Prediction Of Effective Thermal Conductivity Research Articles

Effective thermal conductivity of granular soils: a review of influencing factors and prediction models towards an investigation framework through multiscale characters

The effective thermal conductivity of soil is important to geo-engineering applications, and it is controlled by factors across different length scales. Through a comprehensive review of these factors, we found that while other more traditional factors have been well studied, there is still a lack of characterisation of soil microscale and mesoscale structures and their influence on effective thermal conductivity. In addition, after reviewing the models available in the literature for soil effective thermal conductivity prediction, it was found that compared with empirical and theoretical models, machine learning models can account for the influence of multi-scale factors, however, research into them is scarce. To overcome the limitations of previous research, we proposed a framework that can investigate the factors influencing soil effective thermal conductivity at multiple scale. It includes the impact of soil structural factors at micro to mesoscale, and this impact is integrated with the influence from other factors for accurate thermal conductivity prediction.

An interpretable deep learning strategy for effective thermal conductivity prediction of porous materials

The effective thermal conductivity of porous materials plays a pivotal role in advancing novel thermal insulation materials. Existing theoretical prediction methods are computationally demanding with restricted applicability, and deep learning methods lack interpretability. More importantly, current approaches fail to explore the material structures themselves and leverage those insights to improve the accuracy of thermal conductivity prediction. Herein, we for the first time propose an interpretable deep learning approach with feedback for thermal conductivity prediction. A 3D convolutional neural network is trained on material structures-thermal conductivity data, and heat maps are generated from weighted feature maps to elucidate the prediction processes. Through image processing, incongruous regions are eliminated, resulting in porous structures with improved reasonability. Consequently, more accurate effective thermal conductivities can be obtained. This work may offer a novel predictive approach that refines both the material structure and the predictive model, thereby achieving more precise thermal conductivity predictions for porous materials.

Mathematical modelling and experimental validation of thermal conductivity of outer layer of fire protective clothing

Motivation for development of this mathematical model is the difficulties related to the experimental measurement of the thermal conductivity like frequent sample preparation, experimental setup availability and lack of easier methods for quick estimation of thermal conductivity of outer layer of fire protective clothing. Considering this, various studies were devoted in the past to determine the thermal conductivity of fabrics. Two mathematical approaches for prediction of thermal conductivity of woven outer layer have been presented in the present study. Series-parallel thermal resistance configuration has been used for prediction of effective thermal conductivity of the fabric. First approach uses input values of structural parameters and can be useful in the development of new woven fabrics for outer layer of fire protective clothing. Second approach uses fibre volume fraction and thermal conductivity of fibre and air. It is suitable for predicting thermal conductivity of finished fabrics. The values obtained from mathematical model were validated with experimental values.

Rapid prediction model of effective thermal conductivity of plain weave fabric in space environment

The prediction of effective thermal conductivity of aerospace insulation materials is crucial for insulation design and radiation characteristics control of space targets. In this paper, a rapid and accurate prediction model is proposed for the effective thermal conductivity of plain weave fabrics in space environments. This model assumes that the cross-sectional shape and bending degree of yarns within aerospace fabrics remain unchanged. To represent the structural characteristics of the plain weave fabric, a dimensionless parameter called "f" is defined. Numerical simulations are conducted to investigate the effects of fabric structure, temperature, and yarn thermal properties on the effective thermal conductivity of multilayer fabrics. Three parameters are identified as the most influential factors for the effective thermal conductivity of plain weave fabrics: the structural parameter f, and the axial and radial thermal conductivities of yarns. Based on extensive simulation data, an empirical equation is proposed for the rapid prediction of the effective thermal conductivity of plain weave fabrics. Moreover, polyester, cotton, and wool plain weave fabric samples are tested for their thermal conductivity in a vacuum environment. The predicted results from the empirical equation proposed in this study exhibit a deviation of less than 6 % when compared to experimental measurements. This study can provide valuable insights for the design of plain weave fabrics used in aerospace insulation materials.

Prediction of effective thermal conductivity of packed beds of polyhedral particles

In packed beds, particle shape influences the heat transfer considering different particle-particle contacts and pore morphology. This paper extends a predictive model for effective thermal conductivity, the Zehner, Bauer and Schlünder (ZBS) model for various shapes. Thus, real structures were studied parallel with numerically generated packings and thermal simulations were performed in FEM solver. ZBS model parameters, porosity, shape factor and interparticle contact area ratio were derived. FEM and ZBS results were compared over a wide range of particle-to-gas conductivity ratios. ZBS model predicted well for lower conductivity particles with the newly introduced sphericity term. In the mid-range of particle conductivity, the results are shape factor sensitive, model predicts well with experimental validation. New correlations were built for ZBS model parameters, extending the model for irregular, non-spherical particles. Prospectively, particle-particle heat transfer coefficients for the discrete element method (DEM) can be derived from the effective thermal conductivity of such particles.

A novel fractal model for effective thermal conductivity in granular porous media

Quantitative prediction of effective thermal conductivity in porous media is very important in various industrial applications and scientific researches. As the topology and geometry characteristics of pore-solid space is extremely complicated, an accurately theoretical calculation in porous media is still a great challenge. In this study, a novel theoretical model of effective thermal conductivity is derived in granular porous media originated from the Laplace's Equation with a new boundary condition. The proposed model considers the size of solid particles following the fractal distribution characteristics, which is expressed as a function of porosity, fractal dimension of solid particle, maximum particle radius, representative length, and thermal conductivity of both solid particle and pore phase. The predictions of proposed model show a good agreement with the existing models and various published experimental data, which validates its accuracy and reliability. The effect of different geometrical parameters for proposed model is analyzed and discussed. This novel proposed model of effective thermal conductivity may reveal a better insight for thermophysical mechanisms in granular porous media than conventional models.

Highly accurate and efficient prediction of effective thermal conductivity of sintered silver based on deep learning method

Effective thermal conductivity (ETC) of sintered Ag is an essential parameter for its die-attach application in power electronics packaging, which could vary significantly with sintering conditions. The existing ETC evaluation approaches are either of limited accuracy (analytical methods) or resource- and time-consuming (experiments and numerical simulations). In this study, deep learning method based on convolutional neural network (CNN) was first performed to predict the ETC of sintered Ag. The database was created with 6156 realistic microstructures of sintered Ag and corresponding reliable microstructural finite-element simulated ETC values (relative error of 5% with experimental results). Based on the appropriate design of CNN architecture, the trained model can accurately predict ETC values of the testing dataset samples with determination-coefficient (R2) of 0.987, which significantly outperforms the conventional analytical (R2 of 0.837) and machine learning methods (R2 of 0.951). Besides, the prediction by CNN takes merely 0.14 s for an image, which is almost negligible. The methods presented here open a new way to achieve highly accurate and efficient prediction of ETC, which can help to prepare sintered-Ag die-attachment with desired ETC for power devices and also be applicable to investigate other effective-properties of sintered Ag.

Research on influencing factors and time-varying model of thermal conductivity of concrete at early age

The thermal conductivity of concrete was investigated under the unsaturated condition during early curing. Based on the improved steady-state method, the thermal conductivity of unsaturated concrete at different ages under curing at the constant temperature of 20 ℃, 5 ℃, and −5 ℃ was tested. The influences of the water-binder ratio, initial air content, fly ash content, curing age, and curing temperature on the thermal conductivity of concrete were analyzed. The water-binder ratio, initial air content, fly ash content, curing age, and curing temperature are inversely proportional to the thermal conductivity of early age concrete. Through the analysis of the correlation between these factors and the thermal conductivity, the correlation between various factors and the thermal conductivity of concrete from large to small is as follows: curing temperature, initial air content, curing age, water-binder ratio, fly ash content. A multiple regression prediction time-varying model with acceptable accuracy is proposed to ensure the accuracy of the effective thermal conductivity prediction.

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.

Micro-scale prediction of effective thermal conductivity of CNT/Al composites by finite element method

Thermal conductivity of CNT/Al composites is considered to be an important property on composites design. However, the effect of microstructure on thermal conductivity has few been reported. In this study, a 3D multi-scale finite element model was developed to predict the effective thermal conductivity of CNT/Al composites, and the influences of CNT configuration, heat transfer direction, interfacial thermal resistance and volume fraction were investigated in detail. Five configurations of CNT were constructed including randomly arranged, evenly oriented, layered, bundled and networked. The results show that the CNT configuration plays a major role for the effective thermal conductivity of CNT/Al composites. The CNT/Al composite with layered configuration has the highest thermal conductivity, and when the volume fraction of CNTs is about 3.7 %, the CNT/Al composite displays an excellent effective thermal conductivity of 400 W/m·K, which increases about 84 % than that of the Al alloy. Moreover, the interface and thermal loading direction also have obvious effect on the thermal conductivity of the composites. The calculated results are in good agreement with experimental data existing in literature. The obtained findings in this study could provide a good theoretical basis for designing high thermal conductivity CNT/Al composites.

Prediction of effective thermal conductivity of coated metals foams using cubic unit cell

Metal foam material draws many designers’ attention due to its excellent thermomechanical properties. Coating foam with higher conductive material can enhance those properties. The coating technique is a critical process to attain an optimum foam. The aim of this study is to develop a mathematical model to predict the effective thermal conductivity of the coated metal foam. A spherical geometry which is equivalent to cubic unit cell for foam structure was considered to have more accurate values. The dimensions of the geometry were normalized to represent the effective thermal conductivity. The foam material was carbon and the coating material was copper which has better thermal conductivity than carbon. Coating thickness layer was increased incrementally for each step by adding 5 µm. Average volume technique was adopted and the cubic unit cell was divided into three layers. The effective thermal conductivity of each layer was calculated using the series law of thermal resistance. As the coated thickness increases, the porosity decreases and the thermal conductivity increases. By decreasing the porosity from 97% to 46%, the effective thermal conductivity increases from 6 W/m.K to 176 W/m.K. The result from this study was compared to experimental data from previous study and a very good agreement was achieved. This model can be used to predict the effective thermal conductivity of any foam material coated with any other material as long as the properties of the foam and the coated material are known.

Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

Thermal conductivity and elastic modulus of 3D porous/fractured media considering percolation

Pores, vugs, and cracks configurations affect physical and mechanical properties of porous and fractured (PF) media, specifically the percolations of pores/vugs/cracks trigger the dramatic change of conductive-like properties such as thermal conductivity, diffusivity, elastic modulus of PF media. It has been a key but unresolved issue how to accurately capture the percolation thresholds of these complex networks interacted by anisotropic-shaped pores and cracks, and their quantitative effects on the thermal conductivity and elastic modulus of PF media. This work proposes numerical and theoretical strategies for the accurate determination of percolation thresholds of penetrable spheroidal inclusions over a broad range of aspect ratios κ representing prolate pores (1 < κ ≤ 200), vugs (κ = 1) and oblate cracks (0.001 ≤ κ < 1), and the reliable predictions of effective thermal conductivity, diffusivity, and elastic modulus of PF media. The numerical and theoretical strategies include: (1) an extensive Monte Carlo finite-size scaling analysis (MCFSS) for obtaining the statistical values of percolation threshold of porous and fracture networks with κ from 200 to 0.001; (2) a Padé-type percolation model for predicting the percolation thresholds of penetrable spheroidal inclusions over a broad range of aspect ratios; (3) a continuum percolation-based generalized effective medium theory (CP-GEMT) for predicting effective thermal conductivity, diffusivity, and elastic modulus of PF media over the whole range of volume fractions of spheroidal inclusions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of accurately determining the percolation thresholds of porous and fracture networks and the effective thermal conductivity, diffusivity, and elastic modulus of PF media as resemble to conductor-superconductor and insulator-conductor. The models can be regarded as a general theoretical framework to shed light on the intrinsic and complex interaction of components, structures and transport and elastic properties in porous and fracture materials, meanwhile the proposed models can be also well utilized to predict the percolation thresholds of spheroidal carbon nanotubes (CNTs) and graphenes, and the effective transport and elastic properties of CNT-/graphene-based composites.

Prediction of effective thermal conductivity of porous lattice structures and validation with additively manufactured metal foams

This paper focuses on the development of simple and accurate correlations to predict the effective thermal conductivity (ETC) of lattice structures, viz. Cube, face diagonal (FD)-Cube, Tetrakaidecahedron (TKD), and Octet topologies, which have wide range of applications in the development of advanced heat exchangers and can be additively manufactured in metal. The topology of those structures is preserved through a lattice Boltzmann-based computational model for thermal transport. In particular, a novel decoupled interface treatment was also proposed to effectively model the conjugate heat transfer between different materials or phases of very large transport property ratios. The accuracy and applicability of the ETC prediction were validated with in-house measurements conducted on the additively manufactured TKD and Octet samples and comparison with published experimental and computational results in the literature. The present results show that (1) at high porosities ε ≥ 0.9, the ETC results of those lattice structures are close to each other and they are consistent with previous experimental measurements and theoretical/computational predictions for traditional metal foams, (2) while at relatively lower porosities (ε < 0.9), the structural effect on the ETC becomes more obvious, and the popular correlations in the literature would underpredict the ETC of those structures. With keff predictions on wide range of porosities and solid and fluid phase thermal conductivities, we have identified a normalized ETC, keff/ks, which was found to be insensitive to ks/kf, and therefore considered suitable for the analytical correlation development over the entire range of porosity 0 ≤ ε ≤ 1. The presented correlations are valuable for ETC evaluation when designing new metal foams with different materials and topologies.

A numerical modelling for resin transfer molding (RTM) process and effective thermal conductivity prediction of a particle–filled composite carbon–epoxy

The objective of this paper is to develop a global modelling approach, that simulates both the resin transfer molding (RTM) manufacturing and the prediction of the effective thermal conductivity (ETC) of a carbon–cpoxy (CE) laminated composite reinforced with particles. This numerical approach is based on two main stages. First, a numerical simulation of the suspension flow and the filtration of the charges during the RTM process. A method, for simulating the flow of a resin, loaded with particles in suspension through a fibrous medium, considering its double porosity scale, has been proposed. It is based on the description of the flow by Stokes–Darcy coupling, filtration phenomenon and particle dynamics. Secondly, the ETC of the composite thus produced is evaluated using a numerical homogenisation technique, considering the spherical particles inserted into the carbon–epoxy laminated composite. These obtained results have shown that, the incorporation of particles in the laminated composite leads to a significant increase in their effective thermal conductivity, which depends on their thermal conductivity. Finally, a simple linear thermal model has been proposed to predict the effective thermal conductivity of the composite carbon–epoxy–particles, as a function of that of the base composite carbon–epoxy and that of the particles.

Thermal conductivity of a Jurkat cell measured by a transient laser point heating method

To understand and quantify the thermal energy transfer in a biological cell, the measurement of thermal properties at a cellular level is emerging as great importance. We report herein a unique technique that utilizes a laser point heat source for temporal temperature rise in a micro-pipette thermal sensor; this technique characterizes heat conduction of a measured sample, the Jurkat cell, thus measuring the sample's thermal conductivity (TC). To this end, we incorporated the computational model in COMSOL to solve for the transient temperature and used the multi-parameter fitting of the experimental data using MATLAB. To address the influence of a Jurkat cell's chemical composition on TC, we compared three structural models for prediction of effective thermal conductivity in heterogeneous materials thereby determining the weight percentage of the Jurkat cell. When considering water and protein as the major constituents, we found that a combination of Maxwell-Euken and Effective Medium Theory modeling provides the closest approximation to published weight percent data and, therefore, is recommended for prediction of the cell composition. We validate the accuracy of the measurement technique, itself, by measuring polyethylene microspheres and observed 1% deviation from published data. The unique technique was determined to be mechanically non-invasive, capable of maintaining viable cells, and capable of measuring the thermal conductivity of a Jurkat cell, which was demonstrated to be 0.538 W/(m⋅K) ± 1%.

Prediction of effective thermal conductivity of a porous capillary wick in a vapor chamber

<p indent=0mm>In this paper, a porous capillary wick in a vapor chamber is used as a research specimen and the influencing factors of effective thermal conductivity of the wick are theoretically analyzed. Based on the microstructure of the wick, which is randomly distributed with solid phase connection, three-dimensional diffusion limited aggregation models are reconstructed in this paper. The thermal conductivity of the gas in the confined space is calculated and the heat transfer characteristics under steady-state heat conduction are studied using numerical simulation. The results show that the thermal conductivity of the gas in the confined space is much lower than that in the free space, which is only <sc>0.00986 W/(m K)</sc> under the atmospheric pressure. Besides, the thermal conductivity of the solid phase is 0.9 times that of the bulk material. The influence of different parameters on the effective thermal conductivity of the porous media is analyzed. The results show that the effective thermal conductivity of the capillary wick decreases with the increase in porosity, and the smaller the particle diameter is, the more significant is the trend. When the particle diameter is <sc>40 μm</sc> and porosity is 0.4, the effective thermal conductivity is <sc>12.14 W/(m K),</sc> which is about three times the corresponding thermal conductivity <sc>(3.89 W/(m K))</sc> when the porosity is 0.7. The particle diameter also has a significant effect on the thermal conductivity of the porous capillary wick. In the case of small porosity, the effective thermal conductivity decreases with the increase in particle diameter, while in the case of larger porosity, the trend is opposite. The effective thermal conductivity of the capillary wick with porosity of 0.5 has deviation of 12.1% from the experimental value, which shows good adaptability of the proposed model.

Prediction of effective thermal conductivity of multicomponent tribocomposites taking into account contact thermal resistance between inclusions and matrix

A method is proposed for predicting the effective thermal conductivity of a matrix composite with several types of spherical inclusions with contact thermal resistance at the boundary of the matrix and inclusions. The method is based on a generalized effective-field approximation for an inhomogeneous medium with inclusions with a shell. Model calculations were performed for a matrix tribocomposite with two types of inclusions. Keywords: effective thermal conductivity, contact thermal resistance, composite material, matrix, inclusion with a shell, Maxwell—Garnett approximation, generalized effective-field approximation. alekc_sap@mail.ru

On accounting for thermal resistance between inclusions and matrix in effective thermal conductivity prediction of composites

On accounting for thermal resistance between inclusions and matrix in effective thermal conductivity prediction of composites

Two-Scale Prediction of Effective Thermal Conductivity of 3D Braided C/C Composites Considering Void Defects by Asymptotic Homogenization Method

In order to predict the effective thermal conductivities of three-dimensional (3D) braided carbon/carbon (C/C) composites with randomly distributed void defects. Two-scale prediction model is developed based on the asymptotic homogenization method. Unit cell models both on fiber-scale and fiber bundle-scale are established according to the scanning electron microscopy observation of the material, and the randomly distributed void defects are considered. The effective thermal conductivities of fiber bundles with void defects are predicted firstly, then the effective thermal conductivities of the 3D braided C/C composites are predicted considering void defects in matrix pocket and interface by introducing the predicted thermal conductivities of fiber bundles. The predicted effective thermal conductivities agree well with the experimental results, demonstrating the validity of the two-scale prediction model. A parametric study is then conducted to analyze the effects of void volume fraction and interfacial thermal conductivity on the predictions of the developed model. The results show that the random distribution of void defects has a little effect on the effective thermal conductivities, while the void volume fraction has a significant effect on the effective thermal conductivities. The thermal conductivities decrease generally linearly with the increase of void volume fractions, and the effect of void volume fraction of matrix pocket is greater than that of fiber reinforcement. The effective thermal conductivities increase with the increase of interfacial thermal conductivity, and the effect of void volume fraction of interface becomes larger with the increase of interfacial thermal conductivity. A higher interfacial thermal conductivity have a greater effect on the effective thermal conductivities of the material than a smaller interfacial thermal conductivity.