Evaluation Of Effective Thermal Conductivity Research Articles

Evaluation of effective thermal conductivity of sintered porous materials using an improved discrete element model

This work aims to revise and apply an original discrete element model (DEM) to evaluate effective thermal conductivity of sintered porous materials. The model, based on two-particle sintering geometry, calculates inter-particle neck using Constant Volume (CV) criterion. The model was validated using experimental measurements on sintered porous NiAl. For DEM simulations, heterogeneous samples with real particle size distribution and different densities were obtained by simulation of hot pressing. Neck size evaluated using Coble’s and CV models were compared to show that commonly used Coble’s model overestimates neck size and conductivity. The proposed model was improved by neck-size correction to compensate for non-physical overlaps at higher densities and by adding grain-boundary resistance to account for porosity within necks. Resistance contribution from grain boundaries was shown to decrease with increasing density. Thermal conductivity obtained from the improved model was close to experimental results, suggesting validity of the model.

Evaluation of Effective Thermal Conductivity by 2d Image Simulation And The Effect of Orientation of Copper-Plated Carbon Fiber on Effective Thermal Conductivity of Fe-Based Composites

Evaluation of Effective Thermal Conductivity by 2d Image Simulation And The Effect of Orientation of Copper-Plated Carbon Fiber on Effective Thermal Conductivity of Fe-Based Composites

Evaluation of Effective Thermal Conductivity of Graphite Flake/Aluminum Composites by Two-Dimensional Image Simulation under a Correction Function

Evaluation of Effective Thermal Conductivity of Graphite Flake/Aluminum Composites by Two-Dimensional Image Simulation under a Correction Function

Image-based method for evaluation of effective thermal conductivity of metal foam with hollow ligaments

A feature preserving image-based method was used to estimate the effective thermal conductivity of copper metal foam having hollow ligaments. Hollow portions of the ligament and node were identified from X-ray computed microtomography images, through image processing. The effective thermal conductivity was estimated for foams with hollow ligaments filled with water, air, or vacuum. The fluid filling the pore was considered as water or air. Estimations were also conducted for the case where the metal foam is kept in a vacuum condition, where the heat transfer happens only through the ligaments and nodes. The effective thermal conductivity of metal foam with hollow ligaments was compared with that of metal foams with solid ligaments, maintaining the same ligament cross-sectional area. Two metal foams, having total porosity of 90.8% and 90% and hollowness of 4.45% and 1.65% respectively, were selected for the study. The effective thermal conductivity values obtained were compared with the analytical and empirical models available in the literature. Microtomography-based computational fluid dynamics study was also conducted based on the three-dimensional replica of the metal foam, generated from the two-dimensional tomography images. The thermal conductivity obtained from the computational microtomography based study and the image-based method was found to be in good agreement.

Lattice Boltzmann simulation and fractal analysis of effective thermal conductivity in porous media

Heat transfer in porous media has been attracting wide attention in a variety of scientific researches and engineering applications over the past decades. Due to the complexity of pore-solid microstructural features, an accurate simulation of heat transport process and evaluation of effective thermal conductivity in saturated porous media remain a great challenge. In this work, the lattice Boltzmann method (LBM) simulation of fluid-solid coupling heat transfer and a fractal model are adopted to study the thermal transport property in three-dimensional porous media. The accuracy and reliability of the proposed LBM model is validated by the effective thermal conductivity of a straight capillary tube, which analytical solution is available. The relation between effective thermal conductivity in porous media with different geometrical parameters based on the LBM simulation and fractal model are analyzed and discussed extensively. The result shows that the proposed LBM fluid-solid coupling simulation is an efficient tool to describe the heat transfer in complex porous media and the fractal dimension not only has an important effect on accurately estimating the effective thermal conductivity but also may be a useful parameter to determine the representative elemental volume of porous media. It is also found that compared with LBM simulation, the fractal model over predicates and the Maxwell model under predicates the effective thermal conductivity. The proposed LBM model and fractal model may reveal a better understanding for the thermophysical mechanisms of heat transfer in porous media.

A generalized thermal conductivity model for unsaturated porous media with fractal geometry

Evaluation of effective thermal conductivity (ETC) of unsaturated porous media is significant for many engineering applications and thus has received growing attention in multi-disciplinary fields. However, the existing models for ETC cannot realistically account for the complex pore structures and generally contain empirical parameters. In this study, fractal dimensions for pore size distribution and capillary tortuosity are introduced to characterize the pore-scale structure. A generalized model for ETC of unsaturated porous media is developed based on thermal-electrical analogy. The proposed fractal model has been validated by comparing with available experimental data. The results show that ETC of unsaturated porous media increases with the increase of liquid saturation as the thermal conductivity of solid and liquid phases are larger than that of gas phase. However, ETC is inversely proportional to liquid saturation as the thermal conductivity of solid and liquid phases are smaller than that of gas phase. The pore structures indicate significant effect on ETC of unsaturated porous media. ETC gradually decreases with the increment of porosity and pore fractal dimension as well as tortuosity fractal dimension. All the parameters in the proposed ETC model have specific physical meanings, and it may capture the microstructure characteristics and help understanding the heat transfer mechanisms of unsaturated porous media.

ANALYTICAL MODEL FOR PREDICTION OF EFFECTIVE THERMAL CONDUCTIVITY OF A THREE-PHASE SYSTEM: NANOPARTICLE AS THE THIRD PHASE

The thermal design of various engineering applications plays a prominent role in deciding the overall efficiency of the system. Nowadays, nanofluids have attracted the interest of researchers due to their excellent thermophysical properties. There were several researches emphasising the importance of two-phase materials and nanofluids in the effective thermal design, but none have attempted to integrate both for analyzing their combined potential thermal benefits. This research paper is aimed at formulation of the general analytical expression using the unit cell approach for the evaluation of effective thermal conductivity (ETC) of two-phase system which is comprised of solid and liquid with nanoparticles as a third phase dispersed in the liquid phase (so called nanofluids). The expressions are evaluated for different samples (packed beds and foams dispersed in nanofluid) and compared with the experimental results of conventional two-phase system. The combined effects of influencing parameters on two-phase materials with the static and dynamic mechanisms of nanofluids have been studied and validated with the standard models. The present model is better suit for predicting ETC of two-phase system in different combinations with nanofluids.

Effect of the second outlet location and the applied magnetic field within a ventilated cubic cavity crossed by a nanofluid on mixed convection mode: best configurations

The present numerical study consists of a mixed convection heat transfer, taking place within a ventilated cubic cavity crossed by an alumina–water nanofluid. The ventilation is assured by three openings, practiced on the walls of the cavity. So, the cold nanofluid enters by an opening placed at the top of the left vertical wall and exits by two opening: one is placed at the bottom of the right vertical wall, and the second opening occupied several possibility of location along the four walls of the cavity. All the enclosure’s walls are maintained at a same temperature, higher than that of the entering fluid, except of the side walls which are adiabatic. The governing equations are discretized using the finite volume method and the SIMPLER algorithm to treat the coupling velocity–pressure. The method line by line is used to solve iteratively the algebraic equations. The simulations were carried for different values of the Richardson number (0 ≼ Ri ≼ 10), the Hartmann number (0 ≼ Ha ≼ 100) and a solid volume fractions φ = 4% using Koo–Kleinstreuer–Lee model for the evaluation of effective thermal conductivity and dynamic viscosity of nanofluid. The results are presented in the form of streamlines, isotherms, velocity vectors and average Nusselt number.

Evaluation of effective thermal conductivity in random packed bed: Heat transfer through fluid voids and effect of packing structure

Effective thermal conductivity (ETC) is an important parameter in packed-bed systems and is affected significantly by packing structure. Heat flow through a packed bed can be divided into three parallel paths: the solid-fluid-solid path, the solid-solid path and the fluid path. The models to evaluate ETC in packed beds for the first two paths were previously developed. In the present work, a comprehensive model to consider the heat transfer through the voids of a randomly-packed bed is further developed using the Delaunay tessellation. The results show that heat conduction through the fluid-filled voids becomes significant when the solid-to-fluid conductivity ratio decreases to a certain level (<5). The effect of packing structure on the ETC of packed beds is then investigated based on the packing generated by the discrete element method (DEM). Four cases with different heat transfer mechanisms or paths are considered. The results indicate that the probability density distribution of heat flow is generally dependent on the packing structure, represented by porosity. With an increase in porosity, the heat conduction and radiation via the solid path decrease, while the heat conduction via the fluid-filled voids increases.

Reliable estimation of effective thermal properties of a 2-phase material by its optimized modelling in view of Lattice Monte-Carlo simulation

A correct strategy for evaluation of the effective thermal diffusivity, and, similarly, for the evaluation of effective thermal conductivity of composite materials by Lattice Monte-Carlo (LMC) approach should consider two parameters: one related to a good description of inclusions, the other related to the number of inclusions or material region investigated. The good description of inclusion can be obtained when its size is larger than 30 grid nodes. The selection of square lattice length higher than 5 times the inclusion size, Normalized Effective Thermal Conductivity (NETC) is independent on lattice length selection. Under optimized conditions, calculated NETC becomes practically independent on inclusion size and lattice length. The LMC simulation can be applied to real material, which description as 2-phase lattice can be optimized in terms of representative area (via a proper magnification for micrographs and of the number of nodes of the lattice length).

A new three-dimensional finite-volume model for evaluation of thermal conductivity of periodic multiphase composites

This paper proposes a three-dimensional micromechanical model for evaluation of effective thermal conductivity of multiphase composite materials with periodic microstructure. The model consists in an extension of the parametric finite-volume theory which has demonstrated to be a promising tool for the analysis and homogenization of multiphase heterogeneous solids. The applicability and performance of the proposed formulation are examined through the solutions of different numerical examples of two- and three-phase composites. Such examples consist of composites reinforced with unidirectional solid and hollow long fibers and aligned short fibers. In order to verify the effectiveness of the model, its predictions are compared with analytical and finite-element results, as well as experimental data. The results indicate that the proposed model is efficient and accurate in predicting the effective thermal conductivity of periodic composites and can be seen as a competitive alternative to other existing procedures based on traditional numerical tools like the finite element method.

A semi-analytical model for evaluation of effective thermal conductivity of composites with periodic microstructure

This paper presents a semi-analytical micromechanical model for evaluation of effective thermal conductivity of composite materials with periodic microstructure. The model is based on the equivalent inclusion thermal problem and utilizes Fourier series for representation of periodic functions involved in the material homogenization approach. Two main objectives can be highlighted in the work. The first of them is the derivation of the thermal micromechanical model, which consists in an extension of a formulation originally derived for homogenization of elastic heterogeneous solids. The second objective consists in a detailed investigation on the performance of the model, considering convergence of results and efficiency of strategies employed for the approximate solution of the thermal homogenization problem. Analyses on the complexity of transformation temperature gradient functions are also included in this investigation. The results obtained for two examples of periodic composites with different microstructural architectures are presented and discussed in detail.

Evaluation of Effective Thermal Conductivity of Metal Matrix Composites by Using Image-Based Calculation

Interfacial thermal resistance in Al-SiC composites was evaluated by comparing the measured thermal conductivity and the calculated thermal conductivity. Al-20vol.%SiC composites changing SiC particle size, 3 μm to 30 μm, was fabricated by spark plasma sintering and heat treatment. Effective thermal conductivity was measured with the steady state thermal conductivity measuring device. Effective thermal conductivity was also calculated by using SEM image and the measured relative density. Comparing the measured thermal conductivity and the calculated thermal conductivity, interfacial thermal resistance in Al-SiC composites was evaluated as about 1.0x10-8 (m2K)/W.

A DEM-based heat transfer model for the evaluation of effective thermal conductivity of packed beds filled with stagnant fluid: Thermal contact theory and numerical simulation

The Effective thermal conductivity (keff) is one of the key thermal properties for packed beds in the presence of a stagnant fluid. In this study, a thermal discrete element model (DEM) based on the original Cheng-Yu-Zulli analytical model for mono-sized packed beds has been improved and implemented especially for mixed beds of different particle sizes or materials. In order to perform the DEM simulation for packed beds, a thermal contact theory considering three heat transfer mechanisms (solid contact conduction, solid-fluid-solid conduction and radiation) was derived and applied in the network of Voronoi cells obtained by radical Voronoi tessellation of the relevant beds. The numerical model was validated through a comparison with experimental results already reported in literature and a good prediction for the effective thermal conductivity was obtained for both mono-sized and multi-sized packed beds in a wide range of solid-to-fluid conductivity ratio. The model also showed a good performance to study the heat flow distribution as well as the coupled thermo-mechanical behavior of packed beds.

Image-based numerical prediction for effective thermal conductivity of heterogeneous materials: A quadtree based scaled boundary finite element method

Integrating advantages of the quadtree technique, the SBFEM, the image-based modelling approach, and inverse analysis, a new numerical technique is presented for the evaluation of Effective Thermal Conductivity (ETC) of heterogeneous materials. The quadtree technique provides a convenient way for mesh generation, and facilitates to image-based analysis. The inconvenience of hanging nodes caused in the quadtree mesh generation can be naturally avoided by SBFEM, consequently the temperature solutions of heterogeneous materials can be determined by the combination of quadtree technique and SBFEM, and are partially regarded as ‘experiments values’ for equivalent homogeneous materials. Utilizing a group of such ‘experiments’, the ETC can be obtained by solving a group of inverse heat transfer problems of parameters identification. Numerical examples are provided to demonstrate the effectiveness of the proposed approach, and the impacts of distributions and shapes of inclusions, and volume fractions are taken into account.

Numerical simulation of MHD mixed convection in alumina–water nanofluid filled square porous cavity using KKL model: Effects of non-linear thermal radiation and inclined magnetic field

This study examines the influence of non-linear thermal radiation and inclined magnetic field on mixed convection in a square porous cavity. Here, the cavity is saturated with alumina–water nanofluid. Darcy-Brinkman-Forchheimer-extended model has been adopted to formulate governing differential equations. After transforming equations to dimensionless form, these are solved by utilizing weighted residual Galerkin finite element method. Latest Koo-Kleinstreuer-Lee (KKL) model is employed for the evaluation of effective thermal conductivity and dynamic viscosity of nanofluid. Effect of pertinent parameters in specific ranges such as Richardson number (0.01 ≤ Ri ≤ 100), radiation parameter (0 ≤ Rd ≤ 5), temperature ratio parameter (1.1 ≤ Nr ≤ 1.4), inclined magnetic field parameter (0°≤ γ ≤ 90°), Darcy number (10−6 ≤ Da ≤ 10−3), porosity parameter (0.2 ≤ ϵ ≤ 0.8) and volume fraction of solid particles (0 ≤ ϕ ≤ 0.04) has been studied and presented in the form of streamlines, isotherms and plots. Moreover, kinetic energy and average temperature have also been taken into account for better understanding the flow philosophy. It is found that radiation parameter, temperature ratio parameter, Darcy number and porosity parameter augment heat transfer, kinetic energy and average temperature while inclined magnetic field parameter in selected aforementioned range declines heat transfer due to hot bottom wall.

Evaluation of effective thermal conductivity of unsaturated granular materials using random network model

The effective thermal conductivity of granular materials is widely used in numerous geothermal engineering applications, such as the ground source heat pump (GSHP) system. However, for unsaturated granular materials, it is difficult to predict the thermal conductivity because of the interaction between solid and fluid in media. In this study, the effective thermal conductivity of unsaturated granular materials was measured, reviewed and analysed using a macroscopic pore structure network model with a randomly packed particles. The network model was verified by measured data (soil water characteristics curve, thermal conductivity and etc.) of three different glass beads and also Jumunjin sand (standard sand of South Korea). Upon the series of laboratory experiments, some modification to the existing network model were introduced, such as the use of soil water characteristic curve (SWCC) applied to modelling the thermal conductivity of granular materials. In addition, an empirical correlation between the fraction of the mean radius (χ) and the thermal conductivity at a given saturated condition was developed through comparison with the test results. In the range of lower degree of saturation (5%–20%), the modified network model shows relatively higher thermal conductivity than the laboratory measurements. However, for the higher degree of saturation (>40%), it shows a similar tendency to the laboratory measurements.

Modeling of granular packed beds, their statistical analyses and evaluation of effective thermal conductivity

Thermal conductivity of packed beds plays the key role in the emerging technologies of selective laser melting/sintering. The objective is to study the influence of the packed bed structure on the contact thermal conductivity. The discrete (network) model of the contact thermal conductivity in the packed particle layer is proposed. The task of heat transfer due to the contact thermal conductivity of the system of parallel the located cylinders with the fixed thermal resistance of the contact is solved in the 2D case. The 3D-task on the heat transfer through the layer of spherical particles of finite thickness in between heated solid massive bodies with constant and different temperatures is solved. In the calculations, the package structures were varied: the regular (with the cubic symmetry), random (with the mono- and poly-disperse particles), as well as the porosity and mean coordination number. The effective thermal conductivity coefficient was evaluated as the packed bed structure, the mean porosity, and coordination number were varied. The calculation results agree with the known analytical solutions. The statistical analysis of regular and packed beds of solid spheres is presented.

Prediction of the effective thermal conductivity of packed bed with micro-particles for thermochemical heat storage

The heat transfer property of the powder bed greatly affects the performance of a thermochemical heat storage system. Therefore, an accurate evaluation of effective thermal conductivity (ETC) is a key for developing thermochemical heat storage systems. This paper focuses on the ETCs of commonly used porous thermochemical materials, such as MgO/Mg(OH)2 and CaO/Ca(OH)2 powders, as well as the corresponding composites with embedded metal foams. Random sphere-like particles packing (RSPP) method is proposed to reconstruct the microstructures of the powder and micro-scale generation method and computed tomography are adopted for the metal foams. Energy transport equations through porous media are solved by the lattice Boltzmann method (LBM) to obtain ETC. Results obtained using RSPP-LBM method agree with experimental data better than other existing methods. For thermochemical heat storage, the variation of ETC during chemical reactions is numerically predicted. Metal foam-embedded thermochemical materials are also studied to evaluate the enhancing effects of the metal foams. Results show that ETC of the powders is dominated by the gas phase, whereas that of the metal foam composites is dominated by the metal phase.

Evaluation of effective thermal conductivity of basalt-fiber reinforced composite material by the method of stationary thermal mode

Evaluation of effective thermal conductivity of basalt-fiber reinforced composite material by the method of stationary thermal mode