Research Papers: Experimental Techniques

Combined Microstructure and Heat Conduction Modeling of Heterogeneous Interfaces and Materials

[+] Author and Article Information
Ishan Srivastava

e-mail: isrivast@purdue.edu

Sridhar Sadasivam

e-mail: ssadasi@purdue.edu

Kyle C. Smith

e-mail: kyle.c.smith@gmail.com

Timothy S. Fisher

e-mail: tsfisher@purdue.edu
Birck Nanotechnology Center and School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906

Manuscript received October 15, 2012; final manuscript received December 19, 2012; published online May 16, 2013. Assoc. Editor: Leslie Phinney.

J. Heat Transfer 135(6), 061603 (May 16, 2013) (13 pages) Paper No: HT-12-1568; doi: 10.1115/1.4023583 History: Received October 15, 2012; Revised December 19, 2012

Heterogeneous materials are becoming more common in a wide range of functional devices, particularly those involving energy transport, conversion, and storage. Often, heterogeneous materials are crucial to the performance and economic scalability of such devices. Heterogeneous materials with inherently random structures exhibit a strong sensitivity of energy transport properties to processing and operating conditions. Therefore, improved predictive modeling capabilities are needed that quantify the detailed microstructure of such materials based on various manufacturing processes and correlate them with transport properties. In this work, we integrate high fidelity microstructural and transport models, which can aid in the development of high performance energy materials. Heterogeneous materials are generally comprised of nanometric or larger length scale domains of different materials or different phases of the same material. State-of-the-art structural optimization models demonstrate the predictability of the microstructure for heterogeneous materials manufactured via powder compaction of variously shaped and sized particles. The ability of existing diffusion models to incorporate the essential multiscale features in random microstructures is assessed. Lastly, a comprehensive approach is presented for the combined modeling of a high fidelity microstructure and heat transport therein. Exemplary results are given that reinforce the importance of developing predictive models with rich stochastic output that connect microstructural information with physical transport properties.

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Fig. 1

Combined microstructure and transport modeling framework. The acronyms AGF and MD refer to the techniques of atomistic Green's function and molecular dynamics, respectively.

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Fig. 2

Comparison of microstructures obtained from experiments (SEM micrographs) and modeling. (a) Packing of randomly shaped metal hydride particles [42]. (b) Packing of Bi2Te3 hexagonal platelets, used in thermoelectric applications [59]. (SEM image reprinted with permission from Lu et al., “Bismuth Telluride Hexagonal Nanoplatelets and Their Two-Step Epitaxial Growth,” Journal of the American Chemical Society, 127(28), pp. 10112-10116. Copyright 2005 American Chemical Society.) (c) Vertically oriented CNT arrays. (d) Packing of silica spheres drop coated on a substrate. The black edges in the simulated depictions represent the boundaries of the primary periodic cell.

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Fig. 3

Normalized radial distribution function (RDF) for a jammed system of 1000 spheres and 1600 cubes. The decay of the RDF to unity indicates the lack of long-range translational order.

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Fig. 4

Probability density of face-face alignment angles for jammed systems of 400 tetrahedra, icosahedra, and octahedra. Gaussian kernels with a standard deviation of 0.1 deg were employed to estimate the probability density for each system.

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Fig. 5

Schematic of the granular effective medium approximation. The ‘+’ sign indicates the application of the MG-EMA, and ‘°’ indicates a small incremental volume of the inclusion material. The filled black square indicates the initial host material with no inclusions and the gray square indicates the final effective mixture of the host and inclusions.

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Fig. 6

Comparison of the EMA predictions with discretized finite volume calculations of the normalized effective thermal conductivity for packings of 400 and 1600 tetrahedra. (Based on the model of Ref. [44].)

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Fig. 7

Normalized temperature field for the packing of 400 tetrahedra at a volume fraction of 0.611 with a solid-pore thermal conductivity ratio of 103 [44]. The length scale of the temperature field variations is small compared to the system size, indicating the absence of long-range clusters with preferential heat flow.

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Fig. 8

Mean effective conductivity as a function of the solid-pore conductivity ratio κs/κp for a jammed system of randomly shaped faceted metal hydride particles [42]. The error bars represent bounds on the principal values of the conductivity tensor.

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Fig. 9

A schematic of the CNT resistor network model: Rgc represents the contact resistance between the growth substrate and the CNT, Rd represents the diffusive resistance of the CNT, Rcc,line and Rcc,point represent the contact resistance of the line and point contacts between individual CNTs in an array, Rcs,tip and Rcs,line represent the contact resistance of the tip and line contacts between the CNTs and the opposing substrate

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Fig. 10

The variation of the thermal contact resistance (CNT tips-opposing substrate) of 5 μm tall CNT arrays with applied pressure. The filled red squares and open red triangles, respectively, denote the simulation and experimental data for the variation of the thermal contact resistance with pressure. The blue circles denote the fraction of CNTs in contact with the opposing substrate obtained from the simulations.

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Fig. 11

Comparison of different transport modeling techniques for heterogeneous materials with varying computational complexity and microstructural detail required

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Fig. 12

Variation of the jamming threshold volume fraction of spheres with the system size. The error bars indicate the standard deviation observed over multiple random realizations of this system.

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Fig. 13

Mean and standard deviations in the thermal contact resistance for arrays of 50, 100 and 200 CNTs under varying pressure. The error bars indicate the standard deviation observed over multiple random realizations (∼10) of these systems.




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