Effective Thermal Conductivity Research Articles

A tree-based automated machine learning approach of the obstructed view factor of thermal radiation in nuclear pebble beds

For the nuclear pebble bed of the high temperature gas-cooled reactor (HTGR), a tree-based automated machine learning approach is developed to discuss the complicated thermal radiation behaviors. The AutoML model for calculating the obstructed view factor between any two particles in the pebble bed includes the gradient boosting regression tree model with the fine-tuned hyperparameters and the analytical base model. Using the discrete packing of the HTR-PM nuclear reactor and the leaped Halton sequence, a large dataset of the view factor under different conditions is generated to train the AutoML model. On the same platform, numerical results show that AutoML model is approximately 5 × 105 times faster than the traditional approach. The Pareto front of the AutoML model indicates that the mean squared error decreases with the model complexity until it reaches the optimal solution. Then, the trained AutoML model is applied to the engineering pebble bed. It is shown that the average radiation exchange factor near the wall is lower than that in the bulk region. In addition, the packing height is also an important parameter for evaluating the radiative behaviors. In particular, when the height of the nuclear pebble bed is less than 20 times particle diameter, it is necessary to consider the contribution of the packing height to the radiation effective thermal conductivity.

Theoretical study on the effective thermal conductivity of silica aerogels based on cross-aligned and cubic pore model (CACPM)

Abstract Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very l1ow, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, predicting their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed cross-aligned and cubic pore model (CACPM) based on the actual pore arrangement of SiO2 aerogel. Based on the established cross-aligned and cubic pore model (CACPM), the effective thermal conductivity expression for aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T=298K, a 2=0.85, D 1=90μm, ρ=128kg/m3, within the pressure range of 0-105Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 103-104Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer model and calculation formula.

Investigation of the influence of morphology on thermal conductivity in hexagonal honeycomb structures and computational models with varied volume fraction and conductivity ratio

The effective thermal conductivity (ETC) is a critical parameter for simulating macroscopic heat transfer processes in composite materials, which estimation is particularly critical where the thermal conductivity of the composite phases is completely different. The huge difference in thermal conductivity of the composite phases makes their volume fraction modulation a classical way to reach the desired thermal conductivity. Nevertheless, the typical manufacturing process of honeycomb cellular structures allows various degrees of stretching of the structure, leading to various honeycomb geometries. In these ‘real’ structures some of the honeycomb wall sides are twice as thick as other parts, modifying the symmetry of the system with respect to honeycomb with uniform wall side thickness. A noticeable example of these composites is that of a hexagonal metallic honeycomb structure filled with phase change material (PCM) which is a widely utilized material in the field of thermal storage and thermal management by exploiting the heat absorbed/released by the PCM phase during its melting/solidification. While the thermal response of a PCM composite during a thermal cycle is not only defined by thermal conductivity (but also by cell size), this represents the basis for the with the optimization of a system based on a composite PCM.For this reason, in this study, steady-state simulations of heat transfer in unit honeycomb cells in different directions perpendicular to the cell axis are conducted to quantify the impact of morphology on the thermal property of the different wall types within honeycomb structures. The results demonstrate that in both SHS and DHS, the porosity exhibiting maximum anisotropy of ETC decreases as the thermal conductivity ratio increases. Moreover, simple predictive models for calculating the ETC in all directions are proposed for each type of honeycomb, considering a wide range of porosity and thermal conductivity ratio, with a relative error limited to 2 %.

Micro-CT image-based computation of effective thermal and mechanical properties of fibrous porous materials

Fibrous porous materials are extensively employed as heat shielding material for space vehicles and capsules. To predict the performance of these materials using computational modeling at the vehicle/capsule scale, the effective material properties are needed. In this work, the effective thermal conductivity and elastic constants of a carbon fibrous porous material called FiberForm (precursor of PICA) were calculated using a direct image-based approach. In this image-based approach, the microstructures obtained using X-ray computed tomography technique are represented as binary voxel data. Nonlocal interactions are introduced between neighboring voxels. Integro-differential equations, with respect to spatial and temporal dimensions respectively, are developed to govern material thermal and mechanical behaviors. Using this approach, energy-based computational procedures were developed to calculate the effective material properties of fibrous and porous materials irrespective of the periodicity of underlying microstructures. The size of representative volume element was determined by convergence of effective properties with respect to microstructure size.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.

Analysis of a Novel Method for Generating 3D Mesh at Contact Points in Packed Beds

This study comprehensively analyzes the impact of the novel HybridBridge method, developed by the authors, for generating a 3D mesh at contact points within packed beds within the effective thermal conductivity. It compares HybridBridge with alternative methodologies, highlights its superiority and outlines potential applications. The HybridBridge employs two independent geometry parameters to facilitate optimal flow mapping while maintaining physically accurate effective thermal conductivity and ensuring high mesh quality. A method is proposed to estimate the HybridBridge radius for a defined packed bed and cap height, enabling a presimulative determination of a suitable radius. Numerical analysis of a body-centered-cubic unit cell with varied HybridBridges is conducted alongside previous simulations involving a simple-cubic unit cell. Additionally, a physically based resistance model is introduced, delineating effective thermal conductivity as a function of the HybridBridge geometry and porosity. An equation for the HybridBridge radius, tailored to simulation parameters, is derived. Comparison with the unit cells and a randomly packed bed reveals an acceptable average deviation between the calculated and utilized radii, thereby streamlining and refining the implementation of the HybridBridge methodology.

Multi-scale investigation of heat and momentum transfer in packed-bed TES systems up to 800 K

With the rising cost of energy and the advancement of corporate social responsibility, there is a growing interest in addressing the challenge of recovering and storing high-temperature waste heat. Sensible heat storage in packed beds stands out as a cost-effective and seemingly straightforward solution for high-temperature Thermal Energy Storage (TES). Engineering models developed to design low-temperature TES systems were tentatively used to design this new generation of high-temperature systems. Delving into the physics of coupled heat and mass transfer reveals a lack of validation of this approach. This study seeks to establish a comprehensive bottom-up methodology - from the particle scale up to the system level - to provide informed and validated engineering models for the design of high-temperature TES systems. To achieve this goal, we developed a multi-scale numerical model to explore the physics of heat and momentum transfer in packed-bed TES systems. At the microscopic scale (pore/particle), we consider the flow of a compressible high-temperature gas between the particles, coupled to transient heat conduction within the particles, with particular attention given to incorporating accurate temperature-dependent viscosity for the gas phase and thermal conductivity and density for both solid and gas phases. At the macroscopic scale (engineering), we propose a high-temperature extension of state-of-the-art two-equation TES models. The governing equations considered are the volume-average conservation laws for gas-mass, gas-momentum and energy of both phases. The multi-scale strategy is applied to a randomly packed bed of spherical particles generated with the discrete element method (DEM) software LIGGGHTS. Numerical models for both scales were implemented in the Porous material Analysis Toolbox based on OpenFoam (PATO), which is made available in Open Source by NASA. Microscopic scale simulations were used to infer the effective parameters needed to inform the macroscopic model, namely, permeability, Forchheimer coefficient, effective thermal conductivities, and the heat transfer coefficient. The informed macroscopic model reproduces with excellent accuracy the average temperature fields of the physics-based microscopic model. Pore-scale analysis shows highly three-dimensional flow characterized by reverse flow and strong cross-flow in the packed bed system. Moreover, it indicates the coupling between temperature and velocity fields, where a nonuniform velocity field results in uneven temperature distributions across the fluid and the solid spheres within the packed bed, subsequently affecting the macroscopic heat transfer coefficient. The overall strategy is validated by comparison to available experimental data. This bottom-up methodology contributes to the understanding and opens new perspectives for a more precise design and monitoring of high-temperature TES systems.

ITZ volume fraction and thermal conductivity of concrete: A unified random packing model for gravels and crushed rocks

This work proposes a mesostructure-guided computational framework to evaluate the effective thermal conductivity (ETC) of concrete affected by aggregate and interfacial transition zone (ITZ) configurations at a mesoscopic scale. An unified aggregate shape descriptor for gravels and crushed rocks is characterized by superellipsoid covering from convexity to non-convexity, as well as random static and dynamic packings of superellipsoidal aggregates (SAs) are carried out to generate tri-phase concrete mesostructures consisting of homogeneous mortar, densely packed aggregates and their surrounding ITZs. A closed-form expression for the ITZ volume fraction is theoretically developed in the present concrete mesostructure, which is also validated using the one-point probability function simulation. Moreover, an optimized Browanian motion numerical strategy is developed to estimate the ETC of tri-phase concrete. This strategy is confirmed to be an accurate numerical technique by comparing against the Mori-Tanaka model. The present framework reveals the quantitative responses of various configurations on the ETC, which manifest rigorous “constituent-mesostructure-ETC” relations. The results are available for tailoring components to optimize ITZ structures for the improvement of thermal efficiency and durability of buildings.

The Influence of Reinforced Fibers and Opacifiers on the Effective Thermal Conductivity of Silica Aerogels

Fiber–particle-reinforced silica aerogels are widely applied in thermal insulation. Knowing their effective thermal conductivity (ETC) and radiative characteristics under high temperatures is necessary to improve their performance. This article first analyzes the radiation characteristics of silica aerogels doped with opacifier particles and reinforced fibers, and then a universal model is established to predict the ETC. Furthermore, the impacts of different parameters of opacifier particles and reinforced fibers on the thermal insulation performance of silica aerogels are investigated. The results indicate that SiC exhibits comparatively strong absorption characteristics, making it a good alternative for opacifiers to improve thermal insulation performance under high temperatures. For the given type and volume fraction of opacifier particles, there exists an optimal diameter and volume fraction to achieve the best insulation performance of silica aerogel under a certain temperature. Considering that SiO2 fibers exhibit a limited extinction capability and higher conductive thermal conductivity under high temperatures, for fiber–particle-reinforced silica aerogels, it is beneficial for their insulation performance to reduce the fiber volume fraction when the required mechanical properties are satisfied.

Exploring the influence of nanolayer morphology on magnetized tri-hybrid nanofluid flow using artificial neural networks and Levenberg–Marquardt optimization

This study investigates the impact of morphological nanolayers on the thermal conductivity of magnetized tri-hybrid nanofluid flow using artificial neural networks (ANNs) employing the Levenberg–Marquardt (LM-ANN) scheme. Nonlinear partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) using similarity variables. A dataset covering various parameters such as nanolayer thickness, particle radius, magnetic parameter, expansion/contraction ratio, Schmidt number, volume fraction, and Prandtl number is generated using the Bvp5c numerical algorithm. LM-ANN is then used for testing, training, and validation to analyze approximate solutions for individual cases. Histogram analysis, mean square error (MSE), and regression investigations validate the LM-ANN. The proposed approach closely aligns with suggested and reference findings, showing an accuracy level within 10−10 range. Increasing nanolayer thickness leads to higher effective thermal conductivity. The Nusselt number increases notably with higher hybrid nanoparticle volume fraction. Laminar shape consistently exhibits superior heat transfer performance compared to other shapes. Increasing nanoparticle volume fraction enhances the Nusselt number and reduces skin friction coefficients (SFC). Industry recommendations include integrating nanolayer technologies for improved thermal efficiency.

The Impact of In-Flight Acceleration Environments on the Performance of a Phase-Change Heat Exchanger Unit with Layered Porous Media

The Phase-Change Heat Exchanger Unit in Layered Porous Media (PCEU-LPM) is obtained through frozen pouring processing, and exhibits characteristics such as high thermal conductivity, high latent heat, and high permeability, making it suitable for dissipating heat in airborne electronic devices. This study numerically investigates the impact of aircraft speed acceleration conditions, which lead to weightlessness or overload, on the performance of the PCHEU-LPM, with a particular focus on the influence of natural convection in the liquid-phase region. Initially, a microscale thermal analysis model is established based on the Navier–Stokes equation scanning electron micrograph to calculate the effective thermal conductivity and permeability of the PCHEU-LPM under different porosities. Subsequently, these parameters are incorporated into a macroscale thermal analysis model based on Darcy’s law, employing an average parameter approach. Using the macroscale thermal analysis model, temperature and velocity fields are computed under various porosities, acceleration magnitudes, and directions. The calculation results indicate that as the acceleration increases from α = 0 to α = 10 g, the interface temperature of the PCHTU-LPM decreases by approximately 5.2 K, and the temperature fluctuation decreases by 2.4 K. If the porosity of the PCHTU-LPM is increased from ε = 70% to ε = 85%, the influence of acceleration change on natural convection will be further amplified, resulting in a decrease in the interface temperature of the PCHTU-LPM by approximately 10.2 K and a decrease in temperature fluctuation by 5.8 K. When the acceleration direction is +z, the interface temperature of the PCHTU-LPM is at its lowest, while it is highest when the acceleration direction is −z, with a maximum difference of 15.4 K between the two. When the acceleration direction is ±x and ±y, the interface temperature lies between the former two cases, with the interface temperature slightly higher for ±y compared to ±x, with a maximum difference of 3.9 K between them.

A new method of fuel pebble temperature calculation based on neutronic and thermal coupling equivalent model

As one of the six reactor types in the fourth-generation nuclear energy systems, the Very High Temperature Gas-cooled Reactor (VHTR) possesses inherent safety features. One VHTR fuel pebble contains tens of thousands of randomly distributed TRISO fuel particles, displaying a double heterogeneity characteristic. Current research models employ the homogenized method for fuel pebble temperature calculation, which neglected the neutronic and thermal (N/T) coupling effect and double heterogeneity characteristic. This study proposes a fuel pebble coupled equivalent method (PCEM) for temperature calculation. The method is based on the effective thermal conductivity obtained by the fine structure fuel pebble N/T coupling method. The new method is evaluated on steady-state and transient VHTR multi-scale neutronic and thermal hydraulic (N/TH) coupling calculation. The results show that the traditional temperature calculation method is conservative. Under steady-state conditions, the maximum degree of conservatism of the fuel pebble average temperature and peak temperature are 0.6 K and 14.2 K respectively. For the sudden drop in coolant flow rate transient condition, the average temperature and peak temperature of the fuel pebble calculated by PCEM are smaller than the values calculated by traditional method at the same time. Due to the influence of the fuel Doppler effect, the transient response of the traditional calculation method is slower.

Stochastic microstructure modeling and thermal conductivity of coal-based carbon foam

The mechanical, thermal and electrical properties and applications of coal-based carbon foam (CCF) are based on its porous structure. In the present study, a 3-D stochastic numerical program was used to model the microstructure of CCF considering its non-uniformly distributed elliptical pores (i.e., pore dispersity). The heuristic program derived from the foaming process reflected the heterogeneity of foam. Stochastic seeding was used to regulate the pore location dispersity caused by material unevenness and impurities, while the pore size dispersity was revealed by assigning dissolved gas to adjacent pores during pore growth. The structural similarity was confirmed by comparison between the established model and the actual foam in geometrical features, including ligament edge/wall thickness, pore size and ligament cross-section shape etc. The effective thermal conductivity (ETC) of the stochastic model is more sensitive to changes in porosity, compared to that of uniform model of previous literatures. The reason was suspected to be the longer heat transfer path and less cross-section variation of the ligaments of heterogeneous foam. Pore location and size dispersities were regulated in a stable range by program parameters, which indicated that the stochastic model accurately simulated the microstructural complexity of CCF.

Temperature dependency of electric field treatment for improvement of effective thermal conductivity of functional carbon/silicone rubber composite sheets

Temperature dependency of electric field treatment for improvement of effective thermal conductivity of functional carbon/silicone rubber composite sheets

On the effective thermal conductivity of gallium-based liquid metal filled elastomers

Gallium based alloys are liquid at ambient temperature, combining both metal-like high thermal conductivity and fluidity characteristics, which contributes to their applications in thermal management, soft robotics, stretchable electronics and etc. A great number of experimental researches have been performed in preparing Ga-based liquid metal filled elastomers (LMFEs) with various constituent systems, processing techniques, droplet morphology and filler sizes in attempt to obtain the best thermal conductive efficiency. The thermal conductive mechanisms in these LMFEs are still lacking a comprehensive understanding up to date, and therefore the present work aimed to conduct a thorough analysis on this topic using both theoretical models and finite element method (FEM) simulations. The predictability of four classic micromechanics models was compared with the experiments and FEM simulations, and their relevant thermal conductive principles were identified from the simulated thermal flux evolution. Some deficiencies of these analytical models are identified and amended by reconsidering their special architectures. This work is favorable for establishing a general and quantitative relationship between the effective thermal conductivity and microstructures for most of the synthesized LMFEs available in the literatures.

Extendable origami multilayer insulation thermal characterization

Spacecraft commonly use multilayer insulation (MLI) for passive thermal control, however deployable structures such as telescoping booms impose the need to stow MLI preflight and extend with the structure for in flight operation. This paper investigates an octagonal origami folding pattern that allows predictable stowage and extension of multilayer insulation. Feasibility was demonstrated to fold, compress and extend a MLI blanket comprising 10 layers of aluminized Kapton, each separated by a layer of scrim cloth. Both folded and unfolded 10-layer MLI blankets were tested in thermal vacuum to characterize heat leak of deployed configurations. The 10-layer origami folded configuration increased thermal conductance and radiative heat transport relative to the unfolded configuration. Degradation factors for heat transport were empirically found to be Mk=2.5±0.3 and Me=1.3±0.2 for effective thermal conductance and emittance, respectively.

Capacity Building of Thermal Conductivity in Polymers and Their Composites: A Short Review of the Effect of Various Fillers in Their Composites

In industries like automotive, packaging, structural, electrical, and energy harvesting, polymers and polymer composites have been the preferred material due to their lightweight and long-lasting applications. They are potential replacements for the metal structures used in communication devices, microelectronics, electric vehicles, and generators due to their adaptability and flexibility. However, most of the polymers are not thermal conductors and it difficult to use them in application such as high-performance computing systems, aerospace and electronics. The capacity building of thermal conductivity in the polymers and their composites are current objectives in various applications as compared with metals due to the many advantages of polymers; viz. corrosion resistance and ease of processing. Our study of the literature, as described, here outlines three main features, (a) Various fillers in polymer composites play important roles in the effective thermal conductivity, (b) the effect of filler percentage in thermal conductivity, and (c) various processing method and their effect on the thermal conductivity. This review was aimed to benefit the recent trend of industrial requirements and to highlight the fillers used in polymer composites for various applications.

The relationship between thermal management methods and hydrogen storage performance of the metal hydride tank

Solid-state hydrogen storage tanks are key equipment for fuel cell vehicles and hydrogen storage. However, the low heat transfer properties of hydrogen storage tanks result in the inability to meet the hydrogen supply requirements of fuel cells. In this study, different thermal management approaches were explored through the design of LaNi5-based solid-state hydrogen storage tanks. We experimentally studied the effects of different internal heat transfer methods, that is, expanded natural graphite (ENG), copper foam, and copper fins on the hydrogen absorption and desorption performance. We also studied the effects of external cooling methods with natural convection, air cooling, and water cooling, respectively. Under the same external cooling method of natural convection, a solid hydrogen storage tank filled with 5 wt.% ENG has similar performance to a tank filled with copper foam. Compared to natural convection, air and water cooling can significantly improve the heating performance of metal hydride (MH) beds by increasing the external heat transfer coefficient. The effect of water cooling is better than that of air cooling, and in these two enhanced performance conditions, the tank filled with copper foam performs better than with ENG. In the case of water cooling, by adding copper fins to a hydrogen storage tank filled with 5 wt.% ENG, the tank was saturated with hydrogen absorption in only 29.4 min, which is 55.6 % shorter than the hydrogen uptake time in a hydrogen storage reactor without copper fins. And its stable hydrogen desorption (1 NL/min) has reached 98.1 % of the total hydrogen released. The results show that the effective thermal conductivity and heat transfer area of metal hydride bed play key roles in improving heat transfer and reaction rate. In addition, heat transfer is more important than mass transfer to improve the performance of the hydrogen storage tank.

Computational Requirements for Modeling Thermal Conduction in Polymeric Phase-Change Materials: Periodic Hard Spheres Case.

This research focuses on modeling heat transfer in heterogeneous media composed of stacked spheres of paraffin as a perspective polymeric phase-change material. The main goal is to study the requirements of the numerical scheme to correctly predict the thermal conductivity in a periodic system composed of an indefinitely repeated configuration of spherical particles subjected to a temperature gradient. Based on OpenFOAM, a simulation platform is created with which the resolution requirements for accurate heat transfer predictions were inferred systematically. The approach is illustrated for unit cells containing either a single sphere or a configuration of two spheres. Asymptotic convergence rates confirming the second-order accuracy of the method are established in case the grid is fine enough to have eight or more grid cells covering the distance of the diameter of a sphere. Configurations with two spheres can be created in which small gaps remain between these spheres. It was found that even the under-resolution of these small gaps does not yield inaccurate numerical solutions for the temperature field in the domain, as long as one adheres to using eight or more grid cells per sphere diameter. Overlapping and (barely) touching spheres in a configuration can be simulated with high fidelity and realistic computing costs. This study further extends to examine the effective thermal conductivity of the unit cell, particularly focusing on the volume fraction of paraffin in cases with unit cells containing a single sphere. Finally, we explore the dependence of the effective thermal conductivity for unit cells containing two spheres at different distances between them.

Modelling effective thermal conductivity in polymer composites: A simple cubic structure approach

In this study, we propose the simple cubic model, a distinctive thermal-conductive mathematics for modelling the effective thermal conductivity in polymer composites, taking both filler size and interface thermal resistance into account. This model is constructed by delineating heat transport paths within simple cubic structural units, leveraging principles involving Fourier's law, minimum thermal resistance, specific equivalent thermal conductivity, and thermal resistance network. Demonstrating broad applicability, the simple cubic model accurately predicts effective thermal conductivity within a 0–40 % volume fraction range of filler in polymer composites, maintaining less than 15 % error. Its robustness is validated across over 100 experimental datasets, encompassing various polymer matrices and granular filler types. This extensive validation underscores the model's efficacy, both with our experimental data and existing literature. The simple cubic model's insightful predictions make it valuable in designing and preparing thermally conductive polymer composites.