Effective Thermal Conductivity Model Research Articles

An improved analytical model of effective thermal conductivity for hydrate-bearing sediments during elastic-plastic deformation and local thermal stimulation

As one of the crucial thermal properties controlling the dissociation of natural gas hydrate (NGH), effective thermal conductivity (ETC) should be precisely determined to improve the efficiency of NGH exploitation. But so far, most existing analytical ETC models of hydrate-bearing sediments could not accurately characterize the evolution of ETC. In this paper, an improved analytical model is derived for quantitatively revealing physical relations between ETC and various influencing factors during elastic-plastic deformation and local thermal stimulation processes, including hydrate saturation change, complex pore structures evolution, and hydrate occurrence patterns transition. The effectiveness of the proposed model is validated against available experimental data and compared with other existing models, then effects of various critical parameters on ETC are investigated. Results show that the porosity of hydrate-bearing sediments is accurately predicted during both loading and unloading processes, and the calculated ETC values under various conditions (effective stress, hydrate saturation, and temperature) are satisfactory with the test data. Contributions of elastic deformation and plastic deformation to ETC increments are quantitatively obtained. It is noteworthy that this proposed model is significant to reveal the evolution mechanisms of ETC, helping to accurately predict gas production and offer better plans for efficient NGH exploitations.

Investigation on Thermal Conductivities of Plain-woven Carbon/Phenolic and Silica/Phenolic Composites at High Temperature: Theoretical Prediction and Experiment

Phenolic resin-based ablation materials have found widespread applications in the aerospace industry. The prediction of their thermal conductivity is of paramount importance for the optimization and evaluation for thermal protection systems. However, there is rarely reported thermal conductivity performance of phenolic composites during ablation processes. Therefore, this investigation theoretically predicts the dynamic response of thermal conductivity at high temperatures for plain-woven carbon/phenolic and high silica/phenolic composites. By combining the progressive cubic ablation model with existing composite material property formulas, a multiscale prediction model for effective thermal conductivity is developed. The thermal performance of the resin matrix, reinforcing fibers, yarns, and overall fabric composites is calculated. Additionally, mesoscale representative volume elements are implemented to investigate the overall heat transfer characteristics of carbon/phenolic and high-silica/phenolic composites, including temperature and heat flux distributions. Moreover, both composites thermal conductivities are measured in the range from 298 K to 473 K. The proposed prediction model demonstrates good reliability, with average deviations of 3.76% and 7.36% compared to finite element analysis results and experimental data, respectively.

Macroscopic transport characteristics in packed bed with a multi-physics inversion strategy for solid breeding blanket of HCCB TBM

The solid breeding blanket with typical packed bed structure is a key component for tritium breeding and thermal conversion in future fusion reactors. The pore scale model for multi-physical field solution of solid breeding blanket is fine but very expensive. The simplified packed-bed scale model is more favored in engineering especially for the system-level calculation of the blanket, but it needs to be inputted appropriate macroscopic transport parameters. In this work, the multi-physics calculations of blanket in Chinese HCCB TBM (Helium-Cooled Ceramic-Breeder Test Blanket Module) at pore scale and packed-bed scale were performed. It was found that the packed-bed scale model with traditional macroscopic transport parameters is not accurate enough, especially the prediction deviation of tritium concentration distribution could reach about 25 %. Hence, a novel multi-physics inversion strategy was proposed to predict the macroscopic transport parameters of the packed bed under the multi-field coupling conditions. The inversion results show that the convection of helium significantly enhances the heat and tritium diffusion in the packed bed, and the effective thermal conductivity and effective diffusivity could be increased by 18 % and 46 %, respectively. Then based on the results by multi-physics inversion strategy, the modified effective thermal conductivity and effective diffusivity correlation models for solid breeding blanket packed bed are constructed. With the modified correlation models, the relative prediction deviations of pressure drop, temperature distribution and concentration distribution are within 2.5 %, 0.6 % and 10 % respectively at different inlet velocities (0.05 m/s ∼ 0.25 m/s) and different inlet temperatures (300 K ∼ 900 K). The study in this paper would assist the thermal-hydraulics analysis of the solid breeding blanket in the fusion reactor.

Pore structure characterization and effective thermal conductivity modeling of fibrous building thermal insulation materials based on X-ray tomography

The existing structural characterization methods of building materials as well as thermal conductivity calculation models can not be directly applied when considering fibrous building thermal insulation materials with intricate skeletons. In this study, rock wool is considered the research object, and the X-ray tomography method is used to characterize the pore structure and extract structural parameters. Based on the actual pore morphology of the material, the pores in the representative elementary volume (REV) are reasonably assumed to be cubic. Additionally, considering the contact thermal resistance of fibers and the randomness of pore distribution, the curved pattern of heat conduction pathway with the ever-changing diameter is reasonably simplified into a series-parallel form of the curved heat chain with the same diameter. On this basis, the fractal models of effective thermal conductivity are established in horizontal and vertical directions. Finally, a modified formula for the effective thermal conductivity calculation of fiber thermal insulation materials is proposed, taking into account the influence of fiber orientation on the material thermal conductivity. It was shown that the relative deviation between the calculated correction value and the experimental value of the effective thermal conductivity is all less than 16.13%.

Review of Heat Transfer Characteristics of Natural Gas Hydrate

As a typical unconventional energy reservoir, natural gas hydrate is believed to be the most promising alternative for conventional resources in future energy patterns. The exploitation process of natural gas hydrate comprises a hydrate phase state, heat and mass transfer, and multi-phase seepage. Therefore, the study of heat transfer characteristics of gas hydrate is of great significance for an efficient exploitation of gas hydrate. In this paper, the research methods and research progress of gas hydrate heat transfer are reviewed from four aspects: measurement methods of heat transfer characteristics, influencing factors of heat transfer in a hydrate system and hydrate-containing porous media systems, predictive models for effective thermal conductivity, and heat transfer mechanisms of hydrate. Advanced measurement techniques and theoretical methods that can be adopted for the heat transfer characteristics of gas hydrate in the future are discussed.

A Comparative Study of Selected Models for Effective Thermal Conductivity

This paper conducts a comparative evaluation of 22 models focusing on the effective thermal conductivity of two-phase porous materials. Calculations were performed for each model across a range of solid-to-fluid thermal conductivity ratios, spanning from 1 to 15,000, and for two different porosities: 0.1 and 0.2. The study advocates the use of dimensionless charts that normalised solid thermal conductivity (ks) and effective thermal conductivity (kef) concerning fluid thermal conductivity (kf) for qualitative analysis. Employing this approach, the examined models were categorised into four fundamental groups. The latter portion of the paper compares selected models with experimental data. These experiments involved testing eight porous media samples in the form of packed steel bars, arranged in two configurations: staggered and in-line. The tests were conducted over a temperature range of 75–400°C, corresponding to ks-to-kf ratios ranging from 1,800 to 855. Various graphical representations were used to compare measurement data with model calculations. The findings indicate that the most accurate comparisons can be made using linear charts, which present absolute values of the kef coefficient in relation to the thermal conductivity of the solid phase.

Computational Model of Effective Thermal Conductivity of Green Insulating Fibrous Media.

Modelling effective thermal properties is crucial for optimizing the thermal performance of materials such as new green insulating fibrous media. In this study, a numerical model is proposed to calculate the effective thermal conductivity of these materials. The fibers are considered to be non-overlapping and randomly oriented in space. The numerical model is based on the finite element method. Particular attention is paid to the accuracy of the results and the influence of the choice of the representative elementary volume (REV) for calculation (cubic or rectangular parallelepiped slice). The calculated effective thermal conductivity of fibrous media under different boundary conditions is also investigated. A set of usual mixed boundary conditions is considered, alongside the uniform temperature gradient conditions. The REV rectangular slice and uniform temperature gradient boundary conditions provide a more accurate estimate of the effective thermal conductivity and are therefore recommended for use in place of the usual cubic representative elementary volume and the usual mixed boundary conditions. This robust model represents a principal novelty of the work. The results are compared with experimental and analytical data previously obtained in the literature for juncus maritimus fibrous media, for different fiber volume fractions, with small relative deviations of 7%. Analytical laws are generally based on simplified assumptions such as infinitely long fibers, and may neglect heat transfer between different phases. Both short and long fiber cases are considered in numerical calculations.

FRACTAL STUDY ON HEAT TRANSFER CHARACTERISTICS OF FRACTURED DUAL POROUS MEDIA WITH ROUGH SURFACE

In order to study the influencing factors of heat transport characteristics in the rough fractured dual porous media, the theoretical model of effective thermal conductivity (TC) in rough fractured dual porous media is established in this paper. By calculating the thermal resistance and TC of rough cracks, it is found that the heat transport capacity of the fracture is inversely proportional to the relative roughness and porosity and is proportional to the solid-liquid TC ratio and the fractal dimension of the fracture. The heat conduction in the fractured dual porous media is mainly controlled by the matrix. In addition, by comparing with other models and existing experimental data, it can be seen that the heat transfer capacity of dual media is stronger than that of single porous media. The predicted TC of rough cracks is lower than the experimental data, which is in line with the actual situation, and the model is reasonable.

FRACTAL MODEL FOR EFFECTIVE THERMAL CONDUCTIVITY OF COMPOSITE MATERIALS EMBEDDED WITH A DAMAGED TREE-LIKE BIFURCATION NETWORK

Scientists worldwide have always been interested in the study of networks that resemble trees and porous materials. Therefore, based on fractal theory, this paper systematically studies the heat transfer problem of the damaged tree-like networks under different saturations in multi-medium composite materials and derives their dimensionless thermal conductivity (DTC). The research has shown that the dimensionless thermal conductivity (DTC) decreases with an increase in damaged channels. The saturation significantly impacts the heat transfer of the damaged tree networks, and it exhibits linear changes with the ratio of the gas phase, liquid phase, and solid phase. Additionally, it can be observed that the fractal dimension of length distribution and diameter distribution, bifurcation numbers, bifurcation series, porosity, and other parameters in the networks are related to thermal conductivity. The comparison between the data derived from this model and experimental data shows that the proposed model can effectively deepen our understanding of the heat transfer mechanism of the damaged networks in composite materials under different saturation levels. Additionally, the model in this paper does not have an empirical constant, which avoids the influence of potential factors.

A Comparative Assessment of Different Aerogel-Insulated Building Walls for Enhanced Thermal Insulation Performance.

Aerogel is widely recognized as a superinsulating material with great potential for enhancing the thermal insulation performance of building walls. It can be applied in various forms such as aerogel plasters (AP), aerogel fibrous composites (AFC), and aerogel concrete (AC) in practical engineering applications. This study aims to investigate the most efficient application form for maximizing building insulation performance while minimizing the amount of aerogel used. To predict the thermal insulation performance of aerogel-insulated walls, a resistance-capacitance network model integrating the aerogels' effective thermal conductivity model was developed and was validated by comparing it with Fluent simulation software results in terms of surface temperature. Using the validated models, the thermophysical parameters, transient thermal properties, and transmission load were predicted and compared among AP, AFC, and AC walls. The results indicate that using AFC can result in approximately 50% cost savings to achieve the same thermal resistance. After adding a 20 mm thickness of aerogel to the reference wall without aerogel, the AFC wall exhibited the highest improvement in thermal insulation performance, reaching 46.0-53.5%, followed by the AP wall, and then the AC wall, aligning with considerations of microstructural perspectives, thermal resistance distributions, and thermal non-uniformity factors. Therefore, giving priority to AFC use could reduce the required amount of silica aerogel and enhance economic efficiency. These results provide valuable insights for theoretical models and the application of aerogel-insulated walls in building engineering insulation.

Analyses and Research on a Model for Effective Thermal Conductivity of Laser-Clad Composite Materials

Composite materials prepared via laser cladding technology are widely used in die production and other fields. When a composite material is used for heat dissipation and heat transfer, thermal conductivity becomes an important parameter. However, obtaining effective thermal conductivity of composite materials prepared via laser cladding under different parameters requires a large number of samples and experiments. In order to improve the research efficiency of thermal conductivity of composite materials, a mathematical model of Cu/Ni composite materials was established to study the influence of cladding-layer parameters on the effective thermal conductivity of composite materials. The comparison between the model and the experiment shows that the model’s accuracy is 86.7%, and the error is due to the increase in thermal conductivity caused by the alloying of the joint, so the overall effective thermal conductivity deviation is small. This study provides a mathematical model method for studying the thermodynamic properties of laser cladding materials. It provides theoretical and practical guidance for subsequent research on the thermodynamic properties of materials during die production.

Novel effective thermal conductivity numerical model for distinct shaped pure paraffins (C14–C33)

This paper presents a novel numerical model for “effective thermal conductivity” designed to address the limitations of previous models, which required different constants for each distinct shape. The constants C and m incorporates the natural convection effect through the Rayleigh number (CRam), obviating the need to solve velocity equations such as those for continuity and momentum. Notably, this model is applicable to a wide range of phase change materials (PCMs) using the same constants. Prior investigations predominantly focused on spherical capsule shapes and specific PCMs with varying C and m constants. The present study extends the limitations from spherical to cylindrical, square and rectangular shapes. The PCMs evaluated includes pure paraffins ranging from C14 to C33, all assessed using constant values for the C and m. Initially, the proposed model for effective thermal conductivity, along with the constrained model accounting for natural convection, was verified against experimental data for C18 alkane, achieving a root mean square error of 0.0177 with experimental and 0.0077 with constrained model. Subsequently, the present model's validity was affirmed against a reference constrained model across a wide range of alkanes. Simulations were carried out for both cylindrical and square shapes. For rectangular configurations, the aspect ratio was incorporated into the Rayleigh number to account the effects of both vertical and horizontal orientations.

Computing of temperature-dependent thermal conductivity and viscosity correlation for solar energy and turbulence appliances via artificial neuro network algorithm

The growing popularity of artificial intelligence approaches has led to their application in a wide range of engineering fields. The most widely used artificial intelligence tool, artificial neural networks, can be used to predict data with high accuracy. An artificial neural network approach is being used to predict effective and accurate thermal conductivity and viscosity models for hybrid nanofluid systems. Here, new types of correlations relating to the thermophysical properties of Fly Ash–Cu nanoparticles with diameter sized 15.2[Formula: see text]nm and which are temperature-dependent are developed. The highest thermal conductivity and viscosity values were obtained for hybrid nanofluids with a mixture ratio of 20:80, with maximum amplification exceeding 83.2% and 65%, respectively, over the base fluid. The Fly Ash–Cu/water hybrid nanofluid’s viscosity and thermal conductivity are evaluated for a concentration range of 0–4%. The evaluation of the Fly Ash–Cu/water hybrid nanofluids system at concentrations ranging from 0 to 4% most likely entails a scientific or engineering study aimed at understanding the behavior and properties of this nanofluid mixture. Nanoparticles can agglomerate or settle in the base fluid over time, compromising the stability of the nanofluids. Researchers may be interested in determining how varied quantities of Fly Ash and Cu nanoparticles affect the nanofluid’s stability and sedimentation behavior. The heat transfer potential is examined within the optimistic range of temperatures of 30–80∘C. Many fruitful results for turbulence and solar energy have been drawn. The Mouromtseff number achieved an optimal value for all concentration levels. The heat transfers of turbulent flow and thermal conductivity of hybrid nanofluids increase with the augmented values of concentrations and temperature. Researchers found an increase in thermal conductivity of hybrid nanofluids at 0–4% concentrations, potentially impacting heat transfer applications. The conclusion explores the potential integration of the developed correlations and neural network model into practical engineering or industrial applications involving solar energy and turbulence appliances. In this work, we extend the work of Kanti et al. [Sol. Energy Mater. Sol. Cells 234 (2022) 111423] which is on the properties of water-based fly ash-copper hybrid nanofluid for solar energy applications.

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.

Implementation and validation of effective thermal conductivity model of coal‐rock mass with rough capillary pore structure under CT three‐dimensional reconstruction

AbstractOn the strength of the capillary physical equivalent model and heat transfer law of series‐parallel combined structural unit, the calculation model of effective thermal conductivity of coal‐rock mass is obtained. The model considers the effect of roughness, porosity factor and other factors on effective thermal conductivity. CT digital core technology is applied to reconstruct the 3D model of coal‐rock mass, and one‐way heat transfer numerical simulation is carried out according to the model. It indicates that the internal temperature of coal‐rock mass is non‐uniformly distributed under the influence of pore structure, and the isothermal surface of pore region bulges towards the boundary of heat flux. Comparing the calculated and simulated values under the same conditions, the average error percentage of the theoretical calculation model is 6.95%, and the model has outstanding prediction performance in porous media with medium porosity and regular pore distribution, which provides a reference for predicting the effective thermal conductivity of coal‐rock mass.

Fractal Pore-Scale Model for Effective Thermal Conductivity of Multiscale Unsaturated Porous Media

Fractal Pore-Scale Model for Effective Thermal Conductivity of Multiscale Unsaturated Porous Media

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.

Analytical Fractal Model for Effective Thermal Conductivity of Open-Cell Metallic Foams With Coated Hollow Ligaments

Abstract Coating the hollow ligaments of open-cell (fluid-through) metallic foams (MFs) fabricated via the sintering route with a thin layer of graphene can improve the effective thermal conductivity (ETC) of the foam without significantly increasing its flow resistance, potentially important for thermal storage applications. However, the Euclidean geometry cannot accurately depict the random distribution of pores within MFs. To this end, the present study aims to analyze how such thin coatings affect the ETC of MF by employing the fractal theory to depict the random distribution of its open pores. Subsequently, a cubic representative structure is chosen for self-similar pores in the fractal to establish a correlation between the geometric parameters of MF and its fractal dimension. Upon determining the thermal resistance provided a representative structure of the foam having coated hollow ligaments, its ETC is derived as a function of fractal dimension, dimensionless parameters of pore size, porosity, and thermal conductivity of relevant materials (e.g., ligaments, coatings, and filling medium). For validation, existing experimental data are used to compare with analytical predictions, with good agreement achieved. It is demonstrated that the ligament hollowness weakens the thermal conduction of MFs. In addition, when the coating has a thermal conductivity greater than that of ligament, the coating enhances the ability of the foam to conduct heat. Although the ligament hollowness and coating thickness are imperative factors affecting the ETC, the material makes of ligament and coating plays a decisive role in the ETC.

Assessment of the theoretical models of effective thermal conductivity based on digital rock physics for clean sandstones

Knowledge of the effective thermal conductivity (ETC) of porous media provides valuable insights into the heat flow and profoundly affects the feasibility analysis of thermal enhanced oil recovery methods and geothermal field development. Theoretical assessment of ETC based on structural properties of the porous medium and various simplification assumptions by prediction models have shown acceptable results towards ETC quantification; however, their applicability must be investigated further due to the availability of various types of such models. In this study, we first employed a digital rock approach to simulate the heat conductivity of micro-CT images of 10 clean sandstone samples using Avizo software in different directions for evacuated, air-saturated, and water-saturated conditions. The filtered and segmented images were applied to perform voxel-based ETC simulations under steady state condition. Then, the simulation results were compared to the computed ETCs for each sample by 11 theoretical models. Two well-known thermal conductivity bounds, i.e., Hashin and Shtrikman bounds and Wiener bounds were used to confirm the validity of models and simulation outputs. It was shown that the Haung model generates the best outputs for vacuum (MAPE = 0.08 and RMSE = 0.37) and air-saturated (MAPE = 0.07 and RMSE = 0.32) states. While the water-saturated condition was competently predicted by the Ribaud model (MAPE = 0.05 and RMSE = 0.31). The overall analysis indicated that the Haung model is the best model for the prediction of ETC in all three pore-filling states for clean sandstones.

Computational models of effective thermal conductivity for periodic porous media for all volume fractions and conductivity ratios

The effective thermal conductivity (ETC) of composites is of great significance for simulating the macroscopic heat transfer process. In this paper, an extension of the morphology efficiency is proposed, which quantifies the influence of morphology on composite ETC, and is initially derived from two extreme models-series and parallel ETC bounds. The morphology efficiency obtained from different bound models are compared. It concluded that the morphology efficiency derived from Hashin and Shtrikman bound models is the best representative of the morphology of isotropic composite materials, which can conveniently reveal the optimal volume fraction of inclusion phase and thermal conductivity of the ideal thermal response. For composites with inverse Simple Cubic, Body Centered Cubic, Face-Centered Cubic and Kelvin lattice, the corresponding prediction model of ETC is proposed in a wide range of porosity and thermal conductivity. Among them, the ETC model of Kelvin cell and inverse Simple Cubic cell can well predict the high porosity foam and foams filled with phases with thermal conductivity ratio r in the range of 3 to 8, respectively.