Asymptotic Solutions of Effective Thermal Conductivity of Particle-Laden Polymers

2005 ◽  
Author(s):  
P. Karayacoubian ◽  
M. Bahrami ◽  
J. R. Culham
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Analytical Model ◽  
Volume Fraction ◽  
Effective Medium Theory ◽  
Full Range ◽  
Packed Bed ◽  
Asymptotic Solutions ◽  
Particle Volume ◽  
The Matrix

A general predictive model for the effective thermal conductivity of mixtures is developed. In the limit of very small particle volume fractions, a limiting case is approached where the effective medium theory of Maxwell holds. At higher solid fractions, an analytical model for the conductivity of a packed bed of spheres is developed. These two limiting asymptotic solutions are then combined using a blending procedure. The result is a semi-analytical model that is valid over the full range of solid fractions. The model shows that in addition to the conductivities of the particle/matrix and the solid fraction, the degree of wetting of the particles by the matrix is an important parameter in estimating the effective thermal conductivity of the mixture. In addition, the effect of entrapped air is captured through the definition of an effective volume fraction in Maxwell’s model. The model shows good agreement with experimental data.

scholarly journals Improved Heat Transfer in Guar Gel Composites Reinforced with Randomly Distributed Glass Microspheres

2021 ◽  
Author(s):  
Ruifeng CAO ◽  
Taotao WANG ◽  
Yuxuan ZHANG ◽  
Hui WANG
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Particle Size ◽  
Composite Materials ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Glass Microspheres ◽  
Particle Volume ◽  
Number Of Particles

Improved heat transfer in composites consisting of guar gel matrix and randomly distributed glass microspheres is extensively studied to predict the effective thermal conductivity of composites using the finite element method. In the study, the proper and probabilistic three-dimensional random distribution of microspheres in the continuous matrix is automatically generated by a simple and efficient random sequential adsorption algorithm which is developed by considering the correlation of three factors including particle size, number of particles, and particle volume fraction controlling the geometric configuration of random packing. Then the dependences of the effective thermal conductivity of composite materials on some important factors are investigated numerically, including the particle volume fraction, the particle spatial distribution, the number of particles, the nonuniformity of particle size, the particle dispersion morphology and the thermal conductivity contrast between particle and matrix. The related numerical results are compared with theoretical predictions and available experimental results to assess the validity of the numerical model. These results can provide good guidance for the design of advanced microsphere reinforced composite materials.

Modeling Thermal Conductivity of Aligned CNT-Matrix Composites With Increasing Volume Fraction

2016 ◽  
Author(s):  
Diana Grandio ◽  
Drazen Fabris
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Particle Interaction ◽  
Longitudinal Direction ◽  
Near Neighbor ◽  
Correction Function ◽  
Matrix Composites ◽  
Particle Volume ◽  
Volume Fractions

In prior work an effective medium approach (EMA) has been developed to evaluate composite physical properties such as thermal conductivity, dielectric function or elastic modulus (C.-W. Nan, Prog. Mat. Sci. V. 37, 1993). This model combined with the Kapitza interface resistance can predict the effective thermal conductivity of randomly dispersed long fibers for a very low volume fraction (f < 0.01). The present study compares finite-element (FEA) computations and the EMA model for CNT-matrix compositions with low to moderate volume fractions, 0.001 to 0.02. The FEA results obtained show that the EMA model underestimates the effective thermal conductivity of the composite when the particles are very close to each other, even for small particle volume fractions. For aligned fibers the Kaptiza resistance cannot be neglected in the longitudinal direction. This paper proposes a general correction function for the dependence on particle to particle interaction based on the near neighbor distances and the number of near neighbors. This correction function reduces the EMA under prediction to within several percent (< 5%) in most cases.

Theoretical Prediction of the Anisotropic Effective Thermal Conductivity of Composite Materials

2012 ◽  
Author(s):  
Fabio Gori ◽  
Sandra Corasaniti ◽  
Jean-François Ciparisse
Keyword(s):  
Thermal Conductivity ◽  
Composite Material ◽  
Composite Materials ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Silica Matrix ◽  
Flux Lines ◽  
The Matrix ◽  
Fiber Reinforced Material ◽  
Thermal Conductivities

The composite is made of a matrix and a fiber-reinforced material to form a non-homogeneous anisotropic material. Thermal behaviour of composite materials is very important in many applications as heat shields and heat guides. The present paper investigates theoretically a composite material made of a silica matrix and a fiber reinforcement made of steel. The steady state effective thermal conductivity in the main directions are calculated theoretically for two extreme thermal assumptions, i.e. parallel isothermal lines and parallel heat flux lines. The effective thermal conductivity of the composite is evaluated for a variable thickness of the reinforcement, i.e. for a variable volume fraction. The anisotropy degree, defined as the ratio between the thermal conductivities along the two main directions, increases with the ratio between the thermal conductivities of the reinforcement material and the matrix. The composite material, made of two homogeneous and isotropic materials, is thermally anisotropic and can be used to drive heat towards colder regions. This phenomenon is very useful when a device, such as a spacecraft, must be thermally protected.

scholarly journals A Multi-Scale, Semi-Analytical Model for Transient Heat Transfer in a Nano-Composite Containing Spherical Inclusions

2019 ◽  
Vol 21 (2) ◽  
pp. 101
Author(s):  
A. Dobri ◽  
T.D. Papathanasiou
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Analytical Model ◽  
Transient Response ◽  
Interfacial Thermal Resistance ◽  
Spherical Inclusions ◽  
Macro Scale ◽  
The Matrix ◽  
Two Phases

This paper presents a semi-analytical model for transient heat conduction in a composite material reinforced with small spherical inclusions. Essential to the derivation of the model is the assumption that the size of the inclusions is much smaller than the length scale characterizing the macroscopic problem. An interfacial thermal resistance is also present between the two phases. During heating, the inclusions are treated as heat sinks within the matrix, with the coupling provided by the boundary conditions at the surface of the embedded particles. Application of Duhamel’s Theorem at the particle scale provides the local relationship between the temperature profile in a particle and the matrix that surrounds it. A simple spatial discretization at the macro-scale leads to an easily solvable system of coupled Ordinary Differential Equations for the matrix temperature, particle surface temperature and a series of ψ-terms related to the heat exchange between phases. The interfacial thermal resistance between the two phases can lead to the particle temperature lagging behind that of the surrounding matrix. The resulting transient response of the matrix temperature cannot be reproduced by a material with a single effective thermal conductivity. In the case where transient methods are used to determine effective thermal conductivity, this transient response may introduce errors into the measurement.

Dependence of Thermal Conductivity and Mechanical Rigidity of Particle-Laden Polymeric Thermal Interface Material on Particle Volume Fraction

2003 ◽  
Vol 125 (3) ◽  
pp. 386-391 ◽  
Author(s):  
Ravi S. Prasher ◽  
Paul Koning ◽  
James Shipley ◽  
Amit Devpura
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Effective Medium Theory ◽  
Particle Volume Fraction ◽  
Thermal Interface Material ◽  
Particle Volume ◽  
Thermal Interface ◽  
Medium Theory

This paper reports the measurement of the thermal conductivity of particle-laden polymeric thermal interface materials for three different particle volume fractions. The experimental data are further compared with the percolation model and effective medium theory. We then introduce a method of obtaining the contact resistance between the particles and the polymeric matrix by a combination of percolation modeling and experimental data. We also discuss the dependence of the mechanical response of these particle-laden polymers for different filler or particle loading. A novel mechanical length scale is defined to understand the mechanical response of these materials, and is correlated to the viscosity of these materials.

Hierarchical Modeling and Trade-Off Studies in Design of Thermal Interface Materials

2005 ◽  
Author(s):  
X. Zhang ◽  
S. Kanuparthi ◽  
G. Subbarayan ◽  
B. Sammakia ◽  
S. Tonapi
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Thermal Interface Materials ◽  
Particle Volume ◽  
Heat Spreader ◽  
Thermal Interface ◽  
Volume Fractions ◽  
Interface Materials

Particle laden polymer composites are widely used as thermal interface materials in the electronics cooling industry. The projected small chip-sizes and high power applications in the near future demand higher values of effective thermal conductivity of the thermal interface materials (TIMs) used between the chip and the heat-spreader and the heat-spreader and heat-sink. However, over two decades of research has not yielded materials with significantly improved effective thermal conductivities. A critical need in developing these TIMs is apriori modeling using fundamental physical principles to predict the effect of particle volume fraction and arrangements on effective behavior. Such a model will enable one to optimize the structure and arrangement of the material. The existing analytical descriptions of thermal transport in particulate systems under predict (as compared to the experimentally observed values) the effective thermal conductivity since these models do not accurately account for the effect of inter-particle interactions, especially when particle volume fractions approach the percolation limits of approximately 60%. Most existing theories are observed to be accurate when filler material volume fractions are less than 30–35%. In this paper, we present a hierarchical, meshless, computational procedure for creating complex microstructures, explicitly analyzing their effective thermal behavior, and mathematically optimizing particle sizes and arrangements. A newly developed object-oriented symbolic, java language framework termed jNURBS implementing the developed procedure is used to generate and analyze representative random microstructures of the TIMs.

Effect of Particle Volume Fraction on the Thermal Conductivity and Mechanical Rigidity of Particle-Laden Polymeric Thermal Interface Material

2001 ◽  
Author(s):  
Ravi S. Prasher ◽  
Paul Koning ◽  
James Shipley ◽  
Amit Devpura
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Effective Medium Theory ◽  
Particle Volume Fraction ◽  
Thermal Interface Material ◽  
Particle Volume ◽  
Thermal Interface ◽  
Medium Theory

Abstract This paper reports the measurement of the thermal conductivity of particle-laden polymeric thermal interface materials for three different particle volume fraction. The experimental data is further compared with the percolation model and effective medium theory. This paper also introduces a method of obtaining the contact resistance between the particles and the polymeric matrix by combination of percolation modeling and experimental data. We also discuss the dependence of the mechanical response of these particle-laden polymers for different filler or particle loading. A novel mechanical length scale is defined to understand the mechanical response of these materials and is correlated to the viscosity of these materials.

The Estimation of Thermal Conductivity for Alumina-Epoxy Composite Material with High Filling Volume Fraction

2014 ◽  
Vol 918 ◽  
pp. 21-26
Author(s):  
Chen Kang Huang ◽  
Yun Ching Leong
Keyword(s):  
Thermal Conductivity ◽  
Composite Material ◽  
Composite Materials ◽  
Physical Model ◽  
Electron Scattering ◽  
Volume Fraction ◽  
Epoxy Composite ◽  
The Matrix ◽  
Transport Theorem ◽  
Good Agreement

In this study, the transport theorem of phonons and electrons is utilized to create a model to predict the thermal conductivity of composite materials. By observing or assuming the dopant displacement in the matrix, a physical model between dopant and matrix can be built, and the composite material can be divided into several regions. In each region, the phonon or electron scattering caused by boundaries, impurities, or U-processes was taken into account to calculate the thermal conductivity. The model is then used to predict the composite thermal conductivity for several composite materials. It shows a pretty good agreement with previous studies in literatures. Based on the model, some discussions about dopant size and volume fraction are also made.

Figure of Merit-Based Optimization Approach of Phase Change Material-based Composites for Portable Electronics Using Simplified Model

2021 ◽  
Author(s):  
Ayushman Singh ◽  
Srikanth Rangarajan ◽  
Leila Choobineh ◽  
Bahgat Sammakia
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Phase Change ◽  
Effective Thermal Conductivity ◽  
Phase Change Material ◽  
Figure Of Merit ◽  
Volume Fraction ◽  
Simplified Model ◽  
Transient Temperature ◽  
Change Material

Abstract This work presents an approach to optimally designing a composite with thermal conductivity enhancers (TCEs) infiltrated with phase change material (PCM) based on figure of merit (FOM) for thermal management of portable electronic devices. The FOM defines the balance between effective thermal conductivity and energy storage capacity. In present study, TCEs are in the form of a honeycomb structure. TCEs are often used in conjunction with PCM to enhance the conductivity of the composite medium. Under constrained composite volume, the higher volume fraction of TCEs improves the effective thermal conductivity of the composite, while it reduces the amount of latent heat storage simultaneously. The present work arrives at the optimal design of composite for electronic cooling by maximizing the FOM to resolve the stated trade-off. In this study, the total volume of the composite and the interfacial heat transfer area between the PCM and TCE are constrained for all design points. A benchmarked two-dimensional direct CFD model was employed to investigate the thermal performance of the PCM and TCE composite. Furthermore, assuming conduction-dominated heat transfer in the composite, a simplified effective numerical model that solves the single energy equation with the effective properties of the PCM and TCE has been developed. The effective thermal conductivity of the composite is obtained by minimizing the error between the transient temperature gradient of direct and simplified model by iteratively varying the effective thermal conductivity. The FOM is maximized to find the optimal volume fraction for the present design.

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