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TECHNICAL PAPERS: Porous Media

Buoyancy Driven Flow in Saturated Porous Media

[+] Author and Article Information
H. Sakamoto1

Thermodynamics and Heat Transfer Laboratory, Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455sakamoto@ce.jp.nec.com

F. A. Kulacki

Thermodynamics and Heat Transfer Laboratory, Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455kulacki@me.umn.edu

1

Current address: NEC Corporation, Tokyo, Japan.

J. Heat Transfer 129(6), 727-734 (Sep 24, 2006) (8 pages) doi:10.1115/1.2717937 History: Received October 26, 2005; Revised September 24, 2006

Measurements are reported of heat transfer coefficients in steady natural convection on a vertical constant flux plate embedded in a saturated porous medium. Results show that heat transfer coefficients can be adequately determined via a Darcy-based model, and our results confirm a correlation proposed by Bejan [Int. J. Heat Mass Transfer.26(9), 1339–1346 (1983)]. It is speculated that the reason that the Darcy model works well in the present case is that the porous medium has a lower effective Prandtl number near the wall than in the bulk medium. The factors that contribute to this effect include the thinning of the boundary layer near the wall and an increase of effective thermal conductivity.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Experimental results for free convection between horizontal plates in a saturated porous medium (1-6). Here Nu, Ram, and Da are scaled to the layer thickness, L.

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Figure 2

Geometry used in the scale analysis of Bejan (17)

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Figure 3

Container with heater and plate assembly (a) side view and (b) top view

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Figure 4

Steady state heat transfer data in water with regression equation, Eq. 8

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Figure 5

Nusselt numbers of 6‐mm DIA glass particles in water compared with results of Bejan (17) and Cheng and Minkowycz (9). The two lines for Bejan’s prediction are extreme values based on the aspect ratio pertaining to the present study.

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Figure 6

Steady state temperature profiles as function of longitudinal position with power-law profiles suggested by Cheng and Minkowycz (9) superposed

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Figure 7

Nusselt number for 1.5mm DIA glass particles in water with predictions (17,9)

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Figure 8

Nusselt number of 14mm DIA steel particles in water compared to predictions (17,9).

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Figure 9

Nusselt number of 6mm DIA steel particles in water compared to predictions (17,9)

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Figure 10

Nusselt numbers for all steady state data by particle type compared to predictions (17,9)

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Figure 11

Nusselt number passed on Rayleigh number for the interstitial fluid (water) with the measured correlation for water, Eq. 8

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