Transport in Porous Media

, Volume 104, Issue 2, pp 335–347 | Cite as

Experimental Investigation of Transient Thermal Convection in Porous Media

  • C. A. CooperEmail author
  • J. B. Crews
  • R. Schumer
  • R. J. Breitmeyer
  • H. Voepel
  • D. L. Decker


A laboratory experiment of transient thermal convection in a 1-m-high cell was conducted to compare the length and time scales of plume development to theory. The temperature field was resolved to less than 1 mm and was measured by dissolving a solution of thermochromic crystals into the water–glycerin working fluid. The time-dependent experiment was run by applying heat at the bottom boundary that eventually was \(6\,^\circ \)C above the background temperature of the fluid. After development of a thermal boundary layer, the instability became visible at 26 min, with the development of 11, 3–4 cm width plumes growing from the boundary layer. The initially rapid growth rate reached a limiting velocity of approximately 0.5 cm min\(^{-1}\), and then decelerated throughout the experiment. Plumes interacted primarily by merging together; by the end of the experiment only three plumes were present. The Nusselt number at the onset of convection was 10, although it dropped to 4 after 45 min, which would be expected of a barely unstable system.


Rayleigh number Instability Buoyancy Density-driven flow 



Financial support for this research was provided by the U.S. National Science Foundation under Award EAR 0309618. We thank two anonymous reviewers for their comments which greatly improved the manuscript.


  1. Bear, J.: Dynamics of Fluids in Porous Media, p. 764. Dover (corrected reprint of 1972 Elsevier ed.), New York (1988)Google Scholar
  2. Bejan, A.: Convection Heat Transfer, 3rd edn. Wiley, New York (2004)Google Scholar
  3. Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Oxford University Press, London (1959)Google Scholar
  4. Ciofalo, M., Signorino, M., Simiano, M.: Tomographic particle-image velocimetry and thermography in Rayleigh–Bénard convection using suspended thermochromic liquid crystals and digital image processing. Exp. Fluids 34, 156–172 (2003)CrossRefGoogle Scholar
  5. Elder, J.W.: Steady free convection in a porous medium heated from below. J. Fluid Mech. 27, 29–48 (1967a)CrossRefGoogle Scholar
  6. Elder, J.W.: Transient convection in a porous medium. J. Fluid Mech. 27, 609–623 (1967b)CrossRefGoogle Scholar
  7. Foster, T.D.: Onset of convection in a layer of fluid cooled from above. Phys. Fluids 8(10), 1770–1774 (1965)CrossRefGoogle Scholar
  8. Gonzalez, R.C., Woods, R.E., Eddins, S.L.: Digital Image Processing Using MATLAB. Gatesmark Publishing, Knoxville (2009)Google Scholar
  9. Graham, M.D., Steen, P.H.: Plume formation and resonant bifurcations in porous-media convection. J. Fluid Mech. 272, 67–89 (1994)CrossRefGoogle Scholar
  10. Green, L.L., Foster, T.D.: Secondary convection in a Hele–Shaw cell. J. Fluid Mech. 71, 675–687 (1975)CrossRefGoogle Scholar
  11. Horton, C.W., Rogers, F.T.: Convection currents in a porous medium. J. Appl. Phys. 16, 367–370 (1945)CrossRefGoogle Scholar
  12. Howard, L.N.: Convection at high Rayleigh number. In: Görtler, H. (ed.) Applied Mechanics, Proceedings of the 11th. International Congress of Applied Mechanics, Munich, Federal Republic of Germany, August 1964, pp. 1109–1115 (1966)Google Scholar
  13. Kowalewski, T.A., Ligrani, P., Dreizler, A., Schulz, C., Fey, U.: Temperature and heat flux. In: Tropea, C., Yarin, A., Foss, J.F. (eds.) Springer Handbook of Experimental Fluid Mechanics, pp. 487–561. Springer, Berlin (2007)CrossRefGoogle Scholar
  14. Lapwood, E.R.: Convection of a fluid in a porous medium. Proc. Camb. Philos. Soc. 44, 408–521 (1948)CrossRefGoogle Scholar
  15. Miner, C.S., Dalton, N.N.: Glycerol. Reinhold Publ. Corp., New York (1953)Google Scholar
  16. Nield, D.A.: Onset of thermohaline convection in a porous medium. Water Resour. Res. 11, 553–560 (1968)CrossRefGoogle Scholar
  17. Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (2006)Google Scholar
  18. Phillips, O.M.: Geological Fluid Mechanics. Cambridge University Press, Cambridge (2009)Google Scholar
  19. Raffel, M., Willert, C.E., Kompenhans, J.: Particle Image Velocimetry. Springer, Berlin (1998)CrossRefGoogle Scholar
  20. Riaz, A., Hesse, M., Tchelepi, H.A., Orr, F.M.: Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111 (2006)CrossRefGoogle Scholar
  21. Tritton, D.J.: Physical Fluid Dynamics. Oxford Science Publications, Oxford (1988)Google Scholar
  22. Wooding, R.A.: Convection in a saturated porous medium at large Reynolds number or Péclet number. J. Fluid Mech. 15, 527–544 (1963)CrossRefGoogle Scholar
  23. Wooding, R.A., Tyler, S.W., White, I.: Convection in groundwater below an evaporating salt lake: 1. Onset of instability. Water Resour. Res. 33, 1199–1217 (1997a)CrossRefGoogle Scholar
  24. Wooding, R.A., Tyler, S.W., White, I., Anderson, P.A.: Convection in groundwater below an evaporating salt lake: 2. Evolution of fingers or plumes. Water Resour. Res. 33, 1219–1228 (1997b)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • C. A. Cooper
    • 1
    Email author
  • J. B. Crews
    • 1
  • R. Schumer
    • 1
  • R. J. Breitmeyer
    • 2
  • H. Voepel
    • 1
  • D. L. Decker
    • 1
  1. 1.Division of Hydrologic SciencesDesert Research InstituteRenoUSA
  2. 2.Department of Geological Sciences and EngineeringUniversity of Nevada, RenoRenoUSA

Personalised recommendations