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RESEARCH PAPERS: Conduction

Effective Conductivity of a Composite in a Primitive Tetragonal Lattice of Highly Conducting Spheres in Resistive Thermal Contact With the Isolating Matrix

[+] Author and Article Information
Cristina Filip

Department of Thermics, Universitatea Politehnică, Splaiul Independenţei 153, Bucureşti/România

Bertrand Garnier1

Laboratoire de Thermocinetique, UMR CNRS 6607, Ecole Polytechnique de l’Université de Nantes, 3 rue Christian, Pauc, 44300 Nantes, Francebertrand.garnier@univ-nantes.fr

Florin Danes

Laboratoire de Thermocinetique, UMR CNRS 6607, Ecole Polytechnique de l’Université de Nantes, 3 rue Christian, Pauc, 44300 Nantes, Franceflorin.danes@neuf.fr

1

Corresponding author.

J. Heat Transfer 129(12), 1617-1626 (Apr 20, 2007) (10 pages) doi:10.1115/1.2768096 History: Received July 20, 2006; Revised April 20, 2007

A state-of-the-art study and a physical and numerical 3D finite element study of anisotropic conduction through composites filled with isometric inclusions of different conductivity were performed by modeling the longitudinal conduction across a tetragonal lattice of spheres in imperfect contact with the surrounding matrix. In dimensionless variables, the effective conductivity E is expressible as a function of a geometrical parameter B, reflecting the relative thickness of the gap between spheres, the Kapitza resistance C of the contact inclusion/matrix, and the relative resistivity D of the filler. The computation of some 600 E values at some 25 levels of the factors B, C, and D allows one to find some features, such as the leading role of the factor whose value is the highest of three, the low effect of the interactions between factors, the imperfect equivalence of the effects of the three factors, the slow and linear E dependence on the second and third greatest factor, and finally, the asymptotically exact linear relationship between E and the logarithmated sum of factors, with a slope depending only slightly on the relative magnitudes of factors.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 4

Effective conductivity E as function of the matrix layer resistance B, by constant and much smaller contact and inner resistances, C and D

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Figure 5

(a) Dependence of the effective conductivity E on contact C and inner D resistances, at constant low B(B=0) and (b) Dependence of the effective conductivity E on contact C and inner D resistances, at constant high B(B=0.0625)

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Figure 6

Weights of pure factors B, C, and D within the total variation of the effective longitudinal conductivity E, at nearby equal values of the three factors

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Figure 1

(a) Crystallographic unit cell and (b) FE-computed elementary cell

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Figure 2

(a) Effect of the inner thermal resistance D on the longitudinal heat flux density, along the line from (X=0, Y=0, Z=1.001) to (X=1, Y=0, Z=1.001) and (b) effect of the thermal contact resistance C on the longitudinal heat flux density, along the line from (X=0, Y=0, Z=1.001) to (X=1, Y=0, Z=1.001)

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Figure 3

Effective conductivity E as function of the inner resistance D, for different layer resistances B, for a constant contact resistance C=0.001

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