Page 270 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

CONVECTION IN POROUS MEDIA
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ratio (ratio between outer and inner radii) of 5.338 (see Figure 8.10). The fluid used to
saturate the medium is water with a Prandtl number of 5. The results are generated for
different Grashof numbers (Ra/P r) and compared with the experimental Nusselt number
predictions as shown in Figure 8.11. In general, the comparison is excellent for the range
of Grashof numbers considered.
8.7 Summary

In this chapter, a brief summary of convection in porous media has been discussed. It
is important to fully understand the concepts given in Chapter 7 before carrying out the
porous medium flow calculations. Several details have deliberately not been included in
this chapter in order to keep the discussion brief. It is important that readers, who may be
interested in carrying out further research on the topic, read the books and papers listed in
the bibliography to further enhance their knowledge.

8.8 Exercise

Exercise 8.8.1 Write down the Darcy flow and heat convection equations for a fluid-
saturated porous medium at steady state.

Exercise 8.8.2 Derive the governing equations for flow and convection in a fluid-saturated
porous medium in cylindrical coordinates.

Bibliography

Berenati RF and Brosilow CB 1962 Void fraction distribution in packed beds, AIChE Journal, 8,
359–361.
Brinkman HC 1947 A calculation of viscous force exerted by a flowing fluid on a dense swarm of
particles, Applied Science Research, 1, 27–34.
Darcy H 1856 Les Fontaines Publiques de la ville de Dijon, Dalmont, Paris.
David E, Lauriat G and Cheng P 1991 A numerical solution of variable porosity effects on natural
convection in a packed sphere cavity, ASME Journal of Heat Transfer, 113, 391–399.
Ergun S 1952 Fluid flow through packed column, Chemical Engineering Progress, 48, 89–94.
Forchheimer P 1901 Wasserbewegung durch bodem, Z. Ver. Deutsch. Ing., 45, 1782.
Hsu CT and Cheng P 1990 Thermal dispersion in a porous medium, International Journal of Heat
and Mass Transfer, 33, 1587–1597.
Inaba H and Seki N 1981 An experimental study of transient heat transfer characteristics in a porous
layer enclosed between two opposing vertical surfaces with different temperatures, International
Journal of Heat and Mass Transfer, 24, 1854–1857.
Kaviany M 1991 Principles of Heat Transfer in Porous Media, Springer-Verlag, New York.
Lauriat G and Prasad V 1989 Non-Darcian effects on natural convection in a vertical porous enclosure,
International Journal of Heat Mass Transfer, 32, 2135–2148.