Prediction Of Effective Thermal Conductivity Research Articles

Investigation of Effective Thermal Conductivity for Ordered and Randomly Packed Bed with Thermal Resistance Network Method

In the present paper, the effective thermal conductivities of Li4SiO4-packed beds with both ordered and random packing structures were investigated using thermal resistance network methods based on both an Ohm’s law model and a Kirchhoff’s law model. The calculation results were also validated and compared with the numerical and experimental results. Firstly, it is proved that the thermal resistance network method based on the Kirchhoff’s law model proposed in the present study is reliable and accurate for prediction of effective thermal conductivities in a Li4SiO4-packed bed, while the results calculated with the Ohm’s law model underestimate both ordered and random packings. Therefore, when establishing a thermal resistance network, the thermal resistances should be connected along the main heat transfer direction and other heat transfer directions as well in the packing unit. Otherwise, both the total heat flux and effective thermal conductivity in the packing unit will be underestimated. Secondly, it is found that the effect of the packing factor is remarkable. The effective thermal conductivity of a packed bed would increase as the packing factor increases. Compared with random packing at similar packing factor, the effective thermal conductivity of packed bed would be further improved with an ordered packing method.

Artificial neural network-based prediction of effective thermal conductivity of a granular bed in a gaseous environment

Artificial neural network (ANN), a machine learning technique, is employed to predict the effective thermal conductivity of granular assemblies in the presence of a stagnant gas. ANN is trained with the help of estimated thermal conductivities calculated through resistor network (RN) model. RN model considers the effect of the presence of stagnant gas and the gas pressure (Smoluchowski effect) for the calculation of effective thermal conductivity. Granular assemblies are generated and compacted through discrete element method (DEM). The ANN is trained to predict the effective thermal conductivity of a granular assembly for a set of measurable experimental parameters (stress and packing fraction) without requiring the knowledge of microstructural details (coordination numbers and overlaps) of the assembly. The predicted effective thermal conductivity values through ANN are in good agreement with the experimental results. Estimation of effective thermal conductivity through the trained ANN is much faster (few seconds compared to few hours required for DEM together with RN approach) with very good accuracy.

Prediction of the solid effective thermal conductivity of fatty acid/carbon material composite phase change materials based on fractal theory

The thermal conductivity of a phase change material (PCM) is an important parameter that affects the heat transfer characteristics of PCM. In this study, the fractal theory is conducted to study the prediction model of the effective thermal conductivity of fatty acid/carbon material composite PCMs in the solid phase. Based on the Sierpinski carpet model of fractal geometry, a series of fractal units with different fractal dimensions are developed for the fatty acid/carbon material composite PCMs. Combined with a self-similar principle and thermal resistance network theory, a general solution for the dimensionless effective thermal conductivity of a typical Sierpinski carpet fractal unit is then derived. Further, dimensionless effective thermal conductivity prediction models of three typical structures of fatty acid/carbon material composite PCMs are obtained by comparing the experimental data. Finally, the thermal conductivity prediction model from this study demonstrated a better reliability than that of the commonly used QP prediction model and Maxwell-Eucken prediction model. This prediction model could be used to predict the effective thermal conductivity of composite PCMs.

Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2 D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.

Prediction of pressure dependent effective thermal conductivity of two phase materials in high temperature applications-An analytical method using hexagon and octagon models

The prediction of Effective Thermal Conductivity (ETC) of two phase porous materials is becoming more important to evaluate its suitability in various engineering applications. This article has aimed to develop the geometry dependent resistance models using Hexagon and Octagon by considering the effects of contact resistance, conductivity ratio, concentration, natural convection due to buoyancy effects, pressure dependent Knudsen effects and radiation effects due to elevated temperature. The general analytical expressions have been derived based on unit cell parallel isotherm approach for hexagon and Octagon geometries. The expressions are validated for its correctness using standard models and compared with wide range of experimental data for various geometrical configurations and at different temperatures. The results have declared the suitability of the present models in predicting the ETC of various two phase materials at any kind of ambient conditions.

Prediction of effective thermal conductivity of Nanofluids using homogenization method

In this work, the prediction of the effective thermal conductivity of nanofluids has been performed using the homogenization method. Indeed, the main idea of this approach is to characterize the effective thermal conductivity from a microstructural description of the heterogeneous nanofluid and the knowledge of the local behavior of constituents (fluid and nanoparticles) using the homogenization process. Predicted values of the effective thermal conductivity of Al 2 O 3 -water nanofluidwere confronted with those obtained by experimental approach and also by applying some theoretical models. These comparisons show good agreement between the predicted, theoretical and experimental values. The maximum deviations remain lower than 3.7%.

Measurement of effective thermal conductivity of hydrate-bearing sediments and evaluation of existing prediction models

As a potential alternative strategic energy source, and for their potential impact on global climate, natural gas hydrates have garnered worldwide attention. This study explored the measurement of effective thermal conductivity of methane hydrate-bearing sediments and evaluated existing models for the prediction of effective thermal conductivity. A thermistor-based method combined with Micro-CT observations was employed in the determination of the effective thermal conductivity of porous matrix materials with various hydrate and water saturation levels and physical characteristics. The effects of sample component characteristics, including the volume content of hydrate and water, phase conversion, and properties of porous materials, on the effective thermal conductivity of hydrate-bearing sediments were systematically evaluated. The effective thermal conductivity positively correlated with hydrate saturation, water content, and the thermal conductivity of porous media. In addition, the effective thermal conductivity slightly increased with hydrate dissociation, indicating an increasing heat transfer capacity during gas production. Existing prediction models were evaluated using our measured results, and a hybrid model combining the parallel and series models was proposed with expanded applicability to the scope of our research. The feasibility of the proposed model was also verified in a comparison with previous research. The results of this study are important for future investigation of the actual thermal properties of hydrate-bearing sediment and the understanding of the heat transfer mechanism during gas production. Furthermore, the results can provide guidance in the selection of an optimal technique for gas production from hydrate deposits at the field scale.

LBM prediction of effective thermal conductivity of lithium-ion battery graphite anode

Study of thermal characteristics of a lithium-ion battery plays a vital role in determining and enhancing the performance and safety of the battery. This paper predicts the effective thermal conductivity of a graphite anode having microstructure reconstructed by an ellipsoid based simulated annealing method. A lattice-Boltzmann (LB) model is established for simulating the thermal diffusion process in the computer-generated 3D microstructure of graphite anode. The effective thermal conductivities derived from LB simulation results indicate evident anisotropic feature of the graphite anode. The numerical results show that the particle size does have some effects on the effective thermal conductivity, but the effects are generally not significant. The real graphite may have particles with particle size following a certain statistical distribution, very probably the normal distribution, which is found to weaken the anisotropy of the electrode. Comparing the numerical data with the theoretical predictions by effective media theory (EMT) suggests that the suitable value of the empirical correction factor (f) for the effective thermal conductivity of graphite anode in the electrode through-plane direction is about 6.0 and in the other direction about 4.5.

Modeling Of Frp Composites For The Prediction Of Effective Thermal Conductivity

Present work focuses on prediction of Effective Thermal Conductivities of Unidirectional Fiber Reinforced Composites using Finite Element Method. The Representative Volume Element (RVE) of Elliptical Fiber Mechanical Model is integrated with the Finite Element Software ANSYS 12.0 to estimate the Effective Thermal Conductivities of the composite by taking the Thermal Conductivities of individual components (Fiber, Matrix) of the Composite to investigate the effect of Fiber type and Fiber arrangement on Effective Thermal Conductivities in Transverse (K2) and Through Thickness (K3) directions. Thermal Conductivities of Fiber Reinforced Composites are predicted using Finite Element Method applied to Representative Volume Element in the form of Elliptical models with and without debond at Fiber-Matrix interfaces are discussed. The results have shown that the Effective Thermal Conductivities of Composites can be improved with Voids in a Matrix and random arrangement of Fibers in a Matrix.

Prediction of effective thermal conductivity of nanofluids by modifying renovated Maxwell model

Nanofluids, which are formed by suspending nanoparticles into conventional fluids, exhibit anomalously high thermal conductivity. Renovated Maxwell model was developed by Choi in which the presence of very thin nanolayer surrounding the solid particles was considered, which can measurably increase the effective thermal conductivity of nanofluids. A new model is proposed by introducing a fitting parameter χ in the renovated Maxwell model, which accounts for nanolayer, nonuniform sizes of filler nanoparticles together with aggregation. The model shows that the effective thermal conductivity of nanofluids is a function of the thickness of the nanolayer, the nanoparticle size, the nanoparticle volume fraction and the thermal conductivities of suspended nanoparticles, nanolayer and base fluid. The validation of the model is done by applying the results obtained by the experiments on nanofluids, other theoretical models, and artificial neural network technique. The uncertainty of the present measurements is estimated to be within 5% for the effective thermal conductivity.

Thermal Conductivity Prediction Method of Fiber-Reinforced Material with Microstructure Identification

An innovative method for predicting the thermal conductivity based on the recognition of microstructure features is established. Digital image processing technology is applied to analyze the electron micrograph of typical long fiber-reinforced composites. A novel method for determining the representative volume element is proposed. Once a set of representative volume elements has been established, actual physical information is taken into account by using a technique of image identification for the actual random distribution of fibers. Using the finite element method, the mean value and the standard deviation of the effective thermal conductivity based on the set of representative volume elements are obtained. The laser flash method was applied to measure experimentally the effective thermal conductivity. The novel numerical method proposed herein has been evaluated against these experimental data. It is found that the accuracy of the effective thermal conductivity prediction is guaranteed by image recognition of scanning electron microscope images. For more accurate information on the actual fibers, a random distribution is introduced into calculations. All the results show that the effective thermal conductivity prediction of the fiber-reinforced composite using microstructure identification is reasonably accurate and applicable. Close agreement with the experimental data is obtained. The average relative error is .

Measurement and simplified numerical prediction of effective thermal conductivity of open-cell ceramic foams at high temperature

In the present article, the effective thermal conductivity (ETC) of 10ppi open-cell ceramic foams is measured at temperatures ranging from 22°C to 750°C using the transient plane source (TPS) technique. The detailed morphology of the foam structures is reconstructed from 3D CT-scan images and their structural analysis is carried out using a volume image processing tool. The experimental results are compared with the predictions of directional ETC, obtained using a simplified 1D homogeneous model that considers coupled conduction–radiation heat transfer. The parameters, required by the model, are evaluated based only upon the information that could be extracted from 3D CT-scan images under certain simplifying assumptions. It can be concluded that the predictions of ETC for the present ceramic foam samples clearly correlate with the geometric parameters obtained from their structural analysis. It is also observed that the estimated microscopic porosity of the foam, which is not captured by 3D CT-scan images, has considerable influence on the reconstructed foam structure and hence on the predicted ETC. The predictions of ETC in the measured direction, obtained after the proposed directional averaging, compare extremely well with TPS measurements for the complete range of investigated temperatures. This suggests that the measurements of ETC, obtained employing TPS technique, are the directionally averaged representations of ETC in three perpendicular directions. The present investigation also clearly demonstrates the potential of the simplified modeling approach for characterizing even the directional ETC of open-cell ceramic foams, based primarily on their structural information.

Analysis of fibre waviness effect through homogenization approach for the prediction of effective thermal conductivities of FRP composite using finite element method

In this study, homogenization approach is proposed to analyse the fibre waviness in predicting the effective thermal conductivities of composite. Composites that have wavy fibre were analysed by finite element method to establish equivalence between micro- and macro-mechanics principles, thereby, it is possible to minimize the computational efforts required to solve the problem through only micro-mechanics approach. In the present work, the influence of crest offset, wavy-span on the thermal conductivities of composite for different volume fractions and thermal conductivity mismatch ratios were also studied. It is observed that the homogenization results are in good agreement with minimal % error from those obtained through pure micro-mechanics approach at the cost of low computational facilities and less processing time for converged solutions.

A statistical model for effective thermal conductivity of composite materials

Thermal interface materials composed of polymers and solid particles of high thermal conductivity have been used widely in electronic cooling industries. However, theoretical prediction of effective thermal conductivity of the composites remains as a crucial research topic. Theoretical modelings of the effective thermal conductivity of composites were based mainly on the analog between electric and thermal fields that satisfy Laplace equation under steady condition. Two approaches were employed, either by solving the Laplace equation or by equating the composite to a circuit network of conductors. In this study, the existing models obtained from these two approaches are first briefly reviewed. However, a close examination of the second approach reveals that there exists a paradox in this approach. To resolve this paradox, a statistical approach is then adopted. To this end, a mesoscopic ensemble that contains microscopic states is first constructed. The thermal conductivities of the microstates are identified by the principle of least action. A statistical parameter for each microstate is identified to characterize the effect of interface resistance on heat flow, as well as the connection between microstates. Effective thermal conductivity of the ensemble was then obtained from the variation principle that minimizes the standard deviation with optimal distribution of the parameter. The predictions by the present statistical model fit to experimental data with excellent agreement.

A reconstruction of Maxwell model for effective thermal conductivity of composite materials

Composite materials consisting of high thermal conductive fillers and polymer matrix are often used as thermal interface materials to dissipate heat generated from mechanical and electronic devices. The prediction of effective thermal conductivity of composites remains as a critical issue due to its dependence on considerably factors. Most models for prediction are based on the analog between electric potential and temperature that satisfy the Laplace equation under steady condition. Maxwell was the first to derive the effective electric resistivity of composites by examining the far-field spherical harmonic solution of Laplace equation perturbed by a sphere of different resistivity, and his model was considered as classical. However, a close review of Maxwell’s derivation reveals that there exist several controversial issues (deficiencies) inherent in his model. In this study, we reconstruct the Maxwell model based on a potential mean-field theory to resolve these issues. For composites made of continuum matrix and particle fillers, the contact resistance among particles was introduced in the reconstruction of Maxwell model. The newly reconstructed Maxwell model with contact resistivity as a fitting parameter is shown to fit excellently to experimental data over wide ranges of particle concentration and mean particle diameter. The scope of applicability of the reconstructed Maxwell model is also discussed using the contact resistivity as a parameter.

Effective thermal conductivity prediction of foods using composition and temperature data

Thermal conductivity data are important for food process modelling and design. Where reliable thermal conductivity data are not available, they need to be predicted. The most accurate ‘first approximation’ methodology for predicting the isotropic thermal conductivity of foods based only on data for composition, initial freezing temperature and temperature dependent thermal conductivity of the major food components was sought. A key feature of the methodology was that no experimental measurements were to be required. A multi-step prediction procedure employing the Parallel, Levy and Effective Medium Theory models sequentially for the components other than ice and air, ice and then air respectively is recommended. It was found to provide the most accurate predictions over the range of foods considered (both frozen and unfrozen, porous and non-porous). The Co-Continuous model applied in a single step also provided prediction accuracy within ±20% (on average), except for the porous frozen foods considered. For greater accuracy more rigorous modelling approaches based on knowledge of the foods structure would be required.

A simple and effective model for prediction of effective thermal conductivity of vacuum insulation panels

The excellent thermal insulation performance of vacuum insulation panels (VIPs) make them widely applied in energy conservation fields, especially in buildings engineering. This research work proposes a simple, yet extremely effective, alternative model for prediction of the effective thermal conductivity (ETC.) of VIPs. The ETC. of VIPs is function of the thermal conductivity of the core materials, the equivalent thermal conductivity of the rarefied gas embraced in the core and the equivalent thermal conductivity of radiation in the early studies. The micro structure of the porous core materials and vacuum degree are taken into consideration and the prediction numerical model for the ECT of VIPs is developed. The relationship of the vacuum degree versus the ETC. is theoretical analyzed. Three types VIPs are made from the polyurethane foam materials, superfine fibrous materials and nano-granular silica materials as the core materials. For each type, the vacuum degree and the thermal conductivity are collected, including the comparison between the testing results and the prediction model. The agreement between the model and the experimental results is fairly well when the air pressure is very low. The vacuum maintaining and service life of the VIPs are also discussed. The research work is meaningful for the enhancement of stability and the development of vacuum insulation panels.

A simple and effective model for prediction of effective thermal conductivity of vacuum insulation panels

The excellent thermal insulation performance of vacuum insulation panels (VIPs) make them widely applied in energy conservation fields, especially in buildings engineering. This research work proposes a simple, yet extremely effective, alternative model for prediction of the effective thermal conductivity (ETC.) of VIPs. The ETC. of VIPs is function of the thermal conductivity of the core materials, the equivalent thermal conductivity of the rarefied gas embraced in the core and the equivalent thermal conductivity of radiation in the early studies. The micro structure of the porous core materials and vacuum degree are taken into consideration and the prediction numerical model for the ECT of VIPs is developed. The relationship of the vacuum degree versus the ETC. is theoretical analyzed. Three types VIPs are made from the polyurethane foam materials, superfine fibrous materials and nano-granular silica materials as the core materials. For each type, the vacuum degree and the thermal conductivity are collected, including the comparison between the testing results and the prediction model. The agreement between the model and the experimental results is fairly well when the air pressure is very low. The vacuum maintaining and service life of the VIPs are also discussed. The research work is meaningful for the enhancement of stability and the development of vacuum insulation panels.

Numerical prediction of effective thermal conductivities of 3D four-directional braided composites

The temperature distribution in a representative volume element of three-dimensional and four-directional braided composites is studied with appropriate boundary conditions by the finite element method (FEM) to predict the effective thermal conductivity of the composite. Models with elliptical, circular and hexagonal cross-section of braiding yarns are considered. The model is validated by experiments based on hot disk thermal constant analyzer. The influences of fiber volume fraction Vf, and interior braiding angle γ, on heat transfer of the composite are studied with Vf equal to 0.40, 0.50 and 0.58, and γ from 15° to 50°. The results show that for the composite studied increasing fiber volume fraction results in higher thermal conductivity in both axial and transverse direction, while a larger interior braiding angle leads to higher transverse thermal conductivities but lower axial ones.

Prediction of Effective Thermal Conductivity of Cu/Solder System by Using Interfacial Layer in Two Phase System

A theoretical model is presented to predict effective thermal conductivity of real two phase materials from the values of thermal conductivity of the constituent phases and their volume fraction. Here we develop a numerical expression for effective thermal conductivity of Cu-solder system in two phase system is being comprised of contributions from both the phases with interfacial layer. A new correlation term F is introduced for highly conducting phase, non-linear fl ow of heat fl ux lines and random distribution of the phases. Here, we get best fi tting relation for F. Comparison of the proposed relation with different models has also been made. The values predicted by the proposed model are in close and good agreement with experimental values and more accurate than those obtained from existing models.