Technical Brief

Thermal Convection in Porous Media at High Rayleigh Numbers

[+] Author and Article Information
Daniel J. Keene

Department of Engineering and Computer Science,
Seattle Pacific University,
Seattle, WA 98119
e-mail: keened@spu.edu

R. J. Goldstein

Mechanical Engineering Department,
University of Minnesota,
Minneapolis, MN 55455

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 7, 2014; final manuscript received November 4, 2014; published online December 17, 2014. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 137(3), 034503 (Mar 01, 2015) (4 pages) Paper No: HT-14-1450; doi: 10.1115/1.4029087 History: Received July 07, 2014; Revised November 04, 2014; Online December 17, 2014

An experimental study of thermal convection in a porous medium investigates the heat transfer across a horizontal layer heated from below at high Rayleigh number. Using a packed bed of polypropylene spheres in a cubic enclosure saturated with compressed argon, the pressure was varied between 5.6 bar and 77 bar to obtain fluid Rayleigh numbers between 1.68 × 109 and 3.86 × 1011, corresponding to Rayleigh–Darcy numbers between 7.47 × 103 and 2.03 × 106. From the present and earlier studies of Rayleigh–Benard convection in both porous media and homogeneous fluid systems, the existence and importance of a thin thermal boundary layer are clearly demonstrated. In addition to identifying the governing role of the thermal boundary layer at high Rayleigh numbers, the successful correlation of data using homogeneous fluid dimensionless groups when the thermal boundary layer thickness becomes smaller than the length scale associated with the pore features is shown.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Combarnous, M. A., and Bories, S. A., 1975, “Hydrothermal Convection in a Saturated Porous Media,” Adv. Hydrosci., 10, pp. 231–307. [CrossRef]
Cheng, P., 1978, “Heat Transfer in Geothermal Systems,” Adv. Heat Transfer, 14, pp. 1–105. [CrossRef]
Nield, D. A., and Bejan, A., 2006, Convection in Porous Media, 3rd ed., Springer, New York.
Keene, D. J., 2010, “Thermal Convection in a Porous Medium at High Rayleigh Numbers,” M.S. thesis, University of Minnesota, Minneapolis, MN.
Khashan, S. A., Al-Amiri, A. M., and Pop, I., 2006, “Numerical Simulation of Natural Convection Heat Transfer in a Porous Cavity Heated From Below Using a Non-Darcian and Thermal Non-equilibrium Model,” Int. J. Heat Mass Transfer, 49(5–6), pp. 1039–1049. [CrossRef]
Georgiadis, J. G., and Catton, I., 1986, “Prandtl Number Effect on Benard Convection in Porous Media,” ASME J. Heat. Transfer, 108(2), pp. 284–290. [CrossRef]
Kladias, N., and Prasad, V., 1989, “Natural Convection in Horizontal Porous Layers: Effects of Darcy and Prandtl Numbers,” ASME J. Heat Transfer, 111(4), pp. 926–935. [CrossRef]
Kladias, N., and Prasad, V., 1990, “Flow Transitions in Buoyancy-Induced Convection in a Porous Medium Heated From Below,” ASME J. Heat Transfer, 112(3), pp. 675–684. [CrossRef]
Kladias, N., and Prasad, V., 1991, “Experimental Verification of Darcy-Brinkman-Forchheimer Flow Model for Natural Convection in Porous Media,” J. Thermophys., 5(4), pp. 560–576. [CrossRef]
Lage, J. L., 1992, “Effect of the Convective Inertia Term on Benard Convection in a Porous Medium,” Numer. Heat Transfer, Part A, 22(4), pp. 469–485. [CrossRef]
Neischloss, H., and Dagan, G., 1975, “Convective Currents in a Porous Layer Heated From Below: The Influence of Hydrodynamic Dispersion,” Phys. Fluids, 18(7), pp. 757–761. [CrossRef]
Kvernvold, O., and Tyvand, P., 1980, “Dispersion Effects on Thermal Convection in Porous Media,” J. Fluid Mech., 99(4), pp. 673–686. [CrossRef]
Georgiadis, J. G., and Catton, I., 1988, “Dispersion in Cellular Thermal Convection in Porous Layers,” Int. J. Heat Mass Transfer, 31(5), pp. 1081–1091. [CrossRef]
Howle, L. E., and Georgiadis, J. G., 1994, “Natural Convection in Porous Media With Anisotropic Dispersive Thermal Conductivity,” Int. J. Heat Mass Transfer, 37(7), pp. 1081–1094. [CrossRef]
Braester, C., and Vadasz, P., 1993, “The Effect of a Weak Heterogeneity of a Porous Medium on Natural Convection,” J. Fluid Mech., 254, pp. 345–362. [CrossRef]
Kathare, V., Davidson, J. H., and Kulacki, F. A., 2008, “Natural Convection in Water-Saturated Metal Foam,” Int. J. Heat Mass Transfer, 51(15–16), pp. 3794–3802. [CrossRef]
Davidson, J. H., Kulacki, F. A., and Savela, D., 2009, “Natural Convection in Water-Saturated Reticulated Vitreous Carbon Foam,” Int. J. Heat Mass Transfer, 52(19–20), pp. 4479–4483. [CrossRef]
Lister, C. R. B., 1990, “An Explanation for the Multivalued Heat Transport Found Experimentally for Convection in a Porous Medium,” J. Fluid Mech., 214, pp. 287–320. [CrossRef]
Hollands, K. G. T., Raithby, G. D., and Konicek, L., 1975, “Correlation Equations for Free Convection Heat Transfer in Horizontal Layers of Air and Water,” Int. J. Heat Mass Transfer, 18(7–8), pp. 879–884. [CrossRef]
Fleischer, A. S., and Goldstein, R. J., 2002, “High-Rayleigh-Number Convection of Pressurized Gases in a Horiztonal Enclosure,” J. Fluid Mech., 469, pp. 1–12. [CrossRef]
Coleman, H. W., and Steele, W. G., 1999, Experimentation and Uncertainty Analysis for Engineers, 2nd ed., Wiley, New York.
Wang, M., and Bejan, A., 1987, “Heat Transfer Correlation for Benard Convection in a Fluid Saturated Porous Layer,” Int. Commun. Heat Mass Transfer, 14(6), pp. 617–626. [CrossRef]
Elder, J. W., 1967, “Steady Free Convection in a Porous Medium Heated From Below,” J. Fluid Mech., 27(1), pp. 29–48. [CrossRef]


Grahic Jump Location
Fig. 1

Cross section of experimental convection test cell containing the packed bed of spheres. Fiberglass insulation (not shown) occupies the volume between the test cell assembly and the interior surface of the pressure vessel.

Grahic Jump Location
Fig. 2

Heat transfer data for natural convection in a variety of porous media heated from below plotted using porous media dimensionless groups. See Table 1 for legend details.

Grahic Jump Location
Fig. 3

Heat transfer data for natural convection in a variety of porous media heated from below plotted using homogeneous fluid dimensionless groups. Correlations for the heat transport of a homogeneous fluid layer are included for comparison. See Table 1 for legend details.

Grahic Jump Location
Fig. 4

Thermal boundary layer thickness estimates for the porous media data sets. See Table 1 for legend details.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In