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Research Papers: Porous Media

# Tomography-Based Determination of the Effective Thermal Conductivity of Fluid-Saturated Reticulate Porous Ceramics

[+] Author and Article Information
Jörg Petrasch, Birte Schrader

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

Peter Wyss

Laboratory for Electronics/Metrology, EMPA Material Science and Technology, 8600 Dübendorf, Switzerland

Aldo Steinfeld

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland and Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen, Switzerlandaldo.steinfeld@eth.ch

J. Heat Transfer 130(3), 032602 (Mar 06, 2008) (10 pages) doi:10.1115/1.2804932 History: Received August 30, 2006; Revised May 31, 2007; Published March 06, 2008

## Abstract

The effective thermal conductivity of reticulate porous ceramics (RPCs) is determined based on the 3D digital representation of their pore-level geometry obtained by high-resolution multiscale computer tomography. Separation of scales is identified by tomographic scans at $30μm$ digital resolution for the macroscopic reticulate structure and at $1μm$ digital resolution for the microscopic strut structure. Finite volume discretization and successive over-relaxation on increasingly refined grids are applied to solve numerically the pore-scale conduction heat transfer for several subsets of the tomographic data with a ratio of fluid-to-solid thermal conductivity ranging from $10−4$ to 1. The effective thermal conductivities of the macroscopic reticulate structure and of the microscopic strut structure are then numerically calculated and compared with effective conductivity model predictions with optimized parameters. For the macroscale reticulate structure, the models by Dul’nev, Miller, Bhattachary and Boomsma and Poulikakos, yield satisfactory agreement. For the microscale strut structure, the classical porosity-based correlations such as Maxwell’s upper bound and Loeb’s models are suitable. Macroscopic and microscopic effective thermal conductivities are superimposed to yield the overall effective thermal conductivity of the composite RPC material. Results are limited to pure conduction and stagnant fluids or to situations where the solid phase dominates conduction heat transfer.

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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 1

Photograph of Specimen A: a low-porosity (average porosity of 81%) cylindrical 10pores∕in. Rh-catalyst coated SiC-made RPC sample

Figure 2

CT reconstruction of a cross section of the RPC’s Specimen A. Some central channels are indicated by 1.

Figure 3

3D digital reconstruction of a slice of the RPC’s Specimen A, based on the macroscale CT data set and the isosurface at the segmentation gray value

Figure 4

Photograph of Specimen C: a single strut sample of the Rh-catalyst coated SiC-made RPC sample, showing the triangular cross-sectional geometry of the central channel

Figure 5

CT cross-sectional reconstruction of the strut Specimen C

Figure 6

3D digital reconstruction of the strut Specimen C, based on the microscale CT data set and the isosurface at the segmentation gray value

Figure 7

Schematic of steady-state conduction heat transfer through a two-phase cubic sample of RPC, with temperature boundary conditions T1 and T2 on two of the opposing faces of the cube and adiabatic conditions on the remaining four faces of the cube

Figure 8

Isothermal contour lines of the normalized temperature distribution (T−T2)∕(T1−T2) in a cross-sectional plane obtained from pore-level direct numerical simulation of conduction heat transfer on a subset of Specimen A. Boundary conditions: T=T1 at the bottom (z=0mm) and T=T2 at the top (z=9mm). The solid areas are depicted in black.

Figure 9

Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation of 12 nonoverlapping subsamples of Specimens A and B with varying porosity. Indicated by a dashed line are the regions where the GCI is below and above 10%.

Figure 10

Ratio of the macroscale and microscale effective thermal conductivities (ke,macro∕ke,micro) as a function of the ratio of the fluid and strut thermal conductivities (kf,macro∕ke,micro), obtained by the macroscale direct numerical simulation and by the ke models: (a) parallel and serial bounds, Dul’nev’s model, and three-resistor model; (b) Calmidi’s and Mahajan’s model (analytical), model of Bhattacharya , and Boomsma and Poulikakos’s model for reticulate structures; (c) Calmidi and Mahajan’s (empirical) and Miller’s models

Figure 11

Ratio of the microscale effective thermal conductivity to the pure solid thermal conductivity (ke,micro∕ks) as a function of the ratio of the fluid-to-solid thermal conductivities (kf,micro∕ks), obtained by the microscale direct numerical simulation and by the ke models

Figure 12

Contour map of the ratio of the overall effective thermal conductivity to the pure solid thermal conductivity (ke,macro∕ks) as a function of microscale fluid-to-solid thermal conductivity ratio (kf,micro∕ks) and macroscale fluid-to-solid thermal conductivity ratio (kf,macro∕ks). εmacro=0.90, εmicro=0.12.

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