Sidewall Heating in Shallow Cavities Near the Density Maximum

  • D. M. Leppinen
  • D. A. S. Rees
Conference paper
Part of the NATO Science Series book series (NAII, volume 134)


In this chapter we examine convection in a shallow rectangular porous cavity with the two sidewalls of the cavity maintained at different temperatures. This problem has been examined in a series of papers by Daniels, Simpkins and Blythe [1, 2, 3] and they have shown that when the fluid density decreases linearly with temperature there is a single convection cell which causes fluid to rise along the hot wall and flow along the top half of the cavity towards the cold wall, where it then descends before returning towards the hot wall in the lower half of the cavity. If the fluid density is not a linear function of temperature this flow pattern can change. Of particular relevance to ground watering modelling is that water has a density maximum at about 4°C. Since in many parts of the world, groundwater will be near this temperature for at least part of the year, it is important to examine the effects of the density maximum on convection in porous media.


Porous Medium Core Region Density Maximum Cold Wall Shallow Cavity 
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  1. [1]
    Blythe, P. A., Daniels, P. G. and Simpkins, P. G. (1983). Thermal convection in a cavity filled with a porous media: a classification of limiting behaviours. Int. J. Heat Mass Transfer, 26, 701–8.zbMATHCrossRefGoogle Scholar
  2. [2]
    Blythe, P. A., Daniels, P. G. and Simpkins, P. G. (1983). Thermally driven cavity flows in porous media. I. The vertical boundary layer structure near the corners. Proc. Roy. Soc. Lond., Series A, 380, 119–36.CrossRefGoogle Scholar
  3. [3]
    Daniels, P. G., Simpkins, P. G. and Blythe, P. A. (1989). Thermally driven shallow cavity flows in porous media: the merger layer regime. Proc. Roy. Soc. Lond., Series A, 426, 107–24.zbMATHCrossRefGoogle Scholar
  4. [4]
    Leppinen, D. M. (2002). Natural convection in shallow cylindrical annuli. Int. J. Heat Mass Transfer, 245, 2967–81.CrossRefGoogle Scholar
  5. [5]
    Moore, D. R. and Weiss, N. O. (1973). Nonlinear penetrative convection. J. Fluid Mech., 61, 553–81.CrossRefGoogle Scholar
  6. [6]
    Pop, I., Rees, D. A. S. and Storesletten, L. (1998). Free convection in a shallow annular cavity filled with a porous medium. J. Porous Media, 1, 227–41.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • D. M. Leppinen
    • 1
  • D. A. S. Rees
    • 2
  1. 1.Department of Applied Mathematics and Theoretical Physics Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK
  2. 2.Department of Mechanical EngineeringUniversity of BathClaverton Down, BathUK

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