## Abstract

In the examples of forced and natural convection discussed until now, the fluid that flowed through the pores did not experience a change of phase, no matter how intense the heating or cooling effect. In the present chapter we turn our attention to situations in which a change of phase occurs, for example, melting or evaporation upon heating, and solidification or condensation upon cooling. These convection problems constitute a relatively new and active area in the field of convection in porous media.

## Keywords

Porous Medium Nusselt Number Natural Convection Rayleigh Number Heat Transfer Rate
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## References

- Afzal, N. 1985 Two-dimensional buoyant plume in porous media: Higher-order effects.
*Int. J. Heat Mass Transfer***28**, 2029–2041.zbMATHCrossRefGoogle Scholar - Angirasa, D. and Peterson, G.P. 1997 Natural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium.
*Int. J. Heat Mass Transfer***40**, 4329–4335.zbMATHCrossRefGoogle Scholar - Bejan, A. and Anderson, R. 1981 Heat transfer across a vertical impermeable partition imbedded in a porous medium.
*Int. J. Heat Mass Transfer***24**, 1237–1245.zbMATHCrossRefGoogle Scholar - Bejan, A. and Anderson, R. 1983 Natural convection at the interface between a vertical porous layer and an open space.
*ASME J. Heat Transfer***105**, 124–129.CrossRefGoogle Scholar - Bejan, A. and Nield, D. A. 1991 Transient forced convection near a suddenly heated plate in a porous medium.
*Int. Comm. Heat Mass Transfer***18**, 83–91.CrossRefGoogle Scholar - Braester, C. and Vadasz, P. 1993 The effect of a weak heterogeneity of a porous medium on natural convection.
*J. Fluid Mech*.**254**, 345–362.MathSciNetzbMATHCrossRefGoogle Scholar - Chelghoum, D. E., Weidman, P. D. and Kassoy, D. R. 1987 Effect of slab width on the stability of natural convection in confined saturated porous media.
*Phys. Fluids***30**, 1941–1947.CrossRefGoogle Scholar - Chellaiah, S. and Viskanta, R. 1987 Freezing of water and water-salt solutions around aluminum spheres.
*Int. Comm. Heat Mass Transfer***14**, 437–446.CrossRefGoogle Scholar - Chellaiah, S. and Viskanta, R. 1989a On the supercooling during freezing of water saturated porous media.
*Int. Comm. Heat Mass Transfer***16**, 163–172.CrossRefGoogle Scholar - Essome, G. R. and Orozco, J. 1991 An analysis of film boiling on a binary mixture in a porous medium.
*Int. J. Heat Mass Transfer***34**, 757–766.CrossRefGoogle Scholar - Ebinuma, C. D. and Nakayama, A. 1990b An exact solution for transient film condensation in a porous medium along a vertical surface with lateral mass flux.
*Int. Comm. Heat Mass Transfer***17**, 105–111.CrossRefGoogle Scholar - Echaniz, H. L. 1984 Oscillatory convection with boiling in a water-saturated porous medium. M.S. thesis, Cornell University.Google Scholar
- Egorov, S. D. and Poleshaev, V. I. 1993 Thermal convection in anisotropic porous insulation.
*Heat Transfer Res*.**25**, 968–990.Google Scholar - Ekholm, T. C. 1983 Studies of convection using a Hele-Shaw cell. Project Report, School of Engineering, University of Auckland, NZ.Google Scholar
- Gleason, K. J., Krantz, W. B., Caine, N., George, J. H. and Gunn, R. D. 1986 Geometrical aspects of sorted patterned ground in recurrently frozen soil.
*Science***232**, 216–220.CrossRefGoogle Scholar - Gorla, R. S. R. and Tornabene, R. 1988 Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium.
*Transport in Porous Media***3**, 95–105.CrossRefGoogle Scholar - Gorla, R. S. R. and Zinalabedini, A. H. 1987 Free convection from a vertical plate with nonuniform surface temperature and embedded in a porous medium.
*ASME J. Energy Res. Tech*.**109**, 27–30.Google Scholar - Gorla, R. S. R. and Kumari, M. 1996 Mixed convection in non-Newtonian fluids along a vertical plate in a porous medium.
*Acta Mech*.**118**, 55–64.zbMATHCrossRefGoogle Scholar - Gorla, R. S. R., Bakier, A. Y. and Byrd, L. 1996 Effects of thermal dispersion and stratification on combined convection on a vertical surface embedded in a porous medium.
*Transport Porous Media***25**, 275–282.CrossRefGoogle Scholar - Green, T. and Freehill, R. L. 1969 Marginal stability in inhomogeneous porous media.
*J. Appl. Phys*.**40**, 1759–1762.CrossRefGoogle Scholar - Hadim, A. and Burmeister, L. C. 1988 Onset of convection in a porous medium with internal heat generation and downward flow.
*AIAA J. Thermophys. Heat Transfer***2**, 343–351.CrossRefGoogle Scholar - Huang, P. C. and Vafai, K. 1993 Flow and heat transfer control over an external surface using a porous block array arrangement.
*Int. J. Heat Mass Transfer***36**, 4019–4032.zbMATHCrossRefGoogle Scholar - Kaloni, P. N. and Qiao, Z. 1997 Non-linear stability of convection in a porous medium with inclined temperature gradient.
*Int. J. Heat Mass Transfer***40**, 1611–1615.zbMATHCrossRefGoogle Scholar - Kamiuto, K. and Saitoh, S. 1994 Fully developed forced-convection heat transfer in cylindrical packed beds with constant wall temperatures.
*JSME Int. J. Series B***37**, 554–559.CrossRefGoogle Scholar - Kaneko, T., Mohtadi, M. F. and Aziz, K. 1974 An experimental study of natural convection in inclined porous media.
*Int. J. Heat Mass Transfer***17**, 485–496.CrossRefGoogle Scholar - Kuznetsov, A. V. 1997b Influence of the stress jump condition at the porousmedium/clear-fluid interface on a flow at a porous wall.
*Int. Comm. Heat Mass Transfer***24**, 401–410.CrossRefGoogle Scholar - Kuznetsov, A. V. 1997c Optimal control of the heat storage in a porous slab.
*Int. J. Heat Mass Transfer***40**, 1720–1723.zbMATHCrossRefGoogle Scholar - Kuznetsov, A. V. 1998 Thermal nonequilibrium forced convection in porous media.
*Transport Phenomena in Porous Media*(eds.**D**. B. Ingham and I. Pop). Elsevier, Amsterdam, pp. 103–130.Google Scholar - Lawson, M. L., Yang, W. J. and Bunditkul, S. 1976 Theory of thermal stability of binary gas mixtures in porous media.
*ASME J. Heat Transfer***98**, 35–41.CrossRefGoogle Scholar - Le Breton, P., Caltagirone, J. P. and Arquis, E. 1991 Natural convection in a square cavity with thin porous layers on its vertical walls.
*ASME J. Heat Transfer***113**, 892–898.CrossRefGoogle Scholar - Lebon, G. and Cloot, A. 1986 A thermodynamical modelling of fluid flows through porous media: Application to natural convection.
*Int. J. Heat Mass Transfer***29**, 381–390.zbMATHCrossRefGoogle Scholar - Ledezma, G. A., Bejan, A. and Errera, M. R. 1997 Constructal tree networks for heat transfer.
*J. Appl. Phys*.**82**, 89–100.CrossRefGoogle Scholar - Ledezma, G., Morega, A. M. and Bejan, A. 1996 Optimal spacing between fins with impinging flow.
*J. Heat Transfer***118**, 570–577.CrossRefGoogle Scholar - Mei, C. C., Auriault, J. L. and Ng, C. O. 1996 Some applications of the homogenization theory.
*Adv. Appl. Mech*.**32**, 278–348.Google Scholar - Merkin, J. H. 1978 Free convection boundary layers in a saturated porous medium with lateral mass flux.
*Int. J. Heat Mass Transfer***21**, 1499–1504.zbMATHCrossRefGoogle Scholar - Merkin, J. H. 1979 Free convection boundary layers on axisymmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium.
*Int. J. Heat Mass Transfer***22**, 1461–1462.CrossRefGoogle Scholar - Merkin, J. H. 1980 Mixed convection boundary layer flow on a vertical surface in a saturated porous medium.
*J. Engng. Math*.**14**, 301–313.MathSciNetzbMATHCrossRefGoogle Scholar - Merkin, J. H. and Needham, D. J. 1987 The natural convection flow above a heated wall in a saturated porous medium.
*Quart. J. Mech. Appl. Math*.**40**, 559–574.MathSciNetzbMATHCrossRefGoogle Scholar - Mojtabi, A. and Charrier-Mojtabi, M. C. 1992 Analytic solution of steady natural convection in an annular porous medium evaluated with a symbolic algebra code.
*ASME J. Heat Transfer***114**, 1065–1068.CrossRefGoogle Scholar - Morega, A. M. and Bejan, A. 1994 Heatline visualization of convection in porous media.
*Int. J. Heat Fluid Flow***15**, 42–47.CrossRefGoogle Scholar - Morega, A. M., Bejan, A. and Lee, S. W. 1995 Free stream cooling of a stack of parallel plates.
*Int. J. Heat Mass Transfer***38**, 519–531.CrossRefGoogle Scholar - Morland, L. W., Zebib, A. and Kassoy, D. R. 1977 Variable property effects on the onset of convection in an elastic porous matrix.
*Phys. Fluids***20**, 1255–1259.CrossRefGoogle Scholar - Oberbeck, A. 1879 Ueber die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen.
*Ann. Phys. Chem*.**7**, 271–292.zbMATHGoogle Scholar - Ochoa-Tapia, J. A. and Whitaker, S. 1995a Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development.
*Int. J. Heat Mass Transfer***38**, 2635–2646.zbMATHCrossRefGoogle Scholar - Ochoa-Tapia, J. A. and Whitaker, S. 1995b Momentum transfer at the boundary between a porous medium and a homogeneous fluid—II. Comparison with experiment.
*Int. J. Heat Mass Transfer***38**, 2647–2655.CrossRefGoogle Scholar - Kuznetsov, A. V. and Vafai, K. 1995a Development and investigation of three-phase model of the mushy zone for analysis of porosity formation in solidifying castings.
*Int. J. Heat Mass Transfer***38**, 2557–2567.zbMATHCrossRefGoogle Scholar - Kuznetsov, A. V. and Vafai, K. 1995b Analytical comparison and criteria for heat and mass transfer models in metal hydride packed beds.
*Int. J. Heat Mass Transfer***3 8**, 2873–2884.Google Scholar - Kvernvold,
**O**. 1979 On the stability of nonlinear convection in a Hele—Shaw cell.*Int. J. Heat Mass Transfer***22**395–400.Google Scholar - Kvernvold, O. and Tyvand, P. A. 1979 Nonlinear thermal convection in anisotropic porous media.
*J. Fluid Mech*.**90**, 609–624.zbMATHCrossRefGoogle Scholar - Kvernvold, O. and Tyvand, P. A. 1980 Dispersion effects on thermal convection i n porous media.
*J. Fluid Mech*.**99**, 673–686.zbMATHCrossRefGoogle Scholar - Kvernvold, O. and Tyvand, P. A. 1981 Dispersion effects on thermal convection in a Hele—Shaw cell.
*Int. J. Heat Mass Transfer***24**, 887–990.zbMATHCrossRefGoogle Scholar - Kwendakwema, N.J. and Boehm, R.F. 1991 Parametric study of mixed convection in a porous medium between vertical concentric cylinders.
*ASME J. Heat Transfer***113**, 128–134.CrossRefGoogle Scholar - Kwok, L. P. and Chen, C. F. 1987 Stability of thermal convection in a vertical porous layer.
*ASME J. Heat Transfer***109**, 889–893.CrossRefGoogle Scholar - Lage, J. L. 1992 Effect of the convective inertia term on Bénard convection in a porous medium.
*Numer. Heat Transfer A***22**, 469–485.CrossRefGoogle Scholar - Lage, J. L. 1993a Natural convection within a porous medium cavity: Predicting tools for flow regime and heat transfer.
*Int. Comm. Heat Mass Transfer***20**, 501–513.CrossRefGoogle Scholar - Lage, J. L. 1993b On the theoretical prediction of transient heat transfer within a rectangular fluid-saturated porous medium enclosure.
*ASME J. Heat Transfer***115**, 1069–1071.CrossRefGoogle Scholar - Lage, J. L. 1996 Comments on “The effect of turbulence on solidification of a binary metal alloy with electromagnetic stirring.”
*ASME J. Heat Transfer***118**, 996–997.CrossRefGoogle Scholar - Lage, J. L. 1997 Contaminant clean-up in a single rock fracture with porous obstructions.
*ASME J. Fluids Engng*.**119**, 180–187.CrossRefGoogle Scholar - Lage, J. L. 1998 The fundamental theory of flow through permeable media: From Darcy to turbulence.
*Transport Phenomena in Porous Media*(eds. D.B. Ingham and I. Pop). Elsevier, Amsterdam, pp. 1–30.Google Scholar - Lage, J. L. and Bejan, A. 1990 Numerical study of forced convection near a surface covered with hair.
*Int. J. Heat Fluid Flow***11**, 242–248.CrossRefGoogle Scholar - Lage, J. L. and Bejan, A. 1991 Natural convection from a vertical surface covered with hair.
*Int. J. Heat Fluid Flow***12**, 46–53.CrossRefGoogle Scholar - Lage, J. L. and Bejan, A. 1993 The resonance of natural convection in an enclosure heated periodically from the side.
*Int. J. Heat Mass Transfer***36**, 2027–2038.zbMATHCrossRefGoogle Scholar - Lage, J. L. and Nield, D. A. 1997 Comments on “Numerical studies of forced convection heat transfer from a cylinder embedded in a packed bed.”
*Int. J. Heat Mass Transfer***40**, 1725–1726.CrossRefGoogle Scholar - Lage, J. L. and Nield, D. A. 1998 Convection induced by inclined gradients in a shallow porous medium layer.
*J. Porous Media***1**, 57–69.zbMATHGoogle Scholar - Lage, J. L., Bejan, A. and Georgiadis, J. G. 1992 The Prandtl number effect near the onset of Bénard convection in a porous medium.
*Int. J. Heat Fluid Flow***13**, 408–411.CrossRefGoogle Scholar - Lage, J. L., Weinert, A. K., Price, D. C. and Weber, R. M. 1996 Numerical study of a low permeability microporous heat sink for cooling phased-array radar systems.
*Int. J. Heat Mass Transfer***39**, 3633–3647.CrossRefGoogle Scholar - Lage, J. L., Antohe, B. V. and Nield, D. A. 1997 Two types of nonlinear pressure-drop versus flow-rate relation observed for saturated porous media.
*ASME J. Fluids Engng*,**119**, 701–706.Google Scholar - Lai, C. H., Bodvarsson, G. S. and Truesdell, A. H. 1994 Modeling studies of heat transfer and phase distribution in two-phase geothermal reservoirs,
*Geothermics***23**, 3–20.CrossRefGoogle Scholar - Lai, F. C. 1990a Coupled heat and mass transfer by natural convection from a horizontal line source in saturated porous medium.
*Int. Comm. Heat Mass Transfer***17**, 489–499.CrossRefGoogle Scholar - Lai, F. C. 1990b Natural convection from a concentrated heat source in a saturated porous medium.
*Int. Comm. Heat Mass Transfer***17**, 791–800.CrossRefGoogle Scholar - Lai, F. C. 199la Coupled heat and mass transfer by mixed convection from a vertical plate in a saturated porous medium.
*Int. Comm. Heat Mass Transfer***18**, 93–106.Google Scholar - Lai, F. C. 1991b Non-Darcy natural convection from a line source of heat in a saturated porous medium.
*Int. Comm. Heat Mass Transfer***18**, 445–457.CrossRefGoogle Scholar - Lai, F. C. 1991c Non-Darcy mixed convection from a line source of heat in a saturated porous medium.
*Int. Comm. Heat Mass Transfer***18**, 875–887.CrossRefGoogle Scholar - Lai, F. C. 1993a Improving effectiveness of pipe insulation by using radial baffles to suppress natural convection.
*Int. J. Heat Mass Transfer***36**, 899–908.CrossRefGoogle Scholar - Lai, F. C. 1993b Natural convection in a horizontal porous annulus with mixed type of radial baffles.
*Int. Comm. Heat Mass Transfer***20**, 347–359.CrossRefGoogle Scholar - Lai, F. C. 1994 Natural convection in horizontal porous annuli with circumferential baffles.
*AIAA J. Thermophys. Heat Transfer***8**, 376–378.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1987 Non-Darcy convection from horizontal impermeable surfaces in saturated porous media.
*Int. J. Heat Mass Transfer***3 0**, 2189–2192.Google Scholar - Lai, F. C. and Kulacki, F. A. 1988a Effects of flow inertia on mixed convection along a vertical surface in a saturated porous medium.
*ASME HTD***96**, vol. 1, 643–652.Google Scholar - Lai, F. C. and Kulacki, F. A. 1988b Transient mixed convection in horizontal porous layer locally heated from below.
*ASME HTD***96**, vol. 2, 353–364.Google Scholar - Lai, F. C. and Kulacki, F. A. 1988c Natural convection across a vertical layered porous cavity.
*Int. J. Heat Mass Transfer***31**, 1247–1260.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1989a Thermal dispersion effects on non-Darcy convection over horizontal surfaces in saturated porous media.
*Int. J. Heat Mass Transfer***32**, 971–976.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1989b Effects of variable fluid viscosity on film condensation along an inclined surface in saturated porous medium.
*ASME HTD***127**, 7–12.Google Scholar - Lai, F. C. and Kulacki, F. A. 1990a Coupled heat and mass transfer from a sphere buried in an infinite porous medium.
*Int. J. Heat Mass Transfer***33**, 209–215.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1990b The influence of surface mass flux on mixed convection over horizontal plates in saturated porous media.
*Int. J. Heat Mass Transfer***33**, 576–579.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1990c The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium.
*Int. J. Heat Mass Transfer***33**, 1028–1031.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1990d The influence of lateral mass flux on mixed convection over inclined surfaces in saturated porous media.
*ASME J. Heat Transfer***112**, 515–518.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1991a Non-Darcy mixed convection along a vertical wall in a saturated porous medium.
*ASME J. Heat Transfer***113**, 252–255.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1991b Experimental study of free and mixed convection in horizontal porous layers locally heated from below.
*Int. J. Heat Mass Transfer***34**, 525–541.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1991c Oscillatory mixed convection in horizontal porous layers locally heated from below.
*Int. J. Heat Mass Transfer***34**, 887–890.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1991d Coupled heat and mass transfer by natural convection from vertical surfaces in porous media.
*Int. J. Heat Mass Transfer***34**, 1189–1194.CrossRefGoogle Scholar - Lai, F. C. and Kulacki, F. A. 1991e Experimental study in horizontal layers with multiple heat sources.
*AIAA J. Thermophys. Heat Transfer***5**, 627–630.CrossRefGoogle Scholar - Lai, F. C., Choi, C. Y. and Kulacki, F. A. 1990a Free and mixed convection in horizontal porous layers with multiple heat sources.
*AIAA J. Thermophys. Heat Transfer***4**, 221–227.CrossRefGoogle Scholar - Lai, F. C., Choi, C. Y. and Kulacki, F. A. 1990b Coupled heat and mass transfer by natural convection from slender bodies of revolution in porous media.
*Int. Comm. Heat Mass Transfer***17**, 609–620.CrossRefGoogle Scholar - Lai, F. C., Kulacki, F. A. and Prasad, V. 1987a Mixed convection in horizontal porous layers: effects of thermal boundary conditions.
*ASME HTD***84**, 91–96.Google Scholar - Lai, F. C., Kulacki, F. A. and Prasad, V. 1991a Mixed convection in saturated porous media.
*Convective Heat and Mass Transfer in Porous Media*(eds. S. Kakaç, B. Kilkis, F. A. Kulacki and F. Arinç). Kluwer Academic, Dordrecht, pp. 225–287.Google Scholar - Lai, F. C., Pop, I. and Kulacki, F. A. 1990c Free and mixed convection from slender bodies of revolution in porous media.
*Int. J. Heat Mass Transfer***33**, 1767–1769.CrossRefGoogle Scholar - Lai, F. C., Pop, I. and Kulacki, F. A. 1991b Natural convection from isothermal plates embedded in thermally stratified porous media.
*AIAA J. Thermophys. Heat Transfer***4**, 533–535.Google Scholar - Lai, F. C., Prasad, V. and Kulacki, F. A. 1987b Effects of the size of heat source on mixed convection in horizontal porous layers heated from below.
*Proc. ASME JSME Thermal Engineering Joint Conference*, vol. 2, pp. 413–419.Google Scholar - Lai, F. C., Prasad, V. and Kulacki, F. A. 1988 Aiding and opposing mixed convection in a vertical porous layer with a finite wall heat source.
*Int. J. Heat Mass Transfer***31**, 1049–1061.CrossRefGoogle Scholar - Lan, X. K. and Khodadadi,
*J*. M. 1993 Fluid flow and heat transfer through a porous medium channel with permeable walls.*Int. J. Heat Mass Transfer***36**, 2242–2245.Google Scholar - Lapwood, E. R. 1948 Convection of a fluid in a porous medium.
*Proc. Cambridge Philos. Soc*.**44**, 508–521.MathSciNetzbMATHCrossRefGoogle Scholar - Larbi, S., Bacon, G. and Bories, S. A. 1995 Diffusion d’air humide avec condensation de vapeur d’eau en milieu poreux.
*Int. J. Heat Mass Transfer***38**, 2411–2426.CrossRefGoogle Scholar - Larson, S. E. and Poulikakos, D. 1986 Double diffusion from a horizontal line source in an infinite porous medium.
*Inn. J. Heat Mass Transfer***29**, 492–495.zbMATHCrossRefGoogle Scholar - Lauriat, G. and Prasad, V. 1987 Natural convection in a vertical porous cavity: A numerical study for Brinkman-extended Darcy formulation.
*ASME J. Heat Transfer***109**, 688–696.CrossRefGoogle Scholar - Lauriat, G. and Prasad, V. 1989 Non-Darcian effects on natural convection in a vertical porous layer.
*Int. J. Heat Mass Transfer***32**, 2135–2148.CrossRefGoogle Scholar - Lauriat, G. and Prasad, V. 1991 Natural convection in a vertical porous annulus.
*Convective Heat and Mass Transfer in Porous Media*(eds. S. Kakaç, B. Kilkis, F. A. Kulacki and F. Arinç). Kluwer Academic, Dordrecht, pp. 143–172.Google Scholar - Lauriat, G. and Vafai, K. 1991 Forced convection flow and heat transfer through a porous medium exposed to a flat plate or a channel.
*Convective Heat and Mass Transfer in Porous Media*(eds. S. Kakaç, B. Kilkis, F. A. Kulacki and F. Arinç), Kluwer Academic, Dordrecht, pp. 289–327.Google Scholar - Lawson, M. L. and Yang, W. J. 1975 Thermal instability of binary gas mixtures in a porous medium.
*ASME J. Heat Transfer***97**, 378–381.CrossRefGoogle Scholar - Lawson, M. L., Yang, W. J. and Bunditkul, S. 1976 Theory of thermal stability of binary gas mixtures in porous media.
*ASME J. Heat Transfer***98**, 35–41.CrossRefGoogle Scholar - Le Breton, P., Caltagirone, J. P. and Arquis, E. 1991 Natural convection in a square cavity with thin porous layers on its vertical walls.
*ASME J. Heat Transfer***113**, 892–898.CrossRefGoogle Scholar - Lebon, G. and Cloot, A. 1986 A thermodynamical modelling of fluid flows through porous media: Application to natural convection.
*Int. J. Heat Mass Transfer***29**, 381–390.zbMATHCrossRefGoogle Scholar - Ledezma, G. A., Bejan, A. and Errera, M. R. 1997 Constructal tree networks for heat transfer.
*J. Appl. Phys*.**82**, 89–100.CrossRefGoogle Scholar - Ledezma, G., Morega, A. M. and Bejan, A. 1996 Optimal spacing between fins with impinging flow.
*J. Heat Transfer***118**, 570–577.CrossRefGoogle Scholar - Lee, H. M. 1983 An experimental study of natural convection about an isothermal downward-facing inclined surface in a porous medium. M.S. Thesis, University of Hawaii.Google Scholar
- Lee, J. S. and Ogawa, K. 1994 Pressure drop through packed bed.
*J. Chem. Engng. Japan***27**, 691–693.CrossRefGoogle Scholar - Lee, K. and Howell, J. R. 1987 Forced convective and radiative transfer within a highly porous layer exposed to a turbulent external flow field.
*Proc. 2nd ASME/JSME Thermal Engineering Joint Conference*, vol. 2, pp. 377–386.Google Scholar - Lee, K. B. and Howell, J. R. 1991 Theoretical and experimental heat and mass transfer in highly porous media.
*Int. J. Heat Mass Transfer***34**, 2123–2132.CrossRefGoogle Scholar - Lein, H. and Tankin, R. S. 1992a Natural convection in porous media—I. Nonfreezing.
*Int. J. Heat Mass Transfer***35**, 175–186.CrossRefGoogle Scholar - Lein, H. and Tankin, R. S. 1992b Natural convection in porous media—II. Freezing.
*Int. J. Heat Mass Transfer***35**, 187–194.CrossRefGoogle Scholar - Lesnic, D., Ingham, D. B. and Pop, I. 1995 Conjugate free convection from a horizontal surface in a porous medium.
*Z. Angew. Math. Mech*., 715–722.MathSciNetzbMATHCrossRefGoogle Scholar**75** - Leu, J. S. and Jang, J. Y. 1993 Variable viscosity effects on the vortex instability of the convective boundary layer flow over a horizontal uniform heat flux surface in a saturated porous medium.
*Proc. 6th Int. Sympos. Transport Phenomena and Thermal Engineering*, Seoul, Korea. vol. 1, pp. 203–208.Google Scholar - Leu, J. S. and Jang, J. Y. 1994 The wall and free plumes above a horizontal line source in non-Darcian porous media.
*Int. J. Heat Mass Transfer***37**, 1925–1933.zbMATHCrossRefGoogle Scholar - Leu, J. S. and Jang, J. Y. 1995 The natural convection from a point heat source embedded in a non-Darcian porous medium.
*Int..1. Heat Mass Transfer***38**, 1097–1104.zbMATHCrossRefGoogle Scholar - Levy, T. 1981 Loi de Darcy ou loi de Brinkman?
*C*.**R***. Acad. Sci. Paris Sér. II***292**, 872–874.Google Scholar - Levy, T. 1990 Écoulement dans un milieu poreux avec fissures unidirectionelles.
*C.R. Acad. Sci. Paris Sér*.**11310**, 685–690.Google Scholar - Lewis, S., Bassom, A. P. and Rees, D. A. S. 1995 The stability of vertical thermal boundary-layer flow in a porous medium.
*European J. Mech. B/Fluids***14**, 395–407.MathSciNetzbMATHGoogle Scholar - Poulikakos, D. and Bejan, A. 1984a Natural convection in a porous layer heated and cooled along one vertical side.
*Int. J. Heat Mass Transfer***27**, 1879–1891.zbMATHCrossRefGoogle Scholar - Poulikakos, D. and Bejan, A. 1984a Natural convection in a porous layer heated and cooled along one vertical side.
*Int. J. Heat Mass Transfer***27**, 1879–1891.zbMATHCrossRefGoogle Scholar - Poulikakos, D. and Bejan, A. 1984b Penetrative convection in porous medium bounded by a horizontal wall with hot and cold spots.
*Int. J. Heat Mass Transfer***27**, 1749–1757.zbMATHCrossRefGoogle Scholar - Poulikakos, D. and Bejan, A. 1985 The departure from Darcy flow in natural convection in a vertical porous layer.
*Phys. Fluids***28**, 3477–3484.MathSciNetzbMATHCrossRefGoogle Scholar - Poulikakos, D. and Kazmierczak, M. 1987 Forced convection in a duct partially filled with a porous material.
*ASME J. Heat Transfer***109**, 653–662.CrossRefGoogle Scholar - Prax, C., Sadat, H. and Slagnac, P. 1996 Diffuse approximation method for solving natural convection in porous media.
*Transport in Porous Media***22**, 215–223.CrossRefGoogle Scholar - Prescott, P. J. and Incropera, F. P. 1995 The effect of turbulence on solidification of binary metal alloy with electromagnetic stirring.
*ASME J. Heat Transfer***117**, 716–724.CrossRefGoogle Scholar - Prescott, P. J. and Incropera, F. P. 1996 Convection heat and mass transfer in alloy solidification.
*Adv. Heat Transfer***28**, 231–329.CrossRefGoogle Scholar - Rees, D. A. S. and Riley, D. S. 1985 Free convection above a near horizontal semi-infinite heated surface embedded in a saturated porous medium.
*Int. J. Heat Mass Transfer***28**, 183–190.zbMATHCrossRefGoogle Scholar - Rees, D. A. S. and Riley, D. S. 1989a The effects of boundary imperfections on convection in a saturated porous layer: Near-resonant wavelength excitation.
*J. Fluid Mech*.**199**, 133–154.MathSciNetzbMATHCrossRefGoogle Scholar - Rees, D. A. S. and Riley, D. S. 1989b The effects of boundary imperfections on convection in a saturated porous layer: Non-resonant wavelength excitation.
*Proc. Roy. Soc. London Ser. A***421**, 303–339.zbMATHCrossRefGoogle Scholar - Rees, D. A. S. and Bassom, A. P. 1991 Some exact solutions for free convective flows over heated semi-infinite surfaces in porous media.
*Int. J. Heat Mass Transfer***34**, 1564–1567.CrossRefGoogle Scholar - Rees, D. A. S. and Bassom, A. P. 1993 The nonlinear non-parallel wave instability of boundary-layer flow induced by a horizontal heated surface in porous media.
*J. Fluid Mech*.**253**, 267–295.MathSciNetzbMATHCrossRefGoogle Scholar - Rees, D. A. S. and Bassom, A. P. 1994 The linear wave instability of boundary layer flow induced by a horizontal heated surface in porous media.
*Int. Comm. Heat Mass Transfer***21**, 143–150.CrossRefGoogle Scholar - Rees, D. A. S. and Lage, J. L. 1996 The effect of thermal stratification on natural convection in a vertical porous medium layer.
*Int. J. Heat Mass Transfer***40**, 111–121.CrossRefGoogle Scholar - Rubin, H. 1975 Effect of solute dispersion on thermal convection in a porous medium layer. 2.
*Water Resources Res*.**11**, 154–158.CrossRefGoogle Scholar - Rubin, H. 1976 Onset of thermohaline convection in a cavernous aquifer.
*Water Resources Res*.**12**, 141–147.CrossRefGoogle Scholar - Rubin, H. 1981 Onset of thermohaline convection in heterogeneous porous media.
*Israel J. Tech*.**19**, 110–117.zbMATHGoogle Scholar - Rubin, H. 1982a Thermohaline convection in a nonhomogeneous aquifer.
*J. Hydrol*.**57**, 307–320.CrossRefGoogle Scholar - Rubin, H. 1982b Application of the aquifer’s average characteristics for determining the onset of thermohaline convection in a heterogeneous aquifer.
*J. Hydrol*.**57**, 321–336.CrossRefGoogle Scholar - Schubert, G. and Straus, J. M. 1982 Transitions in time-dependent thermal convection in fluid-saturated porous media.
*J. Fluid Mech*.**121**, 301–303.zbMATHCrossRefGoogle Scholar - Schulenberg, T. and Müller, U. 1984 Natural convection in saturated porous layers with internal heat sources.
*Int. J. Heat Mass Transfer***27**, 677–685.CrossRefGoogle Scholar - Seetharamu, K. N. and Dutta, P. 1990 Free convection in a saturated porous medium adjacent to a non-isothermal vertical impermeable wall.
*Wärme-Stoffübertrag*.**25**, 9–15.CrossRefGoogle Scholar - Selimos, B. and Poulikakos, D. 1985 On double diffusion in a Brinkman heat generating porous layer.
*Int. Comm. Heat Mass Transfer***12**, 149–158.CrossRefGoogle Scholar - Sheridan, J., Williams, A. and Close, D. J. 1992 Experimental study of natural convection with coupled heat and mass transfer in porous media.
*Int. J. Heat Mass Transfer***35**, 2131–2143.CrossRefGoogle Scholar - Shin, U. C., Khedari, J. Mbow, C. and Daguenet, M. 1994 Convection naturelle thermique a l’intérieur d’une calotte cylindrique poreuse d’axe horizontal: Etude théorique.
*Rev. Gén. Thermique***33**, 30–37.Google Scholar - Shiralkar, G. S., Haadjizadeh, M. and Tien, C. L. 1983 Numerical study of high Rayleigh number convection in a vertical porous enclosure.
*Numer. Heat Transfer A***6**, 223–234.zbMATHGoogle Scholar - Storesletten, L. and Tveitereid, M. 1987 Thermal convection in a porous medium confined by a horizontal cylinder.
*ASME HTD***92**, 223–230.Google Scholar - Storesletten, L. and Tveitereid, M. 1991 Natural convection in a horizontal porous cylinder.
*Int. J. Heat Mass Transfer***34**, 1959–1968.zbMATHCrossRefGoogle Scholar - Strange, R. and Rees, D. A. S. 1996 The effect of fluid inertia on the stability of free convection in a saturated porous medium heated from below.
*Proceedings of the International Conference on Porous Media and their Applications in Science, Engineering and Industry*(eds. K. Vafai and P. N. Shivakumar). Engineering Foundation, New York, pp. 71–84.Google Scholar - Straughan, B. 1988 A nonlinear analysis of convection in a porous vertical slab.
*Geophys. Astrophys. Fluid Dyn*.**42**, 269–276.MathSciNetzbMATHCrossRefGoogle Scholar - Thevenin, J. 1995 Transient forced convection heat transfer from a circular cylinder embedded in a porous medium.
*Int. Comm. Heat Mass Transfer***22**, 507–516.CrossRefGoogle Scholar - Thevenin, J. and Sadaoui, D. 1995 About enhancement of heat transfer over a circular cylinder embedded in a porous medium.
*Int. J. Heat Mass Transfer***22**, 205–304.Google Scholar - Tien, C. L. and Vafai, K. 1990 Convective and radiative heat transfer in porous media.
*Adv. Appl. Mech*.**27**, 225–281.zbMATHCrossRefGoogle Scholar - Trevisan, O. V. and Bejan, A. 1986 Mass and heat transfer by natural convection in a vertical slot filled with porous medium.
*Int. J. Heat Mass Transfer***29**, 403–415.zbMATHCrossRefGoogle Scholar - Trevisan, O. V. and Bejan, A. 1987a Combined heat and mass transfer by natural convection in a vertical enclosure.
*ASME J. Heat Transfer***109**, 104–109.CrossRefGoogle Scholar - Trevisan, O. V. and Bejan, A. 1987b Mass and heat transfer by high Rayleigh number convection in a porous medium heated from below.
*Int. J. Heat Mass Transfer***30**, 2341–2356.CrossRefGoogle Scholar - Vadasz, P. 1995 Coriolis effect on free convection in a long rotating box subject to uniform heat generation.
*Int. J. Heat Mass Transfer***38**, 2011–2018.zbMATHCrossRefGoogle Scholar - Vadasz, P. 1996a Stability of free convection in a rotating porous layer distant from the axis of rotation.
*Transport in Porous Media***23**, 153–173.CrossRefGoogle Scholar - Weidman, P. D. and Kassoy, D. R. 1986 Influence of side wall heat transfer on convection in a confined saturated porous medium.
*Phys. Fluids***29**, 349–355.MathSciNetzbMATHCrossRefGoogle Scholar - Wettlaufer, J. S., Worster, M. G. and Huppert, H. E. 1997 Natural convection during solidification of an alloy from above with application to the evolution of sea
*ice. J. Fluid Mech*.**344**, 291–316.CrossRefGoogle Scholar - Vedha-Nayagam, M., Jain, P. and Fairweather, G. 1987 The effect of surface mass transfer on buoyancy induced flow in a variable-porosity medium adjacent to a horizontal heated plate.
*Int. Comm. Heat Mass Transfer***14**, 495–506.CrossRefGoogle Scholar - Vynnycky, M. and Kimura, S. 1994 Conjugate free convection due to a vertical plate in a porous medium.
*Int. J. Heat Mass Transfer***37**, 229–236.zbMATHCrossRefGoogle Scholar - Vynnycky, M. and Kimura, S. 1995 Transient conjugate free convection due to a vertical plate in a porous medium.
*Int. J. Heat Mass Transfer***38**, 219–231.zbMATHCrossRefGoogle Scholar - Vynnycky, M. and Pop, I. 1997 Mixed convection due to a finite horizontal flat plate embedded in a porous medium.
*J. Fluid Mech*.,**351**, 359–378.zbMATHCrossRefGoogle Scholar - Yan, B., Pop, I. and Ingham, D. B. 1997 A numerical study of unsteady free convection from a sphere in a porous medium.
*Int J. Heat Mass Transfer***40**, 893–903.zbMATHCrossRefGoogle Scholar - Yang, Y. T. and Wang, S. J. 1996 Free convection heat transfer of non-Newtonian fluids over axisymmetric and two—dimensional bodies of arbitrary shape embedded in a fluid-saturated porous medium.
*Int. J. Heat Mass Transfer***39**, 203–210.CrossRefGoogle Scholar - Zaturska, M. B. and Banks, W. H. H. 1987 On the spatial stability of free-convection flows in a saturated porous medium.
*J. Engng. Math*.**21**, 41–46.zbMATHCrossRefGoogle Scholar

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