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RESEARCH PAPER: Conduction

# An Effective Unit Cell Approach to Compute the Thermal Conductivity of Composites With Cylindrical Particles

[+] Author and Article Information
Deepak Ganapathy, Kulwinder Singh

Department of Mechanical and Aerospace Engineering,  Arizona State University, Tempe, AZ 85287-6106

Patrick E. Phelan1

Department of Mechanical and Aerospace Engineering,  Arizona State University, Tempe, AZ 85287-6106phelan@asu.edu

Ravi Prasher2

Assembly Technology Development,  Intel Corporation, Chandler, AZ 85226-3699

1

Corresponding author

2

Adjunct Professor, Department of Mechanical and Aero Space Engineering, Arizona State University.

J. Heat Transfer 127(6), 553-559 (Jan 15, 2005) (7 pages) doi:10.1115/1.1915387 History: Received October 06, 2003; Revised January 15, 2005

## Abstract

This paper introduces a novel method, combining effective medium theory and the finite differences method, to model the effective thermal conductivity of cylindrical-particle-laden composite materials. Typically the curvature effects of cylindrical or spherical particles are ignored while calculating the thermal conductivity of composites containing such particles through numerical techniques, such that the particles are modeled as cuboids or cubes. An alternative approach to mesh the particles into small volumes is just about impossible, as it leads to highly intensive computations to get accurate results. On the other hand, effective medium theory takes the effect of curvature into account, but cannot be used at high volume fractions because it does not take into account the effects of percolation. In this paper, a novel model is proposed where the cylindrical particles are still treated as squares (cuboids), but to capture the effect of curvature, an effective conductivity is assigned to the particles by using the effective medium approach. The authors call this the effective unit cell approach. Results from this model for different volume fractions, on average, have been found to lie within $±5%$ of experimental thermal conductivity data.

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Copyright © 2005 by American Society of Mechanical Engineers
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## Figures

Figure 1

ANSYS ™ simulation showing constriction of heat flux lines around a circular particle

Figure 2

Cross section of composite showing how the resistance network is constructed. Shaded regions represent higher conductivity filler particles.

Figure 3

Unit cell with dispersion (temperature gradient along the x-direction)

Figure 4

Completely meshed ANSYS ™ model for a 3×3 matrix with center filler particle

Figure 5

Completely meshed 4×3ANSYS ™ model with 2 filler particles

Figure 6

(a) Completely meshed 5×5ANSYS ™ model with 4 filler particles (b) Completely meshed 5×5ANSYS ™ model with 6 filler particles (c) Completely meshed 5×5ANSYS ™ model with 11 filler particles

Figure 7

Effect of D on the effective conductivity of the composite at a volume fraction of 0.4. Larger D signifies bulk property of composite. Ratio of 185 corresponds to the composite for which experimental data (10) is available.

Figure 8

Comparison of various models with experimental data (10), for hc=∞Wm−2K−1

Figure 9

Effect of varying hc(Wm−2K−1) predicted by EUCM

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