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RESEARCH PAPERS: Porous Media

A Unit Cube-Based Model for Heat Transfer and Fluid Flow in Porous Carbon Foam

[+] Author and Article Information
Qijun Yu

Department of Mechanical and Materials Engineering,  The University of Western Ontario, London, ON, N6A 5B8, Canadayu@fatfoam.com

Brian E. Thompson

 Foam Application Technologies Inc., Mayaguez, Puerto Ricothompson@fatfoam.com

Anthony G. Straatman1

Department of Mechanical and Materials Engineering,  The University of Western Ontario, London, ON, N6A 5B8, Canadaastraatman@eng.uwo.ca

1

Author to whom correspondence should be sent.

J. Heat Transfer 128(4), 352-360 (Oct 24, 2005) (9 pages) doi:10.1115/1.2165203 History: Received October 18, 2004; Revised October 24, 2005

A unit-cube geometry model is proposed to characterize the internal structure of porous carbon foam. The unit-cube model is based on interconnected sphere-centered cubes, where the interconnected spheres represent the fluid or void phase. The unit-cube model is used to derive all of the geometric parameters required to calculate the heat transfer and flow through the porous foam. An expression for the effective thermal conductivity is derived based on the unit-cube geometry. Validations show that the conductivity model gives excellent predictions of the effective conductivity as a function of porosity. When combined with existing expressions for the pore-level Nusselt number, the proposed model also yields reasonable predictions of the internal convective heat transfer, but estimates could be improved if a Nusselt number expression for a spherical void phase material were available. Estimates of the fluid pressure drop are shown to be well-described using the Darcy-Forchhiemer law, however, further exploration is required to understand how the permeability and Forchhiemer coefficients vary as a function of porosity and pore diameter.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Electron micrograph of the carbon foam surface (1); (b) electron micrograph of the carbon foam surface of a single pore

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Figure 2

CAD images showing the proposed unit-cube model: (a) a single unit-cube with spherical void; (b) pore block containing a number of interconnected pores

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Figure 3

A comparison of the idealized geometry (a) and (b) with the structure of porous carbon foam (c) and (d) obtained from ORNL (1)

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Figure 4

Detailed dimensions of the unit cube geometry model at a cross section cut at the center plane of the unit cube

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Figure 5

Interior surface area to volume ratio β plotted as a function of porosity for three different spherical void (pore) diameters

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Figure 6

Illustration of the exposed pore surface area showing the spherical wall surface and the flat surface cross section cut at a location either between 0 and c or between c and H∕2

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Figure 7

(a) Flat cross-section surface cut at a location between 0 and c; (b) flat cross-section surface cut at a location between c and H∕2

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Figure 8

Plot showing the variation of the surface area factor, SF, as a function of porosity

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Figure 9

(a) Carbon foam-spherical void phase pore structure; (b) equivalent solid square bar structure with the same porosity

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Figure 10

(a) Square bar equivalent for thermal-electric analogy; (b) equivalent parallel and series parts; (c) simplified parallel and series parts; (d) equivalent heat transfer circuits

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Figure 11

Plot showing the effective thermal conductivity of porous carbon foam as a function of porosity for ks=1300W∕mK

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Figure 12

Graphical representation of the equivalent sphere particle diameter: (a) the actual spherical void phase and (b) the equivalent solid particle obtained from Eq. 21

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Figure 13

Plot showing the heat transfer as a function of Re for three porous carbon foam specimens reported by Straatman (24). The heat transfer is computed using the area-to-volume ratio β combined with the correlations described in Sec. 3.

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Figure 14

Plot showing the pressure drop as a function of Re for three porous carbon foam specimens reported by Straatman (24).

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