free or natural convective movements, these flows depend on density differences due to temperature gradients and boundary conditions. Generally speaking, convective movements which tend to homogenize the whole fluid volume where they take place have two main effects: produce a non-uniform insitu temperature distribution characterized by hot and cold zones, and increase the overall heat transfer.

Due to its numerous applications in geophysics and energy-related engineering problems, natural convection in porous media has been receiving increased interest over the last few decades (1,2).

In this review, we deal mainly with the presentation of fundamental results obtained through the study of this phenomena in dispersed saturated porous media. Beginning with the formulation of basic equations and boundary conditions, we then successively review:

  • first, the results concerning natural convection in homogeneous isotropic porous layers of wide lateral extent in horizontal or inclined positions,

  • second, the studies on natural convection in confined porous media, i.e., when the lateral extent of the layer is of the same order of magnitude so that the thickness and the lateral thermal boundary effects are taken into account,

  • and finally, the problems related to natural convection in more complex configurations, such as anisotropic porous layers or porous layers saturated by a fluid of non-constant properties.

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References

  1. Combarnous M.A., and Bories S.A., “Hydrothermal Convection in Saturated Porous Media,” Advances in Hydro sciences, Vol. 10, Academic Press, New York, N.Y., 1975, pp. 231–307.

    Google Scholar 

  2. Klarsfeld S., “Champs de temperature associés aux mouvements de convection naturelle dans un milieu poreux limité,” Revue Générale de Thermique, Vol. 9, 1970, pp. 1403–1424.

    Google Scholar 

  3. Marie C., “From the Pore Scale to the Macroscopic Scale: Equation Governing Multiphase Fluid Through Porous Media,” Flow and Transport in Porous Media, A.A. Belkema, ed., 1981, pp. 57–61.

    Google Scholar 

  4. Matheron G., Elements Pour Une Théorie des Milieux Poreux, Masson et Cie Editeurs, Paris VIe, 1967.

    Google Scholar 

  5. Withaker, S., “Simultaneous Heat, Mass and Momentum Transfer in Porous Media. A Theory of Drying,” Advances in Beat Transfer, Vol. 13, 1977, pp. 119–203.

    Google Scholar 

  6. Bear, J., Dynamics of Fluids in Porous Media, American Elsevier, 1972.

    MATH  Google Scholar 

  7. Hassanizadeh M., and Gray, W.G., “General Conservation Equations for Multiphase Systems: 3. Constitutive Theory for Porous Media,” Advances in Water Resources, Vol. 3, 1980, pp. 25–40.

    Google Scholar 

  8. Slattery, J.C., Momentum Energy and Mass Transfer in Continua, Mc Graw Hill Book Company, 1972.

    Google Scholar 

  9. Whitaker, S., “Local Thermal Equilibrium: An Application to Packed Bed Catalytic Reactor Design,” to be published in Chemical Ingr. Science., 1984.

    Google Scholar 

  10. Jaguaribe, E., and Beasley, D., “Modeling of the Effective Thermal Conductivity and Diffusivity of a Packed Bed with Stagnant Fluid,” Journal of Heat and Mass Transfer, Vol.27, No. 3, 1984, pp. 399–407.

    Google Scholar 

  11. Bear, J., and Bachmat, Y., “Transport Phenomena in Porous Media. The Basic Equations,” Review NATO Advanced Study Institute on Mechanics of Fluids in Porous Media, Newark, DE., July 18–27, 1982.

    Google Scholar 

  12. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford at the Clarendon Press, 1961.

    MATH  Google Scholar 

  13. Westbrook, D.R., “Stability of Convective Flow in a Porous Medium,” Physics of Fluids, Vol. 12, 1969, pp. 1547–1551.

    Google Scholar 

  14. Joseph, D.D., “Stability of Fluid Motions,” Springer Tracts in Natural Philosophy, Vol. 27 and 28, Springer, Berlin, Heidelberg, New York, 1976.

    Google Scholar 

  15. Katto, Y., and Masuoka, T., “Criterion for Onset of Convective Flow in a Fluid in a Porous Medium,” International Journal of Heat and Mass Transfer, Vol. 10, 1967, pp. 297–309.

    Google Scholar 

  16. Lapwood, E.R., “Convection of a Fluid in a Porous Medium,” Proceedings of Cambridge Pil. Society, Vol. 44, 1948 pp. 508–521.

    Google Scholar 

  17. Horton, C.W., and Rogers, F.T., “Convection Currents in a Porous Medium,” Journal of Applied Physics, Vol. 16, 1945, pp. 367–370.

    MathSciNet  MATH  Google Scholar 

  18. Nield, D.A., “Onset of Thermohaline Convection in a Porous Medium,” Water Resources Research, Vol. 4, 1968, pp. 553–560.

    Google Scholar 

  19. Caltagirone, J.P., “Stability of a Saturated Porous Layer Subject to a Sudden Rise in Surface Temperature: Comparison Between the Linear and Energy Methods,” The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 23, 1980, pp. 47–58.

    Google Scholar 

  20. Busse, F.H., and Riahi, N., “Non Linear Convection in a Layer With Nearly Insulating Boundaries,” Journal of Fluid Mechanics, Vol. 96, 1980, pp. 243–256.

    MATH  Google Scholar 

  21. Riahi, N., “Non Linear Convection in a Porous Layer with Finite Conducting Boundaries,” Journal of Fluid Mechanics, Vol. 129, 1983, pp. 153–171.

    MATH  Google Scholar 

  22. Malkus, V.W.R., and Veronis, G., “Finite Amplitude Convection,” Journal of Fluid Mechanics, Vol. 4, 1958, pp. 225–260.

    MathSciNet  MATH  Google Scholar 

  23. Gorkov, L.P., “Stationary Convection in a Plane Liquid Layer Near the Critical Heat Transfer Point,” English Transi. Sov. Phys. JETP, Vol. 6, 1957, pp. 311–315.

    MathSciNet  Google Scholar 

  24. Edwards, D.K., and Catton, I., “Prediction of Heat Transfer by Natural Convection in Closed Cylinder Heated From Below,” International Journal of Heat & Mass Transfer, Vol. 12, 1969, pp. 23–30.

    MATH  Google Scholar 

  25. Schluter, A., and Lortz, D., and Bosse, F.H., “On the Stability of Steady Finite Amplitude Convection,” Journal of Fluid Mechanics, Vol. 23, 1965, pp. 129–144.

    MathSciNet  Google Scholar 

  26. Bories, S.A., “Comparaison des prévisions d’une théorie non Linéaire et des résultats expérimentaux en convection naturelle dans une couche poreuse saturée horizontale,” Compte s-rendus Académie des Sciences B, Vol. 271, 1970, pp. 269–272.

    Google Scholar 

  27. Bories, S.A., and Combarnous, M.A., “Natural Convection in a Sloping Porous Layer,” Journal of Fluid Mechanics, Vol. 57, 1973, pp. 63–79.

    MATH  Google Scholar 

  28. Caltagirone, J.P., “Thermoconvective Instabilities in a Porous Layer,” Journal of Fluid Mechanics, Vol. 72, 1975, pp. 269–287.

    MATH  Google Scholar 

  29. Caltagirone, J.P., “Thermoconvective Instabilities in a Porous Medium Bounded by Two Concentric Horizontal Cylinders,” Journal of Fluid Mechanics, Vol. 76, 1976, pp. 337–362.

    MATH  Google Scholar 

  30. Caltagirone, J.P., and Combarnous, M., and Mojtabi, A., “Natural Convection Between Two Concentric Spheres: Transition Towards a Multicellular Flow,” Num. Heat Transfer, Vol. 3, 1980, pp. 107–114.

    Google Scholar 

  31. Caltagirone, J.P., and Meyer, G., and Mojtabi, A., “Structurations Thermoconvectives tridimensionnelles dans une couche poreuse horizontale,” Journal de Mécanique 20, Vol. 2, 1981, pp. 219–232.

    Google Scholar 

  32. Horne, R.N., “Three Dimensional Natural Convection in a Confined Porous Medium Heated From Below,” Journal of Fluid Mechanics, Vol. 92, 1979, pp. 751–766.

    MATH  Google Scholar 

  33. Horne, R.N., and Caltagirone, J.P., “On the Evolution of Thermal Disturbances During Natural Convection in a Porous Medium,” Journal of Fluid Mechanics, Vol. 100, 1980, pp. 385–395.

    MATH  Google Scholar 

  34. Schubert, G., and Straus, J.M., “Three Dimensional and Multicellular Steady and Unsteady Convection in Fluid Saturated Porous Media at High Rayleigh Number,” Journal of Fluid Mechanics, Vol. 94, 1979, pp. 25–38.

    Google Scholar 

  35. Straus, J.M., and Schubert, G., “Three-dimensional Convection in a Cubic Box of Fluid Saturated Porous Material,” Journal of Fluid Mechanics, Vol. 91, 1979, pp. 155–165.

    Google Scholar 

  36. Gottleib, D., and Orstag, S.A., “Numerical Analysis of Spectral Methods: Theory and Applications,” NSF-CBMS Monograph 26, Society of Industrial and Applied Mathematics, Philadelphia, 1978.

    Google Scholar 

  37. Caltagirone, J.P., and Cloupeau, M., and Combarnous, M., “Convection Naturelle Fluctuante dans Une Couche Poreuse Horizontale,” Compte-Rendu á l’Académie des Sciences, B Vol. 273, 1971, pp. 833–836.

    Google Scholar 

  38. Straus, J.M., “Large Amplitude Convection in Porous Media,” Journal of Fluid Mechanics, Vol.64, 1974, pp. 51–63.

    MATH  Google Scholar 

  39. Bories, S.A., and Monferran L., “Conditions de Stabilité et Échanges Thermiques Par Convection Naturelle Dans Une Couche Poreuse Inclinée de Grande Extension,” Compte-rendu á l’Académie des Sciences, B, Vol. 274, 1972, pp. 4–7.

    Google Scholar 

  40. Bories, S.A., and Combarnous, M.A., and Jaffrennou, J.Y., “Observation des différentes formes d’écoulements convectifs dans une couche poreuxe inclinée,” Compte-Rendu à l’Académie des Sciences, A, Vol. 275, 1972, pp. 857–860.

    Google Scholar 

  41. Schneider, K.H., “Investigation of the Influence of Free Thermal Convection on Heat Transfer Through Granular Material,” Proceedings of International Congress on Refrigiration, 11th, Munich, 1963, pp. 11–14.

    Google Scholar 

  42. Elder, J.W., “Steady Free Convection in a Porous Medium Heated from Below,” Journal of Fluid Mechanics, Vol. 27, 1967, pp. 29–48.

    Google Scholar 

  43. Steen, P.H., “Pattern Selection for Finite Amplitude Convection States in Boxes of Porous Media,” Journal of Fluid Mechanics, Vol. 136, 1983, pp. 219–241.

    Google Scholar 

  44. Combarnous, M.A., and Lefur, B., “Transfert de Chaleur Par Convection Naturelle Dans Une Couche Poreuse Horizontale,” Compte Rendu à l’Académie des Sciences, B, 1969, pp. 1009–1012.

    Google Scholar 

  45. Bories, S.A., “Sur Les Mécanismes Fondamentaux de la Convection Naturelle en Milieu Poreux,” Revue Générale de Thermique, Vol. 9, 1970, pp. 1355–1376.

    Google Scholar 

  46. Combarnous, M.A., “Convection Naturelle et Convection Mixte Dans Une Couche Poreuse Horizontale,” Revue Générale de Thermique Vol. 9, 1970, pp. 1335–1355.

    Google Scholar 

  47. Hollard, S., “Structures Thermoconvectives Stationnaires Dans Une Couche Poreuse Plane Inclinée de Grande Extension,” Thèse de Docteur-Ingénieur, Institut National Polytechnique de Toulouse, France, 1984.

    Google Scholar 

  48. Combarnous, M.A., “Convection Naturelle et Convection Mixte Dans Une Couche Poreuse Horizontale,” These Université de Paris, Edition Technip, Paris, 1970.

    Google Scholar 

  49. Klarsfeld, S., “Champs de Temperature Associés Aux Mouvements de Convection Naturelle Dans Un Milieu Limité,” Revue Générale de Thermique, Vol. 9, 1970, pp. 1403–1424.

    Google Scholar 

  50. Betbeder, J., and Jolas, P., “Influence de la Convection Libre Sur La Conductivité Thermique d’une Couche Verticale d’isolant Poreux,” International Journal of Heat & Mass Transfer, Vol.24, No. 3, 1972, pp. 496–506.

    Google Scholar 

  51. Caltagirone, J.P., and Bories, S., “Solutions and Stability Criteria of Natural Convective Flow in an Inclined Porous Layer,” in press in Journal of Fluid Mechanics, 1985 (see also “Solutions Numériques Bidimensionnelles et Tridimensionnelles de l’écoulement de Convection Naturelle Dans Une Couche Poreuse Inclinée,” Compte-Rendu à l’Académie des Sciences, B., Vol. 190, 1980, pp. 197–200).

    Google Scholar 

  52. Beck, J.L., “Convection in a Box of Porous Material Saturated With Fluid,” Physics of Fluids, Vol. 15, 1972, pp. 1377–1383.

    Google Scholar 

  53. Holst, P.H., and Aziz, K., “Numerical Simulation of Three-Dimensional Natural Convection in Porous Media, Preprint S.P.E. 2805, 1970.

    Google Scholar 

  54. Zebib, A., and Kassoy, D.R., “Three-dimensional Natural Convection Motion in a Confined Porous Medium,” The Physics of Fluids, Vol. 21, 1978, pp. 1–3.

    MATH  Google Scholar 

  55. Bories, S., and Deltour, A., “Influence des Conditions Aux Limites Sur La Convection Naturelle Dans Un Volume Poreux Cylindrique,” International Journal of Heat & Mass Transfer, Vol. 23, No. 6, 1980, pp. 63–79.

    Google Scholar 

  56. Bau, H.H., and Torrance, K.E., “Low Rayleigh Number Thermal Convection in a Vertical Cylinder Filled with Porous Material and Heated from Below,” International Journal of Heat & Mass Transfer, Vol. 104, No. 1, 1982, pp. 166–172.

    Google Scholar 

  57. Lowel, R.P., and Hernandez, H., “Finite Amplitude Convection in a Porous Container with Fault-like Geometry: Effect of Initial and Boundary Conditions,” International Journal of Heat & Mass Transfer, Vol. 5, No. 6, 1982, pp. 631–641.

    Google Scholar 

  58. Deltour, A., “Convection Naturelle Au Sein d’un Milieu Poreux Saturé Confiné Dans un Domaine Cylindrique Vertical,” Thèse Institut National Polytechnique Toulouse, France, 1982.

    Google Scholar 

  59. Horne, R.N., “Three-dimensional Natural Convection in a Confined Porous Medium Heated from Below,” Journal of Fluid Mechanics, Vol. 92, 1979, pp. 751–766.

    MATH  Google Scholar 

  60. Jaffrennou, J.Y., and Bories, S., “Convection Naturelle Dans Une Couche Poreuse Inclinée,” Rapport Interne, G.E. 14, Institut de Mécanique des Fluides de Toulouse, 1974.

    Google Scholar 

  61. Caltagirone, J.P., “Convection in Porous Medium. In Convective Transport and Instability Phenomena,” G. Braun Editor Karlsruhe 1981, pp. 199–232.

    Google Scholar 

  62. Vlasuk, M.P., “Transfert de Chaleur Par Convection Dans Une Couche Poreuse,” (in Russian), presented at the 1972, 4th All Union Heat & Mass Transfer Conference, held at Minsk.

    Google Scholar 

  63. Kaneko, T., “An Experimental Investigation of Natural Convection in Porous Media,” thesis presented to the University of Calgary, at Canada, in 1972, in partial fulfillment of the Master of Science.

    Google Scholar 

  64. Walch, J.P., and Dulieu, B., “Natural Convection in a Slightly Inclined Rectangular Box Filled With a Porous Medium,” International Journal of Heat & Mass Transfer, Vol. 22, No. 12, 1979, pp. 1607–1612.

    MATH  Google Scholar 

  65. Gill, A.E., “The Boundary Layer Regime for Convection in a Rectangular Cavity,” Journal of Fluid Mechanics, Vol. 26, 1966, p. 515.

    Google Scholar 

  66. Weber, J.E., “The Boundary Layer Regime for Convection in a Vertical Porous Layer,” International Journal of Heat & Mass Transfer, Vol. 18, 1975, pp. 569–573.

    MATH  Google Scholar 

  67. Walker, K.L., and Homsy, G.M., “Convection in a Porous Cavity,” Journal of Fluid Mechanics, Vol. 87, 1978, p. 449.

    MATH  Google Scholar 

  68. Bejan, A., “On the Boundary Layer Regime in a Vertical Enclosure Filled with a Porous Medium,” International Journal of Heat & Mass Transfer, Vol. 6, No. 2, 1979, pp. 93–102.

    Google Scholar 

  69. Simpkins, P.G., and Blythe, P.A., “Convection in a Porous Layer,” International Journal of Heat & Mass Transfer, Vol. 23, No. 6, 1980, pp. 881–887.

    MATH  Google Scholar 

  70. Bejan, A., and Tien, C.L., “Natural Convection in a Horizontal Porous Medium Subjected to an end-to-end Temperature Difference,” Journal of Heat Transfer, Vol. 100, No. 2, 1978, pp. 191–198.

    Google Scholar 

  71. Chan, B.C.K., and Ivey, G.M., and Barry, J.M., “Natural Convection Enclosed Porous Media with Rectangular Boundaries,” Journal of Heat Transfer, Vol.2, 1970, pp. 21–27.

    Google Scholar 

  72. Bejan, A., “A Synthesis of Analytical Results for Natural Convection Heat Transfer Across Rectangular Enclosures,” International Journal of Heat & Mass Transfer, Vol. 2, No. 2, 1980, pp. 723–726.

    Google Scholar 

  73. Aziz, K., and Kaneko, T., and Mohtadi, M.F., “Natural Convection in Confined Porous Media,” presented at the 1972, 1st Pacific Chemical Engineering Congress, held at Kyoto, Japan.

    Google Scholar 

  74. Bankvall, C.G., “Natural Convection in Vertical Permeable Space,” Stoffubertragung, Vol. 7, 1974, pp. 22–30.

    Google Scholar 

  75. Burns, P.J., and Chow, L.C., and Tien, C.L., “Convection in a Vertical Slot Filled with Porous Insulation,” International Journal of Heat & Mass Transfer, Vol. 20, No. 9, 1977, pp. 919–926.

    Google Scholar 

  76. Hickox, C.E., and Gartlink, D.K., “A Numerical Study of Natural Convection in Horizontal Porous Layer Subjected to an end-to-end Temperature Difference,” Journal of Heat Transfer, Vol. 103, No. 4, 1981, pp. 797–802.

    Google Scholar 

  77. Prasad, V., and Kulacki, F.A., “Convective Heat Transfer in a Rectangular Porous Cavity-Effect of Aspect Ratio on Flow Structure and Heat Transfer,” Journal of Heat Transfer, Vol. 106, 1984, pp. 158–165.

    Google Scholar 

  78. Prasad, V., and Kulacki, F.A., “Natural Convection in a Rectangular Porous Cavity with Constant Heat Flux on one Vertical Wall,” Journal of Heat Transfer, Vol. 106, 1984, pp. 152–157.

    Google Scholar 

  79. Seki, N., Fukusako, S., and Inaba, H.K., “Heat Transfer in a Confined Rectangular Cavity Packed with Porous Media,” Journal of Heat and Mass Transfer, Vol. 21, No. 7, 1978, pp. 985–989.

    Google Scholar 

  80. Inaba, H., and Seki, N., “An Experimental Study of Heat Transfer Characteristics in a Porous Layer Enclosed Between Two Opposing Vertical Surfaces with Different Temperatures,” International Journal of Heat & Mass Transfer, Vol. 24, No. 11, 1981, pp. 1854–1857.

    Google Scholar 

  81. Bejan, A., “Natural Convection Heat Transfer in a Porous Layer With Internal Flow Obstructions,” International Journal of Heat and Mass Transfer, Vol. 26, No. 6, 1983, pp. 815–822.

    MATH  Google Scholar 

  82. Prasad, V., “Natural Convection in Porous Media. An Experimental and Numerical Study for Vertical Annular and Rectangular Enclosures,” thesis presented to the University of Delaware, at Newark, De., in 1983, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

    Google Scholar 

  83. Prasad, V., and Kulacki, F.A., “Natural Convection in a Vertical Porous Annulus,” International Journal of Heat & Mass Transfer, Vol. 27, No. 2, 1984, pp. 207–219.

    MATH  Google Scholar 

  84. Hickox, C.E., and Gartling, G.K., “A Numerical Study of Natural Convection in a Vertical, Annular Porous Layer,” presented at the 1982, ASME, 21st National Heat Transfer Conference (Paper No. 82-HT 68).

    Google Scholar 

  85. Havstad, M.A., and Burns, P.J., “Convective Heat Transfer in Vertical Cylindrical Annuli Filled with a Porous Medium,” International Journal of Heat & Mass Transfer, Vol. 25, No. 11, 1982, pp. 1755–1766.

    Google Scholar 

  86. Mckibbin, R., and O’Sullivan, M., “Onset of Convection in a Layered Porous Medium Heated from Below,” Journal of Fluid Mechanics, Vol. 96, No. 2, 1980, pp. 375–393.

    MathSciNet  MATH  Google Scholar 

  87. Richard, J.P., “Critère d’apparition de la convection naturelle Dans Des Couches Poreuses Stratifiées,” presented at the 1979, 15th Congrès International du Froid, Communication Bl-92.

    Google Scholar 

  88. Richard, J.P., and Combarnous, M., “Critère d’apparition de la Convection Naturelle Au Sein d’une Couche Poreuse Horizontale,” Compte-rendu Académie des Sciences, Paris, B, Vol. 285, 1977, pp. 73–75.

    Google Scholar 

  89. McKibbin, R., and O’Sullivan, M.J., “Heat Transfer in a Layered Porous Medium Heated From Below,” Journal of Fluid Mechanics, Vol. III, 1981, pp. 141–173.

    Google Scholar 

  90. McKibbin, R., and Tyvand, P.A., “Anisotropic Modeling of Thermal Convection in Multilayered Porous Media,” Journal of Fluid Mechanics, Vol. 118, 1982, pp. 315–339.

    MATH  Google Scholar 

  91. McKibbin, R., and Tyvand, P.A., “Thermal Convection in a Porous Medium Composed of Alternating Thick and Thin Layers,” International Journal of Heat and Mass Transfer, Vol. 26, No.5, 1983, pp. 761–780.

    Google Scholar 

  92. McKibbin, R., and Tyvand, P.A., “Thermal Convection in a Porous Medium with Horizontal Cracks,” International Journal of Heat and Mass Transfer, Vol. 27, No. 7, 1984, pp. 1007–1023.

    Google Scholar 

  93. Epherre, J.F., “Critère d’apparition de la Convection Naturelle Dans Une Couche Poreuse Anisotrope,” Revue Générale de Thermique, Vol. 168, 1975, pp. 949–950.

    Google Scholar 

  94. Kvernvold, O., and Tyvand, P.A., “Non Linear Thermal Convection in Anisotropic Porous Media,” Journal of Fluid Mechanics, Vol. 90, 1979, pp. 609–624.

    MATH  Google Scholar 

  95. Epherre, J.F., “Convection Naturelle Dans Une Couche Poreuse Anisotrope Saturée Par Un Gaz Parfait,” Thèse Université de Bordaux I., 1976.

    Google Scholar 

  96. Castinel, G., and Combarnous, M., “Critère d’apparition de la Convection Naturelle Dans Une Couche Poreuse Horizontale Anisotrope,” Compte-rendu Académie des Sciences, Paris B, Vol. 278, 1974, pp. 701–704.

    Google Scholar 

  97. Minkowycz, W.J., and Cheng, P., “Free Convection About a Vertical Cylinder Embedded in a Porous Medium,” International Journal of Heat & Mass Transfer, Vol. 19, No. 7, 1976, pp. 805–813.

    MATH  Google Scholar 

  98. Cheng, P., “Similarity Solutions for Mixed Convection from Horizontal Impermeable Surfaces in Saturated Porous Media,” International Journal of Heat and Mass Transfer, Vol. 20, 1977, pp. 893–898.

    Google Scholar 

  99. Cheng, P., “Combined Free and Forced Convection Flow About Inclined Surfaces in Porous Media,” International Journal of Heat and Mass Transfer, Vol. 20, 1977, pp. 807–814.

    MATH  Google Scholar 

  100. Johnson, CH., and Cheng, P., “Possible Similarity Solutions for Free Convection Boundary Layers Adjacent to Flat Plates in Porous Media,” International Journal of Heat & Mass Transfer, Vol. 21, 1978, pp. 709–718.

    MATH  Google Scholar 

  101. Hsu, G.T., and Cheng, P., and Homsy, G.M., “Instability of free Convection Flow Over a Horizontal Impermeable Surface in Porous Medium,” International Journal of Heat and Mass Transfer, Vol. 21, 1978, pp. 1221–1228.

    MATH  Google Scholar 

  102. Hsu, G.T., and Cheng, P., “The Onset of Longitudinal Vortices in Mixed Convective Flow Over an Inclined Surface in a Porous Medium,” Journal of Heat Transfer, Vol. 102, 1980, pp. 544–549.

    Google Scholar 

  103. Joshi, Y., and Gerbhart, B., “Vertical Natural Convection Flows in Porous Media. Calculations of Improved Accuracy,” International Journal of Heat & Mass Transfer, Vol. 21, No. 1, 1984, pp. 69–75.

    Google Scholar 

  104. Pop, I., and Cheng, P., “The Growth of a Thermal Layer in a Porous Medium Adjacent to a Suddenly Heated Semi-infinite Horizontal Surface,” International Journal of Heat & Mass Transfer, Vol. 26, No. 10, 1983, pp. 1574–1576.

    Google Scholar 

  105. Rees, D.A., and Riley, D.S., “Free Convection Above a Near Horizontal Semi-Infinite Heated Surface Embedded in a Saturated Porous Medium,” International Journal of Heat and Mass Transfer, Vol. 28, No. 1, 1985, pp. 183–190.

    MATH  Google Scholar 

  106. Bejan, A., and Anderson, R., “Natural Convection at the Interfac Between a Vertical Porous Layer and an Open Space,” Journal of Heat Transfer, Vol. 105, 1983, pp. 124–129.

    Google Scholar 

  107. Chandrasekhara, B.C., and Namboodiri, P.M.S., “Influence of Variable Permeability on Combined Free and Forced Convection About Inclined Surfaces in Porous Media,” International Journal of Heat & Mass Transfer, Vol. 28, No. 1, 1985, pp. 199–206.

    MATH  Google Scholar 

  108. Cheng, P., “Heat Transfer in Geothermal Systems,” Advances in Heat Transfer, Vol. 14, 1978, pp. 1–105.

    Google Scholar 

  109. Hozanski, J.M., and Huet, S., “Etude Théorique et Expérimentale de la Convection Naturelle en Milieu Poreux Saturé Produite Par Une Source de Chaleur Concentrée,” Symposium de l’A.I.R.H. sur les Transferts de Chaleur et de Masse en Milieux Poreux, Toulouse, France, 1980.

    Google Scholar 

  110. Bejan, A., “Natural Convection in an Infinite Porous Medium with a Concentrated Heat Source,” Journal of Fluid Mechanics, Vol. 89, 1978, pp. 97–107.

    MATH  Google Scholar 

  111. Hickox, C.E., and Watts, H.A., “Steady Thermal Convection from a Concentrated Source in a Porous Medium,” Journal of Heat Transfer, Vol. 102, No. 2, 1980, p. 248.

    Google Scholar 

  112. Hickox, C.E., “Thermal Convection at Low Rayleigh Number from Concentrated Sources in Porous Media,” Journal of Heat Transfer, Vol. 103, 1981, pp. 232–236.

    Google Scholar 

  113. Poulikakos, D., “On Buoyancy Induced Heat and Mass Transfer from a Concentrated Source in an Infinite Porous Medium,” International Journal of Heat & Mass Transfer, Vol. 28, No. 3, 1985, pp. 621–629.

    MATH  Google Scholar 

  114. Zebib, A., and Kassoy, D.R., “Onset of Natural Convection in a Box of Water-Saturated Porous Media with Large Temperature Variation,” The Physics of Fluids, Vol. 20, No. 1, 1977, pp. 4–9.

    MATH  Google Scholar 

  115. Saatdjian, E., “Natural Convection in a Porous Layer Saturated with a Compressible Ideal Gas,” International Journal of Heat & Mass Transfer, Vol. 23, 1980, pp. 1681–1683.

    MATH  Google Scholar 

  116. Epherre, J.F., “Convection Naturelle au Sein d’une Couche Poreuse Anisotrope Saturée par un Gaz Parfait,” Thèse Université de Bordeaux I., Bordeaux, France, 1976.

    Google Scholar 

  117. Epherre, J.F., and Combarnous, M., and Klarsfeld, S., “Critère d’apparition de la Convection Naturelle Dans des Couches Poreuses Anistropes Saturées d’air Soumises à de Grandes Différences de Température,” Commission Bulletin, Institut. Int. du Froid, Washington, 1976, pp. 55–62.

    Google Scholar 

  118. Blake, K.R., and Bejan, A., and Poulikakos, D., “Natural Convection Near 4°C in a Water Saturated Porous Layer Heated From Below,” International Journal of Heat & Mass Transfer, Vol. 27, No. 2, 1984, pp. 2355–2364.

    MATH  Google Scholar 

  119. Brinkman, H.C., “On the Permeability of Media Consisting of Closely Packed Porous Interface, Aplied Science Research., Vol. A1, 1947, pp. 27–34.

    Google Scholar 

  120. Vafai, K., and Tien, C.L., “Boundary and Intertia Effects on Convective Mass Transfer in Porous Media,” International Journal of Heat and Mass Transfer, Vol. 25, No. 8, 1982, pp. 1183–1190.

    Google Scholar 

  121. Walker, K., and Homsy, G.M., “A Note on Convective Instabilities on Boussinesq Fluids and Porous Media,” Journal of Heat Transfer, Vol. 99, 1977, pp. 338–339.

    Google Scholar 

  122. Tong, T.W., and Subramanian, E., “A Boundary Layer Analysis for Natural Convection in Vertical Porous Enclosures-Use of the Brinkman Extended Darcy Model,” International Journal of Heat and Mass Transfer, Vol. 28, No. 3, 1985, pp. 563–571.

    MATH  Google Scholar 

  123. Hsu, C.T., and Cheng, P., “The Brinkman Model for Natural Convection About Semi-Infinite Vertical Flat Plate in a Porous Medium,” International Journal of Heat & Mass Transfer, Vol. 28, No. 3, 1985, pp. 683–697.

    MATH  Google Scholar 

  124. Rudraiah, N., and Veerappa B., and Balachandra Rao S., “Effects of Non Uniform Thermal Gradients and Adiabatic Boundaries on Convection in Porous Media,” Journal of Heat Transfer, Vol.102, 1980, pp. 254–260.

    Google Scholar 

  125. Nield, D.A., “The Boundary Correction for the Rayleigh Darcy Problem: Limitations of the Brinkman Equation,” Journal of Fluid Mechanics, Vol. 128, 1983, pp. 37–46.

    MathSciNet  MATH  Google Scholar 

  126. Caltagirone, J.P., and Arquis, E., “Natural Convection in a Vertical Fluid Cavity Divided by a Permeable Porous Layer,” in press.

    Google Scholar 

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Authors and Affiliations

  1. Polytechnique de Toulouse - Laboratoire Associé au CNRS N° 0005, Institut de Mécanique des Fluides de l’Institut National, 2, rue Charles Camichel, 31071, Toulouse Cedex, France

    Serge Bories

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  1. Serge Bories
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  1. Department of Civil Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, 32000, Israel

    Jacob Bear

  2. Department of Civil Engineering, City College of New York, New York, NY, 10031, USA

    M. Yavuz Corapcioglu

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© 1987 Martinus Nijhoff Publishers, Dordrecht

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Bories, S. (1987). Natural Convection in Porous Media. In: Bear, J., Corapcioglu, M.Y. (eds) Advances in Transport Phenomena in Porous Media. NATO ASI Series, vol 128. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3625-6_4

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  • DOI: https://doi.org/10.1007/978-94-009-3625-6_4

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