Research Papers: Porous Media

Effective Thermal Diffusivity of Porous Media in the Wall Vicinity

[+] Author and Article Information
H. Sakamoto

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


Corresponding author.

J. Heat Transfer 130(2), 022601 (Feb 04, 2008) (7 pages) doi:10.1115/1.2787022 History: Received June 08, 2006; Revised May 01, 2007; Published February 04, 2008

Transient heat transfer from an impulsively heated vertical constant heat flux plate embedded in a stationary saturated porous medium is studied experimentally and analytically to determine near-wall thermal diffusivity. The effective diffusivity is shown to depend on the properties of the constituent materials and the near-wall particle morphology. For porous media comprising randomly stacked spheres, the near-wall region is characterized by fewer particle contacts with the wall than in the bulk medium, and this difference is the source of larger thermal diffusivity in the context of volume-averaged values, which apply to the bulk property far from the wall. For combinations of different spherical solids and interstitial fluids, which give a range of fluid:solid conductivity ratio from 0.5 to 2400, early-time transient temperature profiles can be predicted using the thermal conductivity of the interstitial fluid. A conjugate heat transfer analysis accurately predicts the time the conductive front takes to travel through the impermeable wall and quantifies the effect of conduction along the wall on the local and overall Nusselt numbers. The present results raise the possibility of reinterpretation of much of the porous media heat transfer experiments in the literature.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Summary of experimental investigations for stagnant thermal conductivity of porous media consisting of various bead materials and fluids (5-12)

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Figure 2

Computational domain for one-dimensional conjugate conduction analysis (not drawn to scale). Similar domains are used to simulate for porous media with appropriate properties and domain size.

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Figure 3

Experimental apparatus with heated plate assembly: (a) side view and (b) top view

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Figure 4

First-layer spheres in a triangular arrangement for model of local porosity dependence on distance from the wall as presented in Eq. 4

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Figure 5

Near-wall porosity profile compared with bulk value obtained from experiments

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Figure 6

Wall temperature profile for a porous medium with 6mm diameter glass spheres and water with an applied heat flux of 5160W∕m2

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Figure 7

Comparison of experimental and computed temperature profiles for high (a) and low (b) applied wall heat fluxes

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Figure 8

Temperature rise for air via measurement and simulation at all thermocouple locations

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Figure 9

Transient temperature for the glass-water porous medium and water only measured at x=0.205m and computed values

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Figure 10

Transient temperature profiles at x=0.025m for the glass-water and steel-water porous media and water alone. qw″≈5200W∕m2.

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Figure 11

Transient temperature profiles at x=0.025m for the glass-air and steel-air porous media and air alone. qw″≈184W∕m2.



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