Convection in Porous Media pp 261-319 | Cite as

# Internal Natural Convection: Heating from the Side

Chapter

## Abstract

Enclosures heated from the side are most representative of porous systems that function while oriented vertically, as in the insulations for buildings, industrial cold-storage installations, and cryogenics. As in the earlier chapters, we begin with the most fundamental aspects of the convection heat transfer process when the flow is steady and in the Darcy regime. Later, we examine the special features of flows that deviate from the Darcy regime, flows that are time-dependent, and flows that are confined in geometries more complicated than the two-dimensional rectangular space shown in Fig. 7.1.

## Keywords

Heat Transfer Porous Medium Nusselt Number Natural Convection Rayleigh Number## Preview

Unable to display preview. Download preview PDF.

## References

- Aboubi, K., Robillard, L. and Bilgen, E. 1995a Convective heat transfer in an annular porous layer with centrifugal force field.
*Numer. Heat Transfer A***28**, 375–388.CrossRefGoogle Scholar - Aboubi, K., Robillard, L. and Bilgen, E. 1995b Natural convection in horizontal annulus filled with an anisotropic porous medium.
*Proc. ASME/JSME Thermal Engineering Joint Conf*. vol. 3, pp 415–422.Google Scholar - Al-Nimr, M. A. and Darabseh, T. T. 1995 Analytical solution for transient laminar free convection in open-ended vertical concentric porous annuli.
*ASME J. Heat Transfer***117**, 762–764.CrossRefGoogle Scholar - Alchaar, S., Vasseur, P. and Bilgen, E. 1995b Hydromagnetic natural convection in a tilted rectangular porous enclosure.
*Numer. Heat Transfer A***27**, 107–127.CrossRefGoogle Scholar - Anderson, D. M. and Worster, M. G. 1996 A new oscillatory instability in a mushy layer during the solidification of binary alloys.
*J. Fluid Mech*.**307**, 245–267.MATHCrossRefGoogle Scholar - Anderson, P. and Glasser, D. 1990 Thermal convection and surface temperatures i n porous media.
*Int. J. Heat Mass Transfer***33**, 1321–1330.Google 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.MATHCrossRefGoogle Scholar - Angirasa, D., Peterson, G. P. and Pop, I. 1997a Combined heat and mass transfer by natural convection in a saturated thermally stratified porous medium.
*Numer. Heat Transfer A***31**, 255–272.CrossRefGoogle Scholar - Angirasa, D., Peterson, G. P. and Pop, I. 1997b Combined heat and mass transfer by natural convection with opposing buoyancy effects in a fluid saturated porous medium.
*Int. J. Heat Mass Transfer***40**, 2755–2773.MATHCrossRefGoogle Scholar - Ansari, A. and Daniels, P. G. 1993 Thermally driven tall cavity flows in porous media.
*Proc. Roy. Soc. London Ser. A***433**, 163–181.Google Scholar - Ansari, A. and Daniels, P. G. 1994 Thermally driven tall cavity flows in porous media: The convective regime.
*Proc. Roy. Soc. London Ser. A***444**, 375–388.MATHCrossRefGoogle Scholar - Antohe, B. V. and Lage, J. L. 1994 A dynamic thermal insulator: Inducing resonance within a fluid saturated porous medium heated periodically from the side.
*Int. J. Heat Mass Transfer***37**, 771–782.MATHCrossRefGoogle Scholar - Antohe, B. V. and Lage, J. L. 1996 Amplitude effect on convection induced by time-periodic heating.
*Int. J. Heat Mass Transfer***39**, 1121–1133.CrossRefGoogle Scholar - Antohe, B. V. and Lage, J. L. 1997a The Prandtl number effect on the optimum heating frequency of an enclosure filled with fluid or with a saturated porous medium.
*Int. J. Heat Mass Transfer***40**, 1313–1323.MATHCrossRefGoogle Scholar - Antohe, B. V. and Lage, J. L. 1997b A general two-equation macroscopic turbulence model for incompressible flow in porous media.
*Int. J. Heat Mass Transfer***40**, 3013–3024.MATHCrossRefGoogle Scholar - Artem’eva, E. L. and Stroganova, E. V. 1987 Stability of a nonuniformly heated fluid in a porous horizontal layer.
*Fluid Dynamics***21**, 845–848.CrossRefGoogle Scholar - Asako, Y., Nakamura, H., Yamaguchi, Y. and Fagri, M. 1992 Three-dimensional natural convection in a vertical porous layer with a hexagonal honeycomb core.
*ASME J. Heat Transfer***114**, 924–927.CrossRefGoogle Scholar - Avroam, D. G. and Payatakes, A. C. 1995 Flow regimes and relative permeabilities during steady-state two-phase flow in porous media.
*J. Fluid Mech*.**293**, 207–236.MathSciNetCrossRefGoogle Scholar - Badr, H. M. and Pop, I. 1988 Combined convection from an isothermal horizontal rod buried in a porous medium.
*Int. J. Heat Mass Transfer***31**, 2527–2541.MATHCrossRefGoogle Scholar - Badr, H. M. and Pop, I. 1992 Effect of flow direction on mixed convection from a horizontal rod embedded in a porous medium.
*Trans. Can. Soc. Mech. Engng*.**16**, 267–290.Google Scholar - Bai, M. and Roegiers, J. C. 1994 Fluid flow and heat flow in deformable fractured media.
*Int. J. Engng. Sci*.**32**, 1615–1663.MATHCrossRefGoogle Scholar - Bai, M., Ma, Q. and Roegiers, J. C. 1994a Dual porosity behaviour of naturally fractured reservoirs.
*Int. J. Numer. Anal. Mech. Geomech*.**18**, 359–376.MATHCrossRefGoogle Scholar - Bai, M., Ma, Q. and Roegiers, J. C. 1994b Nonlinear dual-porosity model.
*Appl. Math. Modelling***18**, 602–610.MATHCrossRefGoogle Scholar - Bai, M., Roegiers, J. C. and Inyang, H. F. 1996 Contaminant transport in nonisothermal fractured porous media.
*J. Env. Engng*.**122**, 416–423.CrossRefGoogle Scholar - Balakotaiah, V. and Portalet, P. 1990a Natural convection effects on thermal ignition in a porous medium. I. Semenov model.
*Proc. Roy. Soc. London Ser. A***429**, 533–554.CrossRefGoogle Scholar - Balakotaiah, V. and Portalet, P. 1990b Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I.
*Proc. Roy. Soc. London Ser. A***429**, 555–567.CrossRefGoogle Scholar - Bankvall, C. G. 1974 Natural convection in a vertical permeable space.
*Wärme-Stoffübertrag*.**7**, 22–30.CrossRefGoogle Scholar - Barak, A. Z. 1987 Comments on “High velocity flow in porous media” by Hassanizadeh and Gray.
*Transport in Porous Media***2**, 533–535.CrossRefGoogle Scholar - Barbosa Mota, J. P. and Saatdjian, E. 1994 Natural convection in a porous, horizontal cylindrical annulus.
*ASME J. Heat Transfer***116**, 621–626.CrossRefGoogle Scholar - Barbosa Mota, J. P. and Saatdjian, E. 1995 Natural convection in porous cylindrical annuli.
*Int. J. Numer. Methods Heat Fluid Flow***5**, 3–17.MATHCrossRefGoogle Scholar - Barbosa Mota, J. P., Le Provost, J. F., Puons, E. and Saatdjian, E. 1994 Natural convection in porous, horizontal eccentric annuli.
*Heat Transfer*,*1994*. Inst. Chem. Engrs, Rugby, vol.**5**, 435–440.Google Scholar - Barenblatt, G. I., Entov, V. M. and Ryzhik, V. M. 1990
*Theory of Fluid Flow Through Natural Rocks*, Kluwer Academic, Dordrecht.Google Scholar - Bartlett, R. F. and Viskanta, R. 1996 Enhancement of forced convection in an asymmetrically heated duct filled with high thermal conductivity porous media.
*J. Enhanced Heat Transfer***3**, 291–299.Google Scholar - Bassom, A. P. and Rees, D. A. S. 1995 The linear vortex instability of flow induced by a horizontal heated surface in a porous medium.
*Quart. J. Mech. Appl. Mech*.**48**, 1–19.MathSciNetMATHCrossRefGoogle Scholar - Bassom, A. P. and Rees, D. A. S. 1996 Free convection from a heated vertical cylinder embedded in a fluid-saturated porous medium.
*Acta Mech*.**116**, 139–151.MATHCrossRefGoogle Scholar - Basu, A. and Islam, M. R. 1996 Instability in a combined heat and mass transfer problem in porous media.
*Chaos*,*Solitons*,*Fractals***7**, 109–123.Google Scholar - Batchelor, G. K. 1967
*An Introduction to Fluid Dynamics*. Cambridge University Press, Cambridge, UK.Google Scholar - Bau, H. H. 1984a Low Rayleigh number thermal convection in a saturated porous medium bounded by two horizontal, eccentric cylinders.
*ASME J. Heat Transfer***106**, 166–175.CrossRefGoogle Scholar - Bau, H. H. 1984b Convective heat losses from a pipe buried in a semi-infinite porous medium.
*Int. J. Heat Mass Transfer***27**, 2047–2056.MATHCrossRefGoogle Scholar - Bau, H. H. 1984c Thermal convection in a horizontal, eccentric annulus containing a saturated porous medium—An extended perturbation expansion.
*Int. J. Heat Mass Transfer***27**, 2277–2287.MATHCrossRefGoogle Scholar - Bau, H. H. 1986 Estimation of heat losses from flows in buried pipes.
*Handbook of Heat and Mass Transfer*(ed. N.P. Cheremisinoff). Gulf Publishing, Houston, TX, vol.**1**, 1009–1024Google Scholar - Bau, H. H. 1993 Controlling chaotic convection.
*Theoretical and Applied Mechanics*,*1992*(eds. S. R. Bodner*et al*.*)*. Elsevier, Amsterdam, 187–203.Google Scholar - Bau, H. H. and Torrance, K. E. 1981 Onset of convection in a permeable medium between vertical coaxial cylinders.
*Phys. Fluids***24**, 382–385.MATHCrossRefGoogle Scholar - Bau, H. H. and Torrance, K. E. 1982a Boiling in low permeability porous materials.
*Int. J. Heat Mass Transfer***25**, 45–55.CrossRefGoogle Scholar - Bau, H. H. and Torrance, K. E. 1982b Low Rayleigh number thermal convection in a vertical cylinder filled with porous materials and heated from below.
*ASME J. Heat Transfer***104**, 166–172.CrossRefGoogle Scholar - Bau, H. H. and Torrance, K. E. 1982c Thermal convection and boiling in a porous medium.
*Lett. Heat Mass Transfer***9**, 431–441.CrossRefGoogle Scholar - Bear, J. and Bachmat, Y. 1990
*Introduction to Modeling of Transport Phenomena in Porous Media*. Kluwer Academic, Dordrecht.CrossRefGoogle Scholar - Beavers, G. S. and Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall.
*J. Fluid Mech*.**30**, 197–207.CrossRefGoogle Scholar - Beavers, G. S., Sparrow, E. M. and Magnuson, R. A. 1970 Experiments on coupled parallel flows in a channel and a bounding medium.
*ASME J. Basic Engng*.**92**, 843–848.CrossRefGoogle Scholar - Beavers, G. S., Sparrow, E. M. and Masha, B. A. 1974 Boundary conditions at a porous surface which bounds a fluid flow.
*AIChE J*.**20**, 596–597.CrossRefGoogle Scholar - Beavers, G. S., Sparrow, E. M. and Rodenz, D. E. 1973 Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres.
*J. Appl. Mech*.**40**, 655–660.CrossRefGoogle Scholar - Beck, J. L. 1972 Convection in a box of porous material saturated with fluid.
*Phys. Fluids***15**, 1377–1383.CrossRefGoogle Scholar - Beckermann, C. and Viskanta, R. 1987 Forced convection boundary layer flow and heat transfer along a flat plate embedded in a porous medium.
*Int. J. Heat Mass Transfer***30**, 1547–1551.CrossRefGoogle Scholar - Beckermann, C. and Viskanta, R. 1988a Natural convection solid/liquid phase change in porous media.
*Int. J. Heat Mass Transfer***31**, 35–46.CrossRefGoogle Scholar - Beckermann, C. and Viskanta, R. 1988b Double-diffusive convection during dendritic solidification of a binary mixture.
*Phys. Chem. Hydrodyn*.**10**, 195–213.Google Scholar - Beckermann, C. and Viskanta, R. 1993 Mathematical modeling of transport phenomena during alloy solidification.
*Appl. Mech. Rev*.**46**, 1–27.MathSciNetCrossRefGoogle Scholar - Beckermann, C. and Wang, C. Y. 1995 Multiphase/- scale modeling of alloy solidification.
*Ann. Rev. Heat Transfer***6**, 115–198.Google Scholar - Beckermann, C., Viskanta, R. and Ramadhyani, S. 1986 A numerical study of nonDarcian natural convection in a vertical enclosure filled with a porous medium.
*Numer. Heat Transfer***10**, 557–570.Google Scholar - Beckermann, C., Viskanta, R. and Ramadhyani, S. 1988 Natural convection in vertical enclosures containing simultaneously fluid and porous layers.
*J. Fluid Mech*.**186**, 257–284.MATHCrossRefGoogle Scholar - Bejan, A. 1978 Natural convection in an infinite porous medium with a concentrated heat source.
*J. Fluid Mech*.**89**, 97–107.MATHCrossRefGoogle Scholar - Bejan, A. 1979 On the boundary layer regime in a vertical enclosure filled with a porous medium.
*Lett. Heat Mass Transfer***6**, 93–102.CrossRefGoogle Scholar - Bejan, A. 1980 A synthesis of analytical results for natural convection heat transfer across rectangular enclosures.
*Int. J. Heat Mass Transfer***23**, 723–726.CrossRefGoogle Scholar - Bejan, A. 1981 Lateral intrusion of natural convection into a horizontal porous structure.
*ASME J. Heat Transfer***103**, 237–241.CrossRefGoogle Scholar - Bejan, A. 1983a Natural convection heat transfer in a porous layer with internal flow obstructions.
*Int. J. Heat Mass Transfer***26**, 815–822.MATHCrossRefGoogle Scholar - Bejan, A. 1983b The boundary layer regime in a porous layer with uniform heat flux from the side.
*Int. J. Heat Mass Transfer***26**, 1339–1346.MATHCrossRefGoogle Scholar - Bejan, A. 1984
*Convection Heat Transfer*, Wiley, New York.MATHGoogle Scholar - Bejan, A. 1985 The method of scale analysis: Natural convection in porous media.
*Natural Convection: Fundamentals and Applications*(eds. S. Kakaç, W. Aung and R Viskanta). Hemisphere, Washington, DC, pp 548–572.Google Scholar - Bejan, A. 1987 Convective heat transfer in porous media.
*Handbook of Single-Phase. Convective Heat Transfer*(eds. S. Kakaç, R. K. Shah and W. Aung), Wiley, New York. Chapter 16Google Scholar - Bejan, A. 1989 Theory of melting with natural convection in an enclosed porous medium.
*ASME J. Heat Transfer*, 407–415.Google Scholar**111** - Bejan, A. 1990a Theory of heat transfer from a surface covered with hair.
*ASME J. Heat Transfer***112**, 662–667.CrossRefGoogle Scholar - Bejan, A. 1990b Optimum hair strand diameter for minimum free-convection heat transfer from a surface covered with hair.
*Int. J. Heat Mass Transfer***33**, 206–209.CrossRefGoogle Scholar - Bejan, A. 1992a Comments on “Coupled heat and mass transfer by natural convection from vertical surfaces in porous media.”
*Int. J. Heat Mass Transfer***35**, 34–98.Google Scholar - Bejan, A. 1992b Surfaces covered with hair: Optimal strand diameter and optimal porosity for minimum heat transfer.
*Biomimetics*, 23–38.Google Scholar**1** - Bejan, A. 1993
*Heat Transfer*. Wiley, New York.Google Scholar - Bejan, A. 1995 The optimal spacing for cylinders in crossflow forced convection.
*J. Heat Transfer***117**, 767–770.CrossRefGoogle Scholar - Bejan, A. 1996a
*Entropy Generation Minimization*. CRC Press, Boca Raton, FL.Google Scholar - Bejan, A. 1996b Street network theory of organization in nature.
*J. Adv. Transportation***30**, 85–107.CrossRefGoogle Scholar - Bejan, A. 1997a Constructal-theory network of conducting paths for cooling a heat generating volume.
*Int. J. Heat Mass Transfer***40**, 799–816.MATHCrossRefGoogle Scholar - Bejan, A. 1997b Constructal tree network for fluid flow between a finite-size volume and one source or sink.
*Rev. Gén. Thermique***36**, 592–604.CrossRefGoogle Scholar - Bejan, A. 1997c
*Advanced Engineering Thermodynamics*, 2nd ed. Wiley, New York.Google 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.MATHCrossRefGoogle 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 Khair, K. R. 1985 Heat and mass transfer by natural convection in a porous medium.
*Int. J. Heat Mass Transfer***28**, 909–918.MATHCrossRefGoogle Scholar - Bejan, A. and Lage,
*J*. L. 1991 Heat transfer from a surface covered with hair.*Convective Heat and Mass Transfer in Porous Media*(eds. S. Kakaç, B. Kilkis, F.A. Kulacki and F. Arinç). Kluwer Academic, Dordrecht, pp 823–845.Google Scholar - Bejan, A. and Morega, A. M. 1993 Optimal arrays of pin fins and plate fins in laminar forced convection.
*ASME J. Heat Transfer***115**, 75–81.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 - Bejan, A. and Poulikakos, D. 1984 The non-Darcy regime for vertical boundary layer natural convection in a porous medium.
*Int. J. Heat Mass Transfer***27**, 717–722.MATHCrossRefGoogle Scholar - Bejan, A. and Sciubba, E. 1992 The optimal spacing of parallel plates cooled by forced convection.
*Int. J. Heat Mass Transfer***35**, 3259–3264.CrossRefGoogle Scholar - Bejan, A. and Tien, C. L. 1978 Natural convection in a horizontal porous medium subjected to an end-to-end temperature difference.
*ASME J. Heat Transfer**100*, 191–198; Errata**105**, 683–684.Google Scholar - Bejan, A. and Tien, C. L. 1979 Natural convection in horizontal space bounded by two concentric cylinders with different end temperatures.
*Int. J. Heat Mass Transfer***22**, 919–927.MATHCrossRefGoogle Scholar - Bejan, A., Zhang, Z. and Jany, P. 1990 The horizontal intrusion layer of melt in a saturated porous medium.
*Int. J. Heat Fluid Flow*, 284–289.Google Scholar**11** - Beji, H. and Gobin, P. 1992 The effect of thermal dispersion on natural dispersion heat transfer in porous media.
*Numer. Heat Transfer A***23**, 487–500.CrossRefGoogle Scholar - Bennon, W. D. and Incropera, F. P. 1987 A continuum model for momentum, heat and species transport in binary-liquid phase change systems. I. Model formulation.
*Int. J. Heat Mass Transfer***30**, 2161–2170.MATHCrossRefGoogle Scholar - Bergman, M. I. and Fearn, D. R. 1994 Chimneys on the Earth’s inner-outer core boundary?
*Geophys. Res. Leu*.**21**, 477–480.CrossRefGoogle Scholar - Bergman, M. I., Fearn, D. R., Bloxham, J. and Shannon, M. C. 1997 Convection and channel formation in solidifying Pb—Sn alloys.
*Metall. Mat. Trans. A***28**, 859–866.Google Scholar - Beukema, K. J. and Bruin, S. 1983 Three-dimensional natural convection in a confined porous medium with internal heat generation.
*Int. J. Heat Mass Transfer***26**, 451–458.MATHCrossRefGoogle Scholar - Bian, W. and Wang, B. X. 1993 Transient freezing and natural convection around a cylinder in saturated porous media.
*Proc. 6th Int. Sympos. Transport Phenomena in Thermal Engineering*, Seoul, Korea, pp 297–302.Google Scholar - Bian, W., Vasseur, P. and Bilgen, E. 1994a Natural convection of non-Newtonian fluids in an inclined porous layer.
*Chem. Engng. Commun*.**129**, 79–97.CrossRefGoogle Scholar - Bian, W., Vasseur, P. and Bilgen, E. 1994b Boundary-layer analysis for natural convection in a vertical porous layer filled with a non-Newtonian fluid.
*Int. J. Heat Fluid Flow***15**, 384–391.CrossRefGoogle Scholar - Bian, W., Vasseur, P. and Bilgen, E. 1996a Effect of an external magnetic field on buoyancy driven flow in a shallow porous cavity.
*Numer. Heat Transfer A***29**, 625–638.CrossRefGoogle Scholar - Bian, W., Vasseur, P. Bilgen, E. and Meng, F. 1996b Effect of an electromagnetic field on natural convection in an inclined porous layer.
*Int. J. Heat Fluid Flow***17**, 36–44CrossRefGoogle Scholar - BjOrlykke, K., Mo, A. and Palm, E. 1988 Modelling of thermal convection i n sedimentary basins and its relevance to diagenetic reactions.
*Marine Petrol. Geol*. 5, 338–351.CrossRefGoogle Scholar - Bjornsson, S. and Stefansson, V. 1987 Heat and mass transport in geothermal reservoirs.
*Advances in Transport Phenomena in Porous Media*(eds. J. Bear and M. Y. Corapcioglu). Martinus Nijhoff, Amsterdam, The Netherlands, pp. 145–153.Google Scholar - Blake, K. R., Bejan, A. and Poulikakos, D. 1984 Natural convection near 4 °C in a water saturated porous layer heated from below.
*Int. J. Heat Mass Transfer***27**, 2355–2364MATHCrossRefGoogle Scholar - Blythe, P. A. and Simpkins, P. G. 1981 Convection in a porous layer for a temperature-dependent viscosity.
*Int. J. Heat Mass Transfer***24**, 497–506.MATHCrossRefGoogle Scholar - Blythe, P. A., Daniels, P. G. and Simpkins, P. G. 1982 Thermally driven cavity flows in porous media.
**I**. The vertical boundary layer structure near the corners.*Proc. Roy. Soc. London*Ser. A**380**, 119–136.MATHCrossRefGoogle Scholar - Boussinesq, J. 1903
*Théorie Analytique de la Chaleur*. Gauthier-Villars, Paris. vol. 2.Google Scholar - Bradean, R., Heggs, P. J., Ingham, D. B. and Pop, I. 1998 Convective heat flow from suddenly heated surfaces embedded in porous media.
*Transport Phenomena in Porous Media*(eds. D. B. Ingham and I. Pop). Elsevier, Amsterdam, pp. 411–438.Google Scholar - Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1995a Buoyancy induced flow adjacent to a periodically heated and cooled horizontal surface in porous media.
*Int. J. Heat Mass Transfer***39**, 615–630.CrossRefGoogle Scholar - Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1995b Free convection fluid flow due to a periodically heated and cooled vertical plate embedded in a porous media.
*Int. J. Heat Mass Transfer***39**, 2545–2557.CrossRefGoogle Scholar - Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1996 Unsteady free convection from a horizontal surface embedded in a porous
*media. Proc. 2nd European Thermal-Sciences and 14th UIT Nat. Heat Transfer Conference*. Edizioni ETS, Pisa, vol. pp.**1**, 329–335.Google Scholar - Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I. 1997a The unsteady penetration of free convection flows caused by heating and cooling flat surfaces in a porous media.
*Int. J. Heat Mass Transfer***40**, 665–687.MATHCrossRefGoogle Scholar - Bradean, R., Ingham, D. B., Heggs, P. and Pop, I. 1997b Unsteady free convection adjacent to an impulsively heated horizontal circular cylinder in porous media.
*Numer. Heat Transfer*A**32**, 325–346.Google Scholar - Bradshaw, S., Glasser, D. and Brooks, K. 1991 Self-ignition and convection patterns in an infinite coal layer.
*Chem. Engng. Commun*.**105**, 255–278.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.MathSciNetMATHCrossRefGoogle Scholar - Brand, H. and Steinberg, V. 1983a Convective instabilities in binary mixtures in a porous medium.
*Physica A***119**, 327–338.MathSciNetCrossRefGoogle Scholar - Brand, H. and Steinberg, V. 1983b Nonlinear effects in the convective instability of a binary mixture in a porous medium near threshold.
*Phys. Lett. A***93**, 333–336.CrossRefGoogle Scholar - Brand, H.
**R**., Hohenberg, P. C. and Steinberg, V. 1983 Amplitude equation near a polycritical point for the convective instability of a binary fluid mixture in a porous medium.*Phys. Rev. A***27**, 591–594.Google Scholar - Bratsun, D. A. and Lyubimov, D. V. 1995 Co-symmetry breakdown in problems of thermal convection in porous medium.
*Physica D***82**, 398–417.MathSciNetMATHCrossRefGoogle Scholar - Brinkman, H. C. 1947a A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles.
*Appl. Sci. Res. A**1*, 27–34.CrossRefGoogle Scholar - Brinkman, H. C. 1947b On the permeability of media consisting of closely packed porous particles.
*Appl. Sci. Res. A***1**, 81–86.CrossRefGoogle Scholar - Buikis, A. and Ulanova, N. 1996 Modelling of non-isothermal gas flow through a heterogeneous medium.
*Int. J. Heat Mass Transfer***39**, 1743–1748.MATHCrossRefGoogle Scholar - Buonanno, G. and Carotenuto, A. 1997 The effective thermal conductivity of a porous medium with interconnected particles.
*Int. J. Heat Mass Transfer***40**, 393–405.MATHCrossRefGoogle Scholar - Buretta, R. J. and Berman, A. S. 1976 Convective heat transfer in a liquid saturated porous layer.
*ASME J. Appl. Mech*.**43**, 249–253.CrossRefGoogle Scholar - Burns, A. S. and Stewart, W. E. 1992 Convection in heat generating porous media in a concentric annulus with a permeable outer boundary.
*Int. Comm. Heat Mass Transfer***19**, 127–136.CrossRefGoogle Scholar - Burns, P. J. and Tien, C. L. 1979 Natural convection in porous media bounded by concentric spheres and horizontal cylinders.
*Int. J. Heat Mass Transfer***22**, 929–939.CrossRefGoogle Scholar - Busse, F. H. 1985 Transition to turbulence in Rayleigh–Bénard convection.
*Hydrodynamic Instabilities and the Transition to Turbulence*(eds. H. L. Swinney and J. Gollub), 2nd ed. Springer-Verlag, Berlin, pp. 97–137.Google Scholar - Busse, F. H. and Joseph, D. D. 1972 Bounds for heat transfer in a porous layer.
*J. Fluid Mech*.**54**, 521–543.MATHCrossRefGoogle Scholar - Caltagirone, J. P. 1975 Thermoconvective instabilities in a horizontal porous layer.
*J. Fluid Mech*.**72**, 269–287.MATHCrossRefGoogle Scholar - Caltagirone, J. P. 1976a Stabilité d’une couche poreuse horizontale soumise a des conditions aux limites périodiques.
*Int. J. Heat Mass Transfer***19**, 815–820.MATHCrossRefGoogle Scholar - Caltagirone, J. P. 1976b Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders.
*J. Fluid Mech*.**76**, 337–362.MATHCrossRefGoogle Scholar - Caltagirone, J. P. 1980 Stability of a saturated porous layer subject to a sudden rise in surface temperature: Comparison between the linear and energy methods.
*Quart. J. Mech. Appl. Math*.**33**, 47–58.MATHCrossRefGoogle Scholar - Caltagirone, J. P. and Bories, S. 1985 Solutions and stability criteria of natural convective flow in an inclined porous layer.
*J. Fluid Mech*.**155**, 267–287.MATHCrossRefGoogle Scholar - Caltagirone, J. P. and Fabrie, P. 1989 Natural convection in a porous medium at high Rayleigh numbers. Part 1—Darcy’s model.
*European. J. Mech. B***8**, 207–227.Google Scholar - Caltagirone, J. P., Cloupeau, M. and Combarnous, M. 1971 Convection naturelle fluctuante dans une couche poreuse horizontale. C.
*R. Acad. Sci. Paris Sér. B***273**, 833–836.Google Scholar - Caltagirone, J. P., Fabrie, P. and Combarnous, M. 1987 De la convection naturelle oscillante en milieu poreux au chaos temporel?
*C. R. Acad. Sci. Paris Sér. II***305**, 549–553.MathSciNetGoogle Scholar - Caltagirone, J. P., Meyer, G. and Mojtabi, A. 1981 Structurations thermoconvectives tridimensionnelles dans une couche poreuse horizontale.
*J. Mécanique***20**, 219–232.MATHGoogle Scholar - Campos, H., Morales, J. C., Lacoa, U. and Campo, A. 1990 Thermal aspects of a vertical annular enclosure divided into a fluid region and a porous region.
*Int. Comm. Heat Mass Transfer***17**, 343–354.CrossRefGoogle Scholar - Cao, W. Z. and Poulikakos, D. 1991a Solidification of a binary mixture saturating a bed of glass spheres.
*Convective Heat and Mass Transfer in Porous Media*(eds. S. Kakaç, B. Kilkis, F. A, Kulacki, and F. Arinç). Kluwer Academic, Dordrecht, pp. 725–772.Google Scholar - Cao, W. Z. and Poulikakos, D. 1991b Freezing of a binary alloy saturating a packed bed of spheres.
*AIAA J. Thermophys. Heat Transfer***5**, 46–53.CrossRefGoogle Scholar - Castinel, G. and Combarnous, M. 1975 Natural convection in an anisotropic porous layer.
*Rev. Gin. Thermique***168**, 937–947. English translation,*Int. Chem. Engng*.**17**, 605–614 (1977).Google Scholar - Catton, I. 1985 Natural convection heat transfer in porous media.
*Natural Convection: Fundamentals and Applications*(eds. S. Kakaç, W. Aung and R. Viskanta). Hemisphere, Washington, DC, 514–547.Google Scholar - Catton, I. and Travkin, V. S. 1996 Turbulent flow and heat transfer in high permeability porous media.
*Proceedings of the International Conference on Porous Media and their Applications in Science*,*Engineering and Industry*, Kona, Hawaii, June 1996, (ed. K.Vafai), Engineering Foundation, New York, pp. 333–368.Google Scholar - Catton, I., Georgiadis, J. G. and Adnani, P. 1988 The impact of nonlinear convective processes in transport phenomena in porous media.
*ASME HTD***96**, Vol. 1, 767–777.Google Scholar - Chakrabarti, A. and Gupta, A. S. 1981 Nonlinear thermohaline convection in a rotating porous medium.
*Mech. Res. Comm*.**8**, 9–22.MathSciNetMATHCrossRefGoogle Scholar - Chamkha, A. J. 1996 Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media.
*Int. Comm. Heat Mass Transfer***23**, 875–887.CrossRefGoogle Scholar - Chan, Y. T. and Banerjee, S. 1981 Analysis of transient three-dimensional natural convection in porous media.
*ASME J. Heat Transfer***103**, 242–248.CrossRefGoogle Scholar - Chandrasekhara, B. C. 1985 Mixed convection in the presence of horizontal impermeable surfaces in saturated porous media with variable permeability.
*Wärme-Stoffübertrag*.**19**, 195–201.CrossRefGoogle Scholar - Chandrasekhara, B. C. and Nagaraju, P. 1988 Composite heat transfer in the case of a steady laminar flow of a gray fluid with small optical density past a horizontal plate embedded in a saturated porous medium.
*Wärme-Stoffübertrag*.**23**, 343–352.CrossRefGoogle Scholar - Chandrasekhara, B. C. and Nagaraju, P. 1993 Composite heat transfer in a variable porosity medium bounded by an infinite flat plate.
*Wärme-Stoffübertrag*.**28**, 449–456.CrossRefGoogle Scholar - Chandrasekhara, B. C. and Namboodiri, P. M. S. 1985 Influence of variable permeability on combined free and forced convection about inclined surfaces in porous media.
*Int. J. Heat Mass Transfer***28**, 199–206.MATHCrossRefGoogle Scholar - Chandrasekhara, B. C., Radha, N. and Kumari, M. 1992 The effect of surface mass transfer on buoyancy-induced flow in a variable porosity medium adjacent to a vertical heated plate.
*Wärme-Stoffübertrag*.**27**, 157–166.CrossRefGoogle Scholar - Chang, I. D. and Cheng, P. 1983 Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium.
*Int. J. Heat Mass Transfer***26**, 163–173.MATHCrossRefGoogle Scholar - Chang, W. J. and Chang, W. L. 1995 Mixed convection in a vertical tube partially filled with porous medium.
*Numer. Heat Transfer A***28**, 739–754.CrossRefGoogle Scholar - Chang, W. J. and Chang, W. L. 1996 Mixed convection in a vertical parallel-plate channel partially filled with porous media of high permeability.
*Int. J. Heat Mass Transfer***39**, 1331–1342..Google Scholar - Chang, W. J. and Hsiao, C. F. 1993 Natural convection in a vertical cylinder filled with anisotropic porous media.
*Int. J. Heat Mass Transfer***36**, 3361–3367.MATHCrossRefGoogle Scholar - Chang, W. J. and Jang, J. Y. 1989a Non-Darcian effects on vortex instability of a horizontal natural convection flow in a porous medium.
*Int. J. Heat Mass Transfer***32**, 529–539.CrossRefGoogle Scholar - Chang, W. J. and Jang, J. Y. 1989b Inertia effects on vortex instability of a horizontal natural convection flow in a saturated porous medium.
*Int. J. Heat Mass Transfer***32**, 541–550.CrossRefGoogle Scholar - Chang, W. J. and Lin, H. C. 1994a Wall heat conduction effect on natural convection in an enclosure filled with a non-Darcian porous medium.
*Numer. Heat Transfer A***25**, 671–684.CrossRefGoogle Scholar - Chang, W. J. and Lin, H. C. 1994b Natural convection in a finite wall rectangular cavity filled with an anisotropic porous medium.
*Int. J. Heat Mass Transfer***37**, 303–312.MATHCrossRefGoogle Scholar - Chang, W. J. and Yang, D. F. 1995 Transient natural convection of water near its density extremum in a rectangular cavity filled with porous medium.
*Numer. Heat Transfer*A**28**, 619–633.Google Scholar - Chang, W. J. and Yang, D. F. 1996 Natural convection for the melting of ice in porous media in a rectangular enclosure.
*Int. J. Heat Mass Transfer***39**, 2333–2348.MATHCrossRefGoogle Scholar - Chao, B. H., Wang, H. and Cheng, P. 1996 Stagnation point flow of a chemical reactive fluid in a catalytic porous bed.
*Int. J. Heat Mass Transfer***39**, 3003–3019.MATHCrossRefGoogle Scholar - Charrier-Mojtabi, M. C. 1997 Numerical simulation of two-and three-dimensional free convective flows in a horizontal porous annulus using a pressure and temperature formulation.
*Int. J. Heat Mass Transfer***40**, 1521–1533.MATHCrossRefGoogle Scholar - Charrier-Mojtabi, M. C. and Mojtabi, A. 1994 Numerical simulation of three-dimensional free convection in a horizontal porous annulus.
*Heat Transfer*,*1994*. Inst. Chem. Engrs, Rugby, vol. 2, pp. 319–324.Google Scholar - Charrier-Mojtabi, M. C. and Mojtabi, A. K. 1998 Natural convection in a horizontal porous annulus.
*Transport Phenomena in Porous Media*(eds. D. B. Ingham and I. Pop), Elsevier, Amsterdam, pp. 155–178.Google Scholar - Charrier-Mojtabi, M. C., Karimi-Fard, M., Azaiez, M. and Mojtabi, A. 1998 Onset of a double-diffusive convective regime in a rectangular porous cavity.
*J. Porous Media***1**, 107–121.MATHGoogle Scholar - Charrier-Mojtabi, M. C., Mojtabi, A., Azaiez, M. and Labrosse, G. 1991 Numerical and experimental study of multicellular free convection flows in an annular porous pipe.
*Int. J. Heat Mass Transfer***34**, 3061–3074.MATHCrossRefGoogle Scholar - Chaudhary, M. A., Merkin, J. H. and Pop. I. 1995 Similarity solutions in free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media: II Prescribed surface heat flux.
*Heat Mass Transfer***30**, 341–347.CrossRefGoogle Scholar - Chaudhary, M. A., Merkin, J. H. and Pop, I. 1996 Natural convection from a horizontal permeable surface in a porous medium—Numerical and asymptotic solutions.
*Transport in Porous Media***22**, 327–344.CrossRefGoogle 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 - Chellaiah, S. and Viskanta, R. 1989b Freezing of water-saturated porous media in the presence of natural convection: Experiments and analysis.
*ASME J. Heat Transfer***111**, 424–432; Errata 648.Google Scholar - Chellaiah, S. and Viskanta, R. 1990 Natural convection melting of a frozen porous medium.
*Int. J. Heat Mass Transfer***33**, 887–899.CrossRefGoogle Scholar - Chen, C. F. 1995 Experimental study of convection in a mushy layer during directional solidification.
*J. Fluid Mech*.**293**, 81–98.CrossRefGoogle Scholar - Chen, C. H. 1996 Non-Darcy mixed convection from a horizontal surface with variable surface heat flux in a porous medium.
*Numer. Heat Transfer*A**30**, 859–869.Google Scholar - Chen, C. H. 1997a Non-Darcy mixed convection over a vertical flat plate in porous media with variable wall heat flux.
*Int. Comm. Heat Mass Transfer***24**, 427–437.CrossRefGoogle Scholar - Chen, C. H. 1997b Analysis of non-Darcian mixed convection from impermeable horizontal surfaces in porous media: The entire regime.
*Int. J. Heat Mass Transfer***40**, 2993–2997.MATHCrossRefGoogle Scholar - Chen, C. H. and Chen, C. K. 1990a Non-Darcian mixed convection along a vertical plate embedded in a porous medium.
*Appl. Math. Modelling***14**, 482–488.MATHCrossRefGoogle Scholar - Chen, C. H. and Chiou, J. S. 1994 Conjugate free convection heat transfer analysis of a vertical plate fin embedded in non-Darcian porous media.
*Int. J. Engng. Sci*.**3 2**, 1703–1716.Google Scholar - Chen, C. H., Chen, T. S. and Chen, C. K. 1996 Non-Darcy mixed convection along nonisothermal vertical surfaces in porous media.
*Int. J. Heat Mass Transfer***39**, 1157–1164.CrossRefGoogle Scholar - Chen, C. K. and Chen, C. H. 1990b Nonuniform porosity and non-Darcian effects on conjugate mixed convection heat transfer from a plate fin in porous media.
*Int. J. Heat Fluid Flow*, 65–71.Google Scholar**11** - Chen, C. K. and Chen, C. H. 1991 Non-Darcian effects on conjugate mixed convection about a vertical circular pin in a porous medium.
*Comput. Struct*.**38**, 529–535.MATHCrossRefGoogle Scholar - Chen, C. K. and Lin, C. R. 1995 Natural convection from an isothermal vertical surface embedded in a thermally stratified high-porosity medium.
*Int. J. Engng Sci*.**33**, 131–138.MATHCrossRefGoogle Scholar - Chen, C. K., Chen, C. H., Minkowycz, W. J. and Gill, U. S. 1992 Non-Darcian effects on mixed convection about a vertical cylinder embedded in a saturated porous medium.
*Int. J. Heat Mass Transfer***35**, 3041–3046.CrossRefGoogle Scholar - Chen, C. K., Hung, C. I. and Horng, H. C. 1987 Transient natural convection on a vertical flat plate embedded in a high-porosity medium.
*ASME J. Energy Res. Tech*.**109**, 112–118.CrossRefGoogle Scholar - Chen, F. 1990 On the stability of salt-finger convection in superposed fluid and porous layers.
*ASME J. Heat Transfer***112**, 1088–1092.CrossRefGoogle Scholar - Chen, F. 1991 Throughflow effects on convective instability in superposed fluid and porous layers.
*J. Fluid Mech*.**231**, 113–133.MATHCrossRefGoogle Scholar - Chen, F. 1992 Salt-finger instability in an anisotropic and inhomogeneous porous substrate underlying a fluid layer.
*J. Appl. Phys*.**71**, 5222–5236.CrossRefGoogle Scholar - Chen, F. and Chen, C. F. 1988 Onset of finger convection in a horizontal porous layer underlying a fluid layer.
*ASME J. Heat Transfer***110**, 403–409.CrossRefGoogle Scholar - Chen, F. and Chen, C. F. 1989 Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below.
*J. Fluid Mech*.**207**, 311–321.CrossRefGoogle Scholar - Chen, F. and Chen, C. F. 1992 Convection in superposed fluid and porous layers.
*J. Fluid Mech*.**234**, 97–119.MATHCrossRefGoogle Scholar - Chen, F. and Chen, C. F. 1993 Double-diffusive fingering convection in a porous medium.
*Int. J. Heat Mass Transfer***36**, 793–807.MATHCrossRefGoogle Scholar - Chen, F. and Hsu, L. H. 1991 Onset of thermal convection in an anisotropic and inhomogeneous porous layer underlying a fluid layer.
*J. Appl. Phys*.**69**, 6289–6301.CrossRefGoogle Scholar - Chen, F. and Lu, J. W. 1991 Influence of viscosity variation on salt-finger instability in a fluid layer, a porous layer, and their superposition.
*J. Appl. Phys*.**70**, 4121–4131.CrossRefGoogle Scholar - Chen, F. and Lu, J. W. 1992a Variable viscosity effects on convective instability in superposed fluid and porous layers.
*Phys. Fluids***4**, 1936–1944.MATHGoogle Scholar - Chen, F. and Lu, J. W. 1992b Onset of salt-finger convection in anisotropic and inhomogeneous porous media.
*Int. J. Heat Mass Transfer***35**, 3451–3464.CrossRefGoogle Scholar - Chen, F. and Wang, C. Y. 1993a Convective instability in a porous enclosure with a horizontal conducting baffle.
*ASME J. Heat Transfer***115**, 810–813.CrossRefGoogle Scholar - Chen, F. and Wang, C. Y. 1993b Convective instabilty in saturated porous enclosures with a vertical insulating baffle.
*Int. J. Heat Mass Transfer***36**, 1897–1904.MATHCrossRefGoogle Scholar - Chen, F. Chen, C. F. and Pearlstein, A.
*J*. 1991 Convective instability in superposed fluid and anisotropic porous layers.*Phys. Fluids A***3**, 556–565.Google Scholar - Chen, F., Lu, J. W. and Yang, T. L. 1994 Convective instability in ammonium chloride solution directionally solidified from below.
*J. Fluid Mech*.**276**, 163–187.CrossRefGoogle Scholar - Chen, G. and Hadim, H. A. 1995 Numerical study of forced convection of a power-law fluid in a porous channel.
*ASME HTD***309**, 65–72.Google Scholar - Chen, G. and Hadim, H. A. 1998 Numerical study of non-Darcy forced convection in a packed bed saturated with a power-law fluid.
*J. Porous Media***1**, 147–157.MATHGoogle Scholar - Chen, H. T. and Chen, C. K. 1987 Natural convection of non-Newtonian fluids about a horizontal surface in a porous medium.
*ASME J. Energy Res. Tech*.**109**, 119–123.CrossRefGoogle Scholar - Chen, H. T. and Chen, C. K. 1988a Free convection flows of non-Newtonian fluids along a vertical plate embedded in a porous medium.
*ASME J. Heat Transfer***110**, 257–259.CrossRefGoogle Scholar - Chen, H. T. and Chen, C. K. 1988b Natural convection of a non-Newtonian fluid about a horizontal cylinder and a sphere in a porous medium.
*Int. Comm. Heat Mass Transfer***15**, 605–614.CrossRefGoogle Scholar - Chen, K. S. and Ho, J. R. 1986 Effects of flow inertia on vertical natural convection in saturated porous media.
*Int. J. Heat Mass Transfer***29**, 753–759.MATHCrossRefGoogle Scholar - Cheng, P. 1977a Constant surface heat flux solutions for porous layer flows.
*Lett. Heat Mass Transfer***4**, 119–128.CrossRefGoogle Scholar - Cheng, P. 1977b The influence of lateral mass flux on free convection boundary layers in a saturated porous medium.
*Int. J. Heat Mass Transfer***20**, 201–206.CrossRefGoogle Scholar - Cheng, P. 1977c Combined free and forced boundary layer flows about inclined surfaces in a porous medium.
*Int. J. Heat Mass Transfer***20**, 807–814.MATHCrossRefGoogle Scholar - Cheng, P. 1977d Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media.
*Int. J. Heat Mass Transfer***20**, 893–898.CrossRefGoogle Scholar - Cheng, P. 1978 Heat transfer in geothermal systems.
*Adv. Heat Transfer***14**, 1–105.CrossRefGoogle Scholar - Cheng, P. 1981a Thermal dispersion effects in non-Darcian convective flows in a saturated porous medium.
*Lett. Heat Mass Transfer***8**, 267–270.CrossRefGoogle Scholar - Cheng, P. 1981b Film condensation along an inclined surface in a porous medium.
*Int. J. Heat Mass Transfer***24**, 983–990.MATHCrossRefGoogle Scholar - Cheng, P. 1982 Mixed convection about a horizontal cylinder and a sphere in a fluid saturated porous medium.
*Int. J. Heat Mass Transfer***25**, 1245–1247.MATHCrossRefGoogle Scholar - Cheng, P. 1985a Natural convection in a porous medium: External flows.
*Natural Convection: Fundamentals and Applications*(eds. S. Kakaç, W. Aung and R. Viskanta). Hemisphere, Washington, DC, pp. 475–513.Google Scholar - Cheng, P. 1985b Geothermal heat transfer.
*Handbook of Heat Transfer Applications*(eds. W. M. Rohsenow, J. P. Hartnett and E. N. Ganic), 2nd ed., McGraw-Hill, New York, Chapter 11.Google Scholar - Cheng, P. 1987 Wall effects on fluid flow and heat transfer in porous media.
*Proc. 1987 ASME JSME Thermal Engineering Joint Conf*. vol. 2, pp. 297–303.Google Scholar - Cheng, P. and Ali, C. L. 1981 An experimental investigation of free convection about an inclined surface in a porous medium.
*ASME 20th National Heat Transfer Conference*, Paper No. 81-HT-85.Google Scholar - Cheng, P. and Chang, I. D. 1976 On buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces.
*Int. J. Heat Mass Transfer***19**, 1267–1272.MATHCrossRefGoogle Scholar - Cheng, P. and Chang, I. D. 1979 Convection in a porous medium as a singular perturbation problem.
*Lett. Heat Mass Transfer***6**, 253–258.CrossRefGoogle Scholar - Cheng, P. and Chau, W. C. 1977 Similarity solutions for convection of groundwater adjacent to horizontal surface with axisymmetric temperature distribution.
*Water Resource Res*.**13**, 768–772.CrossRefGoogle Scholar - Cheng, P. and Chui, D. K. 1984 Transient film condensation on a vertical surface in a porous medium.
*Int. J. Heat Mass Transfer***27**, 795–798.CrossRefGoogle Scholar - Cheng, P. and Hsu, C. T. 1984 Higher-order approximations for Darcian free convective flow about a semi-infinite vertical flat plate.
*ASME J. Heat Transfer***106**, 143–151.CrossRefGoogle Scholar - Cheng, P. and Hsu, C. T. 1986a Fully developed, forced convective flow through an annular packed-sphere bed with wall effects.
*Int. J. Heat Mass Transfer***29**, 1843–1853.MATHCrossRefGoogle Scholar - Cheng, P. and Hsu, C. T. 1986b Applications of Van Driest’s mixing length theory to transverse thermal dispersion in forced convective flow through a packed bed.
*Int. Comm. Heat Mass Transfer***13**, 613–626.CrossRefGoogle Scholar - Cheng, P. and Hsu, C. T. 1998a The effective stagnant thermal conductivity of porous media with periodic structure.
*J. Porous Media*, to appear.Google Scholar - Cheng, P. and Hsu, C. T. 1998b Heat conduction.
*Transport Phenomena in Porous Media*(eds. D. B. Ingham and I. Pop). Elsevier, Amsterdam, pp. 57–76.Google Scholar - Cheng, P. and Minkowycz, W. J. 1977 Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike.
*J. Geophys. Res*.**82**, 2040–2044.CrossRefGoogle Scholar - Cheng, P. and Pop, I. 1984 Transient free convection about a vertical flat plate imbedded in a porous medium.
*Int. J. Engng. Sci*.**22**, 253–264.MATHCrossRefGoogle Scholar - Cheng, P. and Teckchandani, L. 1977 Numerical solutions for transient heating and fluid withdrawal in a liquid-dominated geothermal reservoir.
*The Earth’s Crust*(ed.*J*. G. Heacock). Amer. Geophys. Union, Washington, DC, pp. 705–721.Google Scholar - Cheng, P. and Verma, A. K. 1981 The effect of subcooled liquid on film boiling about a vertical heated surface in a porous medium.
*Ina. J. Heat Mass Transfer***24**, 1151–1160.MATHCrossRefGoogle Scholar - Cheng, P. and Vortmeyer, D. 1988 Transverse thermal dispersion and wall channelling in a packed bed with forced convective flow.
*Chem. Engng. Sci*.**43**, 2523–2532.CrossRefGoogle Scholar - Cheng, P. and Zheng, T. M. 1986 Mixed convection in the thermal plume above a horizontal line source of heat in a porous medium of infinite extent.
*Heat Transfer*,*1986*. Hemisphere, Washington, DC vol. 5, pp. 2671–2675.Google Scholar - Zhang, X. L. and Kahawita, R. 1994 Ice water convection in an inclined rectangular cavity filled with a porous medium.
*Wärme-Stoffübertrag*.**30**, 9–16.CrossRefGoogle Scholar - Zhang, Z., Bejan, A. and Lage, J. L., 199lb Natural convection in a vertical enclosure with internal permeable screen.
*ASME J. Heat Transfer***113**, 377–383.Google Scholar

## Copyright information

© Springer Science+Business Media New York 1999