Effective Thermal Conductivity Of Composites Research Articles

Understanding macroscopic thermal conduction in composites reinforced with 2D nanosheets

Two-dimensional (2D) nanosheets, such as graphene and hexagonal boron nitride, are considered as the most promising fillers for enhancing thermal conductivity of polymers and phase-change materials. Nevertheless, the effect of various 2D nanosheets on the effective thermal conductivity of composites is not fully understood, and the corresponding prediction model is still lacking, since numerous influence factors and complex thermal transfer networks are involved. This paper aims to study the macroscopically effective thermal conductivity of the nanosheets-reinforced composites in a systematical way, and develop a robust machine learning based prediction model. To this end, a series of representative volume elements are reconstructed based on the SEM observations of experimental samples, and high-throughput simulations are performed via the updated lattice Boltzmann scheme proposed in our recent work. The effects of shape, size, orientation, intrinsic thermal conductivity, interface thermal resistance, surface coating, and hybrid filling of the 2D nanosheets are clarified. This work could provide a deep insight into the effective thermal conductivity of the nanosheets-reinforced composites, and may offer important guidelines for the custom-design of polymer and phase-change composites with targeted thermal performances.

The Effect of Porosity on the Thermal Conductivity of Highly Thermally Conductive Adhesives for Advanced Semiconductor Packages.

This study suggests promising candidates as highly thermally conductive adhesives for advanced semiconductor packaging processes such as flip chip ball grid array (fcBGA), flip chip chip scale package (fcCSP), and package on package (PoP). To achieve an extremely high thermal conductivity (TC) of thermally conductive adhesives of around 10 Wm-1K-1, several technical methods have been tried. However, there are few ways to achieve such a high TC value except by using spherical aluminum nitride (AlN) and 99.99% purified aluminum oxide (Al2O3) fillers. Herein, by adapting highly sophisticated blending and dispersion techniques with spherical AlN fillers, the highest TC of 9.83 Wm-1K-1 was achieved. However, there were big differences between theoretically calculated TCs that were based on the conventional Bruggeman asymmetric model and experimentally measured TCs due to the presence of voids or pores in the composites. To narrow the gaps between these two TC values, this study also suggests a new experimental model that contains the porosity effect on the effective TC of composites in high filler loading ranges over 80 vol%, which modifies the conventional Bruggeman asymmetric model.

Thermal contact resistance measurement between two intersecting PAN type carbon fibers using the T-type 3ω method

The prediction of the effective thermal conductivity of composites filled with carbon fibers requires the knowledge of the microstructure, the relative amount and thermal properties of filler and matrix materials, the orientation of non-isometric filler phases and the thermal contact resistances between fibers and matrix and also between fibers. However, information at small scale are often missing especially thermal contact resistances. The present work describes the measurement of the thermal contact resistance (TCR) between two crossed carbon fibers which is performed by an adaptation of the T-type 3ω method for thermal conductivity measurement of wires. The first carbon fiber is connected to two copper blocks supplied by a modulated electrical current providing a volumetric heating. The second fiber fixed on a U-shape holder is delicately implemented over the first one. After performing a secondary vacuum, the 3ω voltage V3ω of the first fiber is recorded as function of the frequency of the modulated current. Knowing the applied force, the contact area between the two carbon fibers is calculated from bending and deformations then a 3D numerical model describing heat transfer in two crossed carbon fibers is used to estimate the TCR at their intersection. In addition, a detailed sensitivity analysis of the unknown parameter TCR is performed allowing to find optimal operating conditions especially the frequency range. Measurements are performed with PAN type carbon fibers (FT300B) picked up from the same bundle. Different TCR estimations were performed by fitting numerical and computed V3ω voltage as function of frequency. Finally, values of TCR between crossed carbon fibers were found equal (10.4 ± 10.1) 105 kW−1 which provides an order of magnitude for such phenomenon.

Effective thermal conductivity of composites with anisotropic particles of various shapes embedded in an isotropic matrix

The paper demonstrates a method to calculate effective thermal conductivity in a two-phase medium with an isotropic host phase and embedded anisotropic particles. The presented scheme enables easy incorporation of various regular shapes of filler particles if the principal values of their Eshelby tensor are supplied. Basic shapes, such as spheroids, may approximate a wide range of fillers used to enhance thermal conduction, such as polymers filled with highly conductive metal and ceramic powders, graphite and graphene flakes, and nanotubes. Different spatial orientations and sizes of particles may be supplied to the model in the form of probability distributions. The method is well suited to numerical implementation, and the resulting computations are less demanding than popular mesh-based methods, i.e., Finite Volume and Finite Element Methods. It does not include interfacial thermal resistance between particles and matrix, but the addition of this component is planned in future papers.

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

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.

Modelling of the effective thermal conductivity of composites reinforced with fibers and particles by two-step homogenization method

Fiber-particle-reinforced hybrid composites are widely applied in many fields. Knowing their effective thermal conductivity (ETC) is essential. This paper first calculates the ETC of different fillers reinforced composites by the Lattice Boltzmann method and proposes a correlation for the ETC of fiber-reinforced composites based on Lewis-Nielson's model with an average deviation of less than 2.7%. In what follows, a two-step model for the ETC of fiber-particle reinforced composite is proposed by combining the correlations for fiber-reinforced composites and particle-reinforced composites based on the two-step homogenization method. The results show that the two-step homogenization method could accurately predict the ETC of fiber-particle reinforced composites with randomly arranged fibers; however, a reasonable choice for the phase pair is crucial for this method. In addition, the accurate combinability of Lewis-Nielson's model for particle-reinforced composites with the parallel model and Perrins et al.'s model could accurately predict the ETC of fiber-particle-reinforced composites with aligned fibers with a maximum deviation of less than 3.9%. Finally, the two-step homogenization method is also validated for the particle-particle reinforced composites, and the phase pair selection hardly influences the results. However, this method fails to predict the ETC of fiber-fiber reinforced composites no matter how to choose the phase pair.

Effective thermal conductivity measurement of PCM composites during phase transition by using the transient plane source method

The thermal conductivity of phase change materials (PCMs) during phase transitions is of great significance to the evaluation of the thermal performance of energy-saving buildings. Based on the transient plane source method, a method for measuring the effective thermal conductivity of PCM composites was proposed, by which the variations in effective thermal conductivity with liquid fraction and temperature during phase transitions can be obtained. The correctness of the proposed method was verified through matched simulation experiments. Three kinds of PCM samples were prepared for experimental measurement on the basis of the direct incorporation method, and the volume proportions of decanoic acid to gypsum were set to 10%, 12%, and 15%. The phase transition regions and latent heat values of these PCM samples were measured using the differential scanning calorimetry technique. Results showed that the effective thermal conductivity of the PCM first increased and then decreased during the phase transition. As the fraction of PCM content increased, the phase transition regions gradually expanded, and the effective thermal conductivity changed more drastically. The good measurement repeatability demonstrated the feasibility of this method for measuring the effective thermal conductivity of composites during phase transition.

Radial thermal conductivity of a PAN type carbon fiber using the 3 omega method

The prediction of the effective thermal conductivity of composites filled with carbon fibers requires the knowledge of the microstructure and composition of the composite, the orientation of nonisometric filler, the thermal conductivities of both phases and the thermal contact resistances between fibers and also between fibers and matrix. Due to the anisotropy of carbon fibers, one should know both their axial and radial thermal conductivities. Contrary to the axial thermal conductivity of carbon fiber, there are not much work on the radial one. The present work describes the characterization of the thermal conductivity of carbon fiber in the radial direction using the 3 Ω method with a constant current source. One key point is the use of de-ionized water around the carbon fibers to enhance radial heat transfer. An appropriate thermal model is required in order to estimate the radial thermal conductivity. Therefore, analytical 1D and 2D thermal models are developed using quadrupole methods to describe heat transfer in the carbon fiber using periodic regime and are compared with a 2D numerical model. It appeared that the use of a 1D heat transfer model induces some bias until 50.3% on the estimation of the radial thermal conductivity showing that residual axial heat transfer still occurs. Therefore the 2D thermal model is more appropriate and is used with the experimental data to estimate the radial thermal conductivity. In addition, a detailed sensitivity analysis of the unknown parameter is performed that allows to find the best range of operating conditions especially the frequency range and the effect of the type of surrounding material. Measurements are performed with PAN type carbon fiber (FT300B) of 6–8 μm diameter and various lengths from 0.5 to 2.5 mm embedded in de-ionized water. Finally, radial thermal conductivity values are shown to be about 10 times smaller than the axial one, revealing strong anisotropy of the studied carbon fiber.

Determination of the effective thermal conductivity of particulate composites based on VO2 and SiO2

The effective thermal conductivity of composites made up of VO2 (SiO2) spherical particles randomly distributed and embedded in a SiO2 (VO2) matrix are numerically studied in a range of temperatures around the metal-insulator transition of VO2. This is done by means of three-dimensional finite element simulations for different concentrations and sizes of the particles as well as various interface thermal resistances. Our results are validated against the Mori-Tanaka analytical model. In addition, we develop a numerical method to calculate the heat storage capacity for composites with VO2 particles dispersed into a SiO2 matrix. It is shown that: i) The effective thermal conductivity of VO2/SiO2 composites increases with the VO2 particles' size, while the one of SiO2/VO2 composites is pretty much independent of the SiO2 particles' radius. ii) At the VO2 transition temperature (342.5 K), the effective thermal conductivity of VO2/SiO2 composites increases significantly at a rate of 2.7 × 10−3 Wm−1K−2, such that its value doubles up the SiO2 matrix thermal conductivity at the particle concentration of 40.2%. By contrast, the effective thermal conductivity of SiO2/VO2 composites decreases at a rate of 8.6 × 10−3 Wm−1K−2. iii) The effective thermal conductivity is strongly affected by the thermal resistance in VO2/SiO2 composites, by contrast the resistance effect does not play an important role for particle volume fractions of SiO2 up to 34.1% in SiO2/VO2 composites. The Mori-Tanaka model and our simulations predict the same trend of the effective thermal conductivity values of VO2/SiO2 composites. However, the analytical model fails when the matrix is made up of VO2 and the volumetric fraction of SiO2 exceeds 34.1%. The latent heat storage capacity of VO2/SiO2 composites increases with the VO2 particles’ concentration, such that at 40.2%, it takes the value of 24553 J kg−1 (486.7 cal mol−1), which is about half that of the pure VO2.

A comprehensive study on the effective thermal conductivity of random hybrid polymer composites

Polymer composites have a wide range of applications in frontier science and technology, such as flexible electronic packaging and thermally actuated soft robotics. However, most of the theoretical and numerical researches on the thermal properties of polymer composites have been focusing on the composites with homogenous mono-fillers. In this paper, a comprehensive study on the effective thermal conductivity of the composites containing both particulate and fibrous fillers is performed through experimental, numerical and theoretical approaches. Firstly, the PDMS composites with aluminum nitride particles and/or multiwalled carbon nanotubes are prepared. Then, a series of random digital models are constructed by the simulated annealing method and monte carlo method to characterize the microstructure of such composites. And then, the lattice Boltzmann method is used to calculate the effective thermal conductivity of the random microstructure. The present numerical results are fully verified by experiments. Finally, a phenomenological prediction model is developed by the nonlinear regression method based on the systematic numerical simulations. To show the versatility of the present model, an interesting experiment on thermal management materials is designed and performed. By virtue of this model, quantitatively controlling the temperature of electronic devices may be fulfilled.

Prediction of effective thermal conductivity of multiphase composites with periodic microstructures using an expanded micromechanical model

Most of the available approaches for the prediction of effective thermal conductivity of composites are proposed for two-phase cases with inhomogeneities of simple geometry. Here, a procedure originally developed for two-phase composites is extended to obtain effective thermal conductivities of periodic composites with an arbitrary number of phases and geometric shapes of the inhomogeneities. The procedure is based on a generalization of the equivalent inclusion method for steady-state heat conduction, using Fourier series to represent the periodic fluctuating fields of the quantities involved in the problem. Applications to three-phase composites with different microstructural features are presented and discussed in detail. The model predictions are compared with analytical and numerical results obtained from other homogenization procedures, as well as with available experimental data. These comparisons show a very good performance of the model regardless of the volume fraction of the inhomogeneities, enabling it to be presented as an interesting alternative to the limited number of existing approaches for evaluating the effective thermal conductivity of multiphase/multi-inclusion periodic composites.

Computational microstructure modeling of transverse thermal behavior in cementitious composites filled with randomly dispersed natural fibers coated by functionally graded interphase

To assess the overall thermal properties of lightweight natural fiber-reinforced cementitious composites (NFRCCs) developed for low-carbon constructions, the comprehensive understanding of properties and characteristics of graded interphase between fiber and matrix is vital. However, there is rare study on the graded interphase in the NFRCCs so far. The main objective of this work is to present a comprehensive numerical investigation of the influence of functionally graded interphase on the effective thermal conductivity of such composites. A computational microstructure model including randomly dispersed fibers coated by functionally graded interphase is established and verified by comparison to the experimental results. Then, the effective thermal conductivity of the composites is characterized with respect to the microstructure parameters. It is found that the overall thermal conductivity is weakly dependent of the fiber distribution, whilst it is significantly affected by fiber content, constituent properties, as well as interphase graded form and thickness. Moreover, the study reveals that the linear variation of the interphase property can cause higher predictions than the nonlinear variation. The proposed work will provide fundamental insight about the role of functionally graded interphase in NFRCCs, which is helpful in guiding the designing and processing of NFRCCs.

Enhanced Effective Thermal Conductivity of Composite Materials by Incorporating Constructal Fillers

It is a feasible way to use constructal filler to increase the effective thermal conductivity of polymer. However, the combined effect of filler constructal-shape, contact, anisotropy and interface thermal resistance on the effective thermal conductivity of the composites has not been considered, and the heat transfer mechanisms remain unclear. In this study, these effects are evaluated at the same time. The results show that the filler contact is a key factor in increasing the effective thermal conductivity of composite. The constructal fillers are easy to contact and form heat conduction network than common filler. The filler content of 5 % is the percolation threshold of constructal filler. It is lower than common filler and previous reports. The enhanced heat transfer performance of constructal filler is insensitive to directional angle and has no significant anisotropy. The composite with constructal filler has high effective thermal conductivity in different directions. Series numerical models are proposed to predict the effective thermal conductivity of composite. These models have high accuracy and reliability, the deviations with experiment results is in an acceptable range. The interface thermal resistance should be considered in predicting the effective thermal conductivity of composite with nano-fillers.

The effective thermal conductivity of coated/uncoated fiber-reinforced composites with different fiber arrangements

Fiber-reinforced composites are attractive for many applications in energy fields, such as thermal energy storage and building energy-saving. In these applications, their effective thermal conductivity is extremely important; however, research addressing the effect of various parameters on effective thermal conductivity is scarce. In this paper, the influences of different parameters, including volume fraction, aspect ratio, and orientation of fibers, and the thickness of coating layers on the effective thermal conductivity of fiber-reinforced composites, are numerically investigated by the Lattice Boltzmann method. Based on numerous numerical results, a correlation of the effective thermal conductivity is proposed for the composites with fibers randomly distributed in space. It is found that the thermal conductivity of fiber and coating layers are the two most dominant factors which influence the effective thermal conductivity of fiber-reinforced composites. The thickness of the coating layer affects the effective thermal conductivity of composites with fibers randomly distributed in space remarkably, while its effect on the effective thermal conductivity of composites with fibers arranged perpendicular to the heat transfer is negligible. The results of this work could provide important references for the process design and improvement of thermal performance of fiber-reinforced composites.

Generalized modeling of the effective thermal conductivity of particulate composites

Accurate and computationally efficient predictive models for the effective thermal conductivity of composites are needed to accelerate the design of new materials with improved properties and behavior. The predictive capabilities of previously developed models for particulate composites (PC) apply to limited ranges of component properties and proportions. Furthermore, existing material models that account for particle contiguity and filler-matrix thermal contact resistance fail to distinguish between those two effects. In this work, two novel and complementary predictive models for the effective thermal conductivity of two-phase isotropic particulate composites are derived: (i) a simple yet efficient analytical model for non-contiguous filler particles, and (ii) a generalized semi-analytical model accounting for both filler particle contiguity and thermal resistance at the filler-matrix interface. The latter model is powered by a thermal conduction grid solver algorithm that allows the incorporation of an unlimited number of elements and components to match increasingly complex particulate composite material configurations and behaviors. The two models proposed in this work can match previously published experimental data fairly well. The grid model is further leveraged to relate the effective thermal conductivity to filler particle size and size distribution. It is found that the formation of filler conduction chains is favored by well-graded particle size distributions.

Finite element modelling and simulations on effective thermal conductivity of particulate composites

In this paper, the finite element simulation approach for studying the steady-state heat transfer and predicting the effective thermal conductivity of composites has been proposed. 3D representative volume elements considering the polyhedral- and spherical-shaped inclusions are generated. Different meshing approaches for meshing these complex structured composites have been used, and the mesh quality is studied based on mesh metrics: element quality and skewness, and next, a convergence study is conducted to ensure mesh-independent results. Three different boundary conditions: mixed, constant temperature gradient and uniform flux has been used to predict the effective thermal conductivity of composites. The predicted results from simulations are in good agreement with the experimental values reported in the literature. It has been observed that the random orientation and interpenetration of particles lead to a much better heat flow and hence the higher values of effective thermal conductivity of composites. For high volume fraction composites, as the number of particles having interpenetration increases, their effective thermal conductivity increases. For low volume fraction composites, constant temperature gradient boundary condition overpredicts the effective thermal conductivity and for high volume fraction composites, uniform heat flux and mixed boundary conditions predict higher values. A design point study was conducted, considering the ratio of thermal conductivity of constituents, as a design parameter. It has been observed that by reinforcing the high thermal conductivity inclusions as an interpenetrating phase, the effective thermal conductivity of composites can be increased substantially. The reinforcement of very high conductivity material cannot yield the desired ETCs if the reinforced particles are rendered uniformly oriented with no contacts between them.

A new differential scheme for the development of thermally conductive polymer-composites with non-dilute filler concentrations

The recent approach for enhancing the thermal conductivity of polymer-composites is to generate an interconnecting network of thermally conductive fillers. However, the existing models for effective thermal conductivity of composites are, generally, based on effective medium theory and valid for dilute filler concentration (low volume fraction), which leads to inaccurate predictions with non-dilute and percolating filler concentrations. In this work, the model is developed focusing on non-dilute filler concentrations, which is more practical for the recent approach towards thermally conductive polymer-composites. The existing model for dilute filler concentrations is modified based on Bruggeman's differential scheme wherein the ‘non-dilute concentrations’ are obtained by integrating the effect of adding ‘dilute concentrations’ in small increments. The proposed model can handle particulate fillers of variable geometry. The proposed model is validated by producing different polymer matrix composite systems with ceramic fillers. Using Al2O3 or AlN as filler, and high-density polyethylene or polypropylene as matrix, different binary composite systems were processed with volume fractions up to 0.5. From the parametric studies, conducted to establish the understandings of the model, the aspect ratio of filler particles is found the most critical. The proposed model is expected to be the mathematical ground for the industry and researchers to produce computationally designed polymer composites with tailorable ultrahigh thermal conductivity in corrosive environment-heat transfer applications such as polymeric heat exchangers for seawater desalination.

Processing and characterization of TiO2 filled polymer composites

This paper reports on the research dealing with the processing and characterization of TiO 2 filled polymer composites. It also presents the test results in regard to the physical, mechanical and micro-structural characteristics of the epoxy and polypropylene composites filled with micro-sized TiO 2 particles. The effective thermal conductivity of polymer composites with uniformly distributed micro-sized particulates are estimated using a theoretical heat conduction model proposed previously by the authors and the correlation is validated for TiO 2 filled polymers through numerical analysis and experimentation. Some other important thermal characteristics, such as glass transition temperature (T g ) and coefficient of thermal expansion (CTE) of epoxy and polypropylene composites are also estimated. The effects of TiO 2 content on these properties of epoxy and polypropylene have been studied experimentally. The estimation of effective thermal conductivity of the composites using finite element method (FEM) and the proposed theoretical model is done and the results are validated by corresponding experimental results. The findings of this research suggest that incorporation of TiO 2 into epoxy and polypropylene leads to substantial improvement in thermal conductivity and glass transition temperature of the resins. At the same time, TiO 2 helps in lowering the coefficient of thermal expansion of such composites. This work further shows that the FEM serves as a good predictive tool for assessment of thermal conductivity of these composites. The theoretical correlation proposed in this work can serve as a very good empirical model for spherical inclusions to estimate the effective thermal conductivity of the composites within the percolation limit. With light weight and improved heat conduction capability, the TiO 2 filled polymer composites can be used for applications such as electronic packaging, encapsulations, communication devices, thermal interface material, printed circuit board substrates etc.

Modelling of Effective Thermal Conductivity of Composites Filled with Core-Shell Fillers.

An effective model to calculate thermal conductivity of polymer composites using core-shell fillers is presented, wherein a core material of filler grains is covered by a layer of a high-thermal-conductivity (HTC) material. Such fillers can provide a significant increase of the composite thermal conductivity by an addition of a small amount of the HTC material. The model employs the Lewis-Nielsen formula describing filled systems. The effective thermal conductivity of the core-shell filler grains is calculated using the Russel model for porous materials. Modelling results are compared with recent measurements made on composites filled with cellulose microbeads coated with hexagonal boron nitride (h-BN) platelets and good agreement is demonstrated. Comparison with measurements made on epoxy composites, using silver-coated glass spheres as a filler, is also provided. It is demonstrated how the modelling procedure can improve understanding of properties of materials and structures used and mechanisms of thermal conduction within the composite.

An XFEM-based computational homogenization framework for thermal conductivity evaluation of composites with imperfectly bonded inclusions

In many engineering applications, such as thermal coating and structural insulation, 2D modelling is deemed sufficient to identify design parameters. For the effective thermal conductivity evaluation of heterogeneous composites, a 2D computational homogenization procedure is developed in this study. The inclusions are distributed randomly within the plane. The boundary conditions tested for homogenization procedure introduced include the periodic temperature, uniform temperature, and uniform flux boundary conditions. The bond between the inclusions and the surrounding matrix is assumed imperfect allowing partial heat transfer at the interface. Randomly distributed inclusions can be introduced without altering the underlying regular mesh of the matrix by using the XFEM, providing an efficient way of introducing the inclusions. Implementation details of the proposed computational homogenization scheme based on the XFEM are provided. The results are validated by comparisons with available analytical solutions. Effect of assumed boundary conditions on the results are shown. Parametric studies illustrate the influence of the interface properties, volume ratio of inclusions as well as the distributions of the inclusions on the effective thermal conductivity of composites.