Effective Thermal Conductivity Of Material Research Articles

The thermal conductivity properties of porous materials based on TPMS

In this study, the effective thermal conductivity of materials based on a porous TPMS structure is investigated. The resulting structure is similar to a matrix and consists of identical pore cells that are strictly periodic in all directions. These pores have several characteristic sizes, and by altering them, materials with predictable effective thermal conductivity can be created. This work investigated materials based on Triply Periodic Minimal Surface (TPMS) of Schwarz P, Schoen IWP and Neovius. The calculation of thermophysical properties was performed using the numerical finite element method in the Ansys software package. Heat transfer in the structures was studied both with and without considering air. The empirical coefficient “n” for the Aivazov–Domashnev formula is expressed analytically. This relationship allows for the creation of materials with predictable thermophysical properties, taking into account the thermal conductivity of non-porous materials. The results of numerical modeling are validated by analytical Austin’s models and experimental data. The samples for the experimental study were made using additive technologies from PETG, ABS, PLA plastic and photopolymer resin. The study has scientific and applied significance, since a method is proposed for predicting the thermal conductivity of materials with an ordered structure. Several solid-state samples of elementary cells were made publicly available for designing materials with predictable thermal conductivity. The novelty of the work lies in obtaining the dependence of effective thermal conductivity on the geometric parameters of the ordered structure for materials with thermal conductivity in a wide range from 0.12 to 400 W/(m°C).

A developed convolutional neural network model for accurately and stably predicting effective thermal conductivity of gradient porous ceramic materials

Accurate and stable prediction of the effective thermal conductivity (ETC) of porous ceramic materials is of great significance for their application in areas such as optimizing the design of thermal barrier coatings and improving energy conversion efficiency. Porous ceramic materials exhibit complex porous structures with gradient porosity distributions that pose a great challenge for effective medium theory (EMT) and conventional convolutional neural networks (CNN) in attempting to accurately and stably predict the ETC of porous media. In this study, a CNN model that integrates self-attention and a multiscale feature-fusion mechanism is proposed to predict the ETC of porous media with greater accuracy and stability. The integration of the self-attention and multiscale feature-fusion mechanisms enhances the CNN's ability to learn long-range dependencies and preserve detailed information. The optimization of the CNN's accuracy and stability is visually illustrated using gradient-weighted class activation mapping (Grad-CAM) for ETC. Additionally, by employing the proposed gradient quartet structure generation set (QSGS), a gradient porous ceramic media dataset comprising 10 000 images was built to train the CNN model. Finally, the prediction results and relative error distribution of the ETC were compared across different models. Our model demonstrated improvements in statistical metrics, including a 33.7 % decrease in mean error, 25.2 % decrease in median error, and 59.6 % decrease in maximum error. The decreases in these metrics and Grad-CAM for the ETC strongly demonstrates that the model proposed in this work greatly improved the accuracy and stability of predicting the ETC of ceramic materials with gradient porosity distributions.

Neural Network Aided Homogenization Approach for Predicting Effective Thermal Conductivity of Composite Construction Materials.

Thermal conductivity is a fundamental material parameter involved in various infrastructure design guides around the world. This paper developed an innovative neural network (NN) aided homogenization approach for predicting the effective thermal conductivity of various composite construction materials. The 2-D meso-structures of dense graded asphalt mixture, porous asphalt mixture, and cement concrete were generated and divided into 2n × 2n square elements with specific thermal conductivity values. A two-layer feed-forward neural network with sigmoid hidden neurons and linear output neurons was built to predict the effective thermal conductivity of the 2 × 2 block. The Levenberg-Marquardt backpropagation algorithm was used to train the network. By repeatedly using the neural network, the effective thermal conductivities of 2-D meso-structures were calculated. The accuracy of the above NN aided homogenization approach was validated with experiment, and various factors affecting the effective thermal conductivity were analyzed. The analysis results show that the accuracy of the NN aided approach is acceptable with relative errors of 1.92~4.34% for the dense graded asphalt mixture, 1.10~6.85% for the porous asphalt mixture, and 1.13~3.14% for the cement concrete. The relative errors for all the materials are lower than 5% when the heterogeneous structures are divided into 512 × 512 elements. Ignoring the actual material meso-structures may lead to significant errors (134.01%) in predicting the effective thermal conductivity of materials with high heterogeneity such as porous asphalt mixture. While proper simplification is acceptable for dense construction composite materials. The effective thermal conductivity of composite cement-asphalt mixtures increases with higher saturation of grouted material. However, the improvement effect of the high-conductive cement paste on the composite cement-asphalt mixtures could be significantly reduced when the cement paste concentrates at the bottom of the mixture. Cracked aggregates and segregation of material components tend to decrease the effective thermal conductivity of construction materials. The NN aided homogenization approach presented in this paper is useful for selecting the effective thermal conductivity of construction materials.

A NOVEL ANALYTICAL MODEL OF THE EFFECTIVE THERMAL CONDUCTIVITY OF POROUS MATERIALS UNDER STRESS

With the increasing demand for energy, heat and mass transfer through porous media has been widely studied. To achieve accuracy in studying the behavior of heat transfer, a good knowledge of the effective thermal conductivity (ETC) of porous materials is needed. Because pore structure dominates the ETC of porous materials and effective stress leads to a change in pore structure, effective stress is one of the key influencing factors affecting ETC. In this study, considering the structure of surface roughness and pore size, based on fractal theory, a novel analytical solution at the pore scale for ETC of porous materials under stress conditions is proposed. Furthermore, in this model, capillaries in porous materials saturated with multiple phases have sinusoidal periodically constricted boundaries. The derived ETC model is validated against available experimental data. Moreover, the influences of the effective stress, initial effective porosity, roughness structure characterization, and wetting phase saturation on the ETC are analyzed. Compared with previous models, the rough surfaces of porous materials and the coupling of heat conduction and mechanics are taken into consideration to make the model more reasonable. As a result, this ETC model can better reveal the mechanism of heat conduction in porous media under stress conditions.

A Fractal Model of Effective Thermal Conductivity of Porous Materials Considering Tortuosity

Accurate estimation of the thermal conductivity of porous materials is crucial for the modeling of heat transfer and energy consumption calculation in energy, aerospace, biomedicine and chemical engineering, etc. The series-parallel model is a simple and direct method and is usually used in the prediction of the effective thermal conductivity (ETC) of porous materials. In this work, the weighted coefficients of the series and parallel section were obtained based on the tortuosity of the porous materials. Then, the physical model of the ETC of the porous materials was established. Furthermore, the ETC of the porous materials was developed using the fractal model to calculate the pore cross-sectional area of the porous materials. Finally, quantitative analysis of the characteristic parameters, e.g., porosity, tortuosity, tortuous fractal dimension and pore diameter distribution, of the ETC of the porous materials was conducted. The results show that the proposed model can provide an accurate prediction of the ETC of porous materials.

Modeling and Measurement of Effective Thermal Conductivity of Materials Reinforced with Bars

Modeling and Measurement of Effective Thermal Conductivity of Materials Reinforced with Bars

Improved thermal conductivity of fluids and composites using boron nitride (BN) nanoparticles through hydrogen bonding

A new method, which utilized hydrogen bonding to enhance the effective thermal conductivity of materials is presented and discussed. Spherical boron nitride (BN) nano particles were mixed and exfoliated to form hydrogen bonds between the particles, fluids, and polymer solutions containing glycerol, water, krytox oil, polyurethane solutions, and other similar substances. The resulting long chain carbon fibers were found to significantly enhance the thermal conductivity of these substances, due to increases in the contact and interfacial surface area. The experimental results indicated that a 35 wt% BN loading in polyurethane could increase the effective thermal conductivity of the base polyurethane composite to a value of 1.78 W/mK, which is a 390 % increase over the base polyurethane composite. In addition, a 20 wt% BN loading in polyurethane with a 5 wt% carbon fiber loading, was found to increase the effective thermal conductivity to a value of 2.10 W/mK, or a 480 % increase over the base polyurethane composite. These results are among the highest values ever reported and can in part, be attributed to the three roll-milling technique utilized to enhance the contact. This work may open the way to further explore enhanced thermal materials with numerous and significant potential commercial applications.

Decorated Dislocations against Phonon Propagation for Thermal Management

The impact of decorated dislocations on the effective thermal conductivity of GaN is investigated by means of equilibrium molecular dynamics simulations via the Green-Kubo approach. The formation of "nanowires" by a few atoms of In in the core of dislocations in wurtzite GaN is found to affect the thermal properties of the material, as it leads to a significant decrease of the thermal conductivity, along with an enhancement of its anisotropic character. The thermal conductivity of In-decorated dislocations is compared to the ones of pristine GaN, InN, and random and ordered InxGa1-xN alloy, to examine the impact of doping. Results are explained by the stress maps, the bonding properties and the phonon density of states of the aforementioned systems. The decorated dislocations engineering is a novel way to tune, among other transport properties, the effective thermal conductivity of materials at the nanoscale, which can lead to the manufacturing of interesting candidates for thermoelectric or anisotropic thermal dissipation devices.

Thermal conductivity of composite building materials: A pore scale modeling approach

In this article the effective thermal conductivity (ETC) of a wide range of multiphase porous building materials has been estimated numerically. The numerical random generation macro-meso pores (RGMMP) method, which is based on the macroscopic statistical information, such as the porosity, volume fraction of macro-meso pores, is used here for the reconstruction of microstructures of various porous building materials. The distribution of macro-meso pores and their sizes are controlled by core distribution probability and porosity. The lattice Boltzmann method equipped with the conservation of energy and suitable boundary conditions at multiple interfaces is adopted for the numerical solution of energy transport equations through the porous media. After comparison with the benchmark of some theoretical solutions and existing experimental observations, it is employed for the estimation of ETC of different multiphase building materials. The resultant predictions through proposed model accord much better with the existing experimental data than the values obtained through traditional theoretical models. Moreover, comparison of the current reconstruction method, RGMMP, with previously proposed Quartet Structure Generation Set (QSGS) method indicated that predictions with present model is more accurate than those obtained with QSGS. Finally the method is applied for analyzing the variation of ETC with temperature and found that value of thermal conductivity rises with increase in temperature for all the mentioned building materials.

Impact of temperature and moisture dependent conductivity of building insulation materials on estimating heating and cooling load using typical and historical weather data

This paper investigates the impact on heating and cooling load estimation when effective thermal conductivity of materials is incorporated into building energy simulation in conjunction with historical weather data. Under current practice, thermal performance of building envelope systems is usually represented by a lumped nominal conductivity value. In reality, effective conductivity is influenced by many factors such as temperature and moisture content. To minimize computing time, building energy simulation is also conducted with typical meteorological weather data, which is sufficient in estimating average energy use of buildings, but lacks the ability to truly reflect building performance under long term weather conditions. Preliminary research has been conducted by simulating a typical residential house in Toronto using WUFI plus - a comprehensive hygrothermal building simulation program. Historical CWEED - 1998 to 2014 weather data and typical weather files CWEC-1990s and 2016 have been used for this work. The results shows:1)a reduced representativeness of typical weather data in building energy simulation as climate changes over time; 2)estimation using typical weather data is not representative of any individual historical year and 3)performance of insulation materials changes when temperature and moisture dependant conductivity is considered and affects the results of building energy simulation.

A spatially-varying relaxation parameter Lattice Boltzmann Method (SVRP-LBM) for predicting the effective thermal conductivity of composite material

Functional filler-reinforced composite materials play critical roles in thermal management in various engineering applications. In this study, an in-house coded spatially-varying relaxation parameter Lattice Boltzmann Method (SVRP-LBM) solver has been developed for predicting the effective thermal conductivity (ETC) of simulated composite materials. A randomly dispersed filler generator (RDFG) incorporating Monte Carlo random sampling method has been developed for reconstructing the microstructure of composite materials. The artificial composite materials with functional fillers of different geometries and particle size are studied. The SVRP-LBM is validated against FVM perditions and theoretical models. The spatially-varying relaxation parameters method has been used to reflect materials with different thermophysical properties, including the interfacial contact resistance between the matrix-filler interfaces. It is demonstrated that the lowest relaxation parameters should be around 1.0 in order to achieve a higher accuracy of LBM predictions. The effects of filler geometry and particle sizes on the ETC are also assessed. The shape and orientation of the anisotropic filler have strong effects on the ETC. After the geometry of the filler in the numerical models being adjusted accordingly to the real fillers, the predictions show good agreement with experimental data. All in all, the SVRP-LBM solver has shown good capability and accuracy for predicting the ETC of composite material.

An efficient strategy for large scale 3D simulation of heterogeneous materials to predict effective thermal conductivity

The behavior of heterogeneous materials (e.g. composite, polycrystalline) is one of the most challenging subjects for researchers. Imaging techniques based on X-ray tomography permit one to obtain the inner structure of these materials. To account for such detailed information and understand the material behavior, the use of tomographic images as an input for numerical simulations is becoming more and more common. The main difficulty is the computational cost, mesh generation in the context of finite element simulations and the large discontinuities of the material properties, which can lead to divergence. The subject of this paper is to resolve these problems and understand the behavior of a material with high heterogeneity. The application of a MultiGrid method coupled with homogenization technique is proposed. The MultiGrid method is a well known method to increase convergence speed. The homogenization technique is applied to compute the coarse grid operators of the MultiGrid process. The combination of the two methods can efficiently deal with large property variations. Hybrid MPI/OpenMP parallel computing is used to save computational time. The influence of material heterogeneity is analyzed as well as the ratio of material properties for the thermal conduction. The effective thermal conductivity of material is illustrated.

Designing effective thermal conductivity of materials of core-shell structure: Theory and simulation

We introduce the phenomenon of golden touch from myth to thermotics. We define golden touch as extending the core property to a shell with an extremely small core fraction. We obtain the requirement of golden touch by making the effective thermal conductivity of the core-shell structure equal to the thermal conductivity of the core. We summarize three types (A, B, and C) of golden touch in two dimensions, and only two types (A and B) of golden touch in three dimensions. We theoretically analyze the distinct properties of different types of golden touch by delicately designing the anisotropic thermal conductivity of the shell. Golden touch is also validated by finite-element simulations which echo the theoretical analyses. Golden touch has potential applications in thermal camouflage, thermal management, etc. Our work not only lays the foundation for golden touch in thermotics, but also provides guidance for exploring golden touch in other diffusive fields like electrostatic and magnetostatic fields.

Estimation of Effective Thermal Conductivity of Two-Phase Material for Hollow Circular Model

Two-phase materials are commonly used in engineering application because of its various properties like strength, thermal conductivity, durability and toughness etc. Effective thermal conductivity (ETC) of two-phase material is the fundamental property to predict its thermal performance. Various geometry (spheres, cylinders, irregular particles) have been considered by researchers for calculating ETC of two-phase materials. Due to complex structure, hollow circular cylinder geometry is not reported yet. In this paper, two-dimensional periodic two-phase system, with hollow circular cylinder shape is considered for calculating ETC. In present work unit cell approach method is used to derive collocated parameters model for estimation of ETC. Hollow circular cylinder model with Ψ = 0.2 gives good result for estimating ETC with average percentage error of 6.46%.

Nonlinear Effect of Moisture Content on Effective Thermal Conductivity of Building Materials with Different Pore Size Distributions

Understanding the quantitative relationship between the effective thermal conductivity and the moisture content of a material is required to accurately calculate the envelope heat and mass transfer and, subsequently, the building energy consumption. We experimentally analyzed the pore size distributions and porosities of common building materials and the influence of the moisture content on the effective thermal conductivity of building materials. We determined the quantitative relationship between the effective thermal conductivity and moisture content of building materials. The results showed that a larger porosity led to a more significant effect of the moisture content on the effective thermal conductivity. When the volumetric moisture content reached 10 %, the thermal conductivities of foam concrete and aerated concrete increased by approximately 200 % and 100 %, respectively. The effective thermal conductivity increased rapidly in the low moisture content range and increased slowly in the high moisture content range. The effective thermal conductivity is related to the moisture content of the materials through an approximate power function. As the moisture content in the walls of a new building stabilizes, the effective thermal conductivity of normal concrete varies only slightly, whereas that of aerated concrete varies more significantly. The effective thermal conductivity of the material is proportional to the relative humidity of the environment. This trend is most noticeable when the wall material is aerated concrete.

The influence of gaseous heat conduction to the effective thermal conductivity of nano-porous materials

A thermal conductivity test apparatus based on transient plane source method is built and developed to measure effective thermal conductivity of open porous materials at different gas pressures. The effective thermal conductivity of open nano-porous silica materials with porosity of 88.5% is measured under gas pressures ranging from 0.001Pa to 1MPa. The contribution of gaseous heat conduction to the effective thermal conductivity of materials is decomposed by subtracting the effective thermal conductivity at ultimate vacuum from that at different gas pressure. It is found that the contribution of gaseous heat conduction is much different with the gas thermal conductivity in nano-porous materials and that in free space. The result is also demonstrated by theoretical analysis and numerical simulation.

A generalized correlation for predicting the thermal conductivity of composites with heterogeneous nanofillers

Adding dual kinds of nanoparticle fillers with higher thermal conductivity (TC) into matrix materials provides versatile and effective means for enhancing the TC of polymer materials. In this study, the effective thermal conductivity (ETC) of composite materials with heterogeneous-filler-nanoparticles is investigated based on an extensive FEM numerical study, in terms of the TC ratios between the filler particles and the matrix material (κ1 and κ2), and the volume fractions (VFs) of each filler particle (ϕ1 and ϕ2). The results indicate that the ETC of composite material significantly depends on TC ratio between two fillers (κ1/κ2). In addition, there exists a maximum ETC according to each sum of TC ratio (κ1+κ2). The asymmetric behavior of ETC in terms of the TC ratio between two fillers becomes symmetric when two fillers has the same VF. Based on the numerical results for a wide range of geometric parameters, a generalized correlation for predicting ETC is proposed as a function of four non-dimensional parameters: ϕ1, ϕ2, κ1, and κ2. The correlation is valid for the entire practical range of parameters (0<ϕ1 or ϕ2<0.4; 1<κ1 or κ2<104), and can be widely utilized for predicting the TC of nanoparticle-added composite materials.

An ideal nano-porous insulation material: Design, modeling and numerical validation

Based on the mechanisms of conductive heat transfer in nano-porous insulation materials, such as suppressed gaseous heat conduction at micro- and nanoscale, and low volume fraction of solid, a nano-porous material of hollow spherical pellets packing stack is designed. Its effective thermal conductivity is derived based on one-dimensional steady-state heat conduction, which is validated and improved by numerical simulation. Analysis on geometrical parameters, thermodynamic parameters and solid thermal conductivity indicates that the designed nano-porous material has the excellent thermal insulation performance. Decreasing the spherical shell thickness and the contact area can efficiently lower the effective thermal conductivity of material. Conductive heat transfer trough solid spherical shell has significant impact on the effective thermal conductivity of material. Under the same conditions, hollow spheres packed in line has the lowest effective thermal conductivity of about 0.01 W m−1 K−1, if properly designed.

Effective thermal conductivity of random two-phase composites

This work aims to establish a new three-dimensional method for automatically generating three-dimensional FEM models of two-phase composite materials with complex materials arrangement for the purpose of effective thermal conductivity (ETC) evaluation. Tests were carried out in which the shape, spatial distribution, thermal contact resistance and particles volume fraction were taken into account. Thermal conductivity ratio between both component materials was also varied. The aim of the work was to examine how each variable influences the ETC of the composite material. ETC was calculated numerically using COMSOL™ software and a 3D-representative volume element (3D-RVE) was employed to represent the composite material. The results were analysed and compared to various analytical models and experimental data reported in the literature.

Intermingled fractal units model and electrical equivalence fractal approach for prediction of thermal conductivity of porous materials

The effective thermal conductivity of porous materials is a function of the intrinsic characteristic of the solid and the fluid phases that occupy the pores, of the volume fraction of the pores, and of their dimensional distribution. This last aspect is less known and studied than the others because the porous microstructure is difficult to define in conventional geometric terms. In this work, an Intermingled Fractal Units model (denominated IFU) is presented, developed by varying some constructive aspects of the Sierpinski carpet. Simple fractals can be used effectively to describe pore size distributions which present a regular growth toward the larger diameters and therefore are not suited to describe very common structures which present one or more peaks in their distribution. But the use of more fractal units means that the IFU is able to effectively simulate the pore size distribution, the volume fractions of the voids as well as the geometry of the microstructure of non-fractal porous materials.By turning IFU model into electrical fractal pattern, it is possible to calculate effective thermal conductivity of the materials. In this approach the value of effective thermal conductivity coefficient derived from the nth stage was used as a default value for the solid phase in the nth + 1 step.This full fractal procedure has been verified with deterministic or random fractal models as well as with some porosity–conductivity experimental data, namely, those obtained from advanced ceramics (Yitria stabilized zirconia) already available in the scientific literature and the results are comparable and very close.