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

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 low, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, prediction of 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 a cross-aligned and cubic pore model(CACPM) based on the actual pore arrangement of SiO_(2) aerogel. Based on the established CACPM, the effective thermal conductivity expression for the 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 = 298 K, a_(2)= 0.85, D_(1)= 90 μm, ρ = 128 kg/m^(3), within the pressure range of 0–10^(5)Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 10^(3)–10^(4)Pa, 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 models and calculation formulae.

Two-step homogenization for the effective thermal conductivities of twisted multi-filamentary superconducting strand

For the accurate prediction of the effective thermal conductivities of the twisted multi-filamentary superconducting strand,a two-step homogenization method is adopted.Based on the distribution of filaments,the superconducting strand can be decomposed into a set of concentric cylinder layers.Each layer is a two-phase composite composed of the twisted filaments and copper matrix.In the first step of homogenization,the representative volume element(RVE)based finite element(FE)homogenization method with the periodic boundary condition(PBC)is adopted to evaluate the effective thermal conductivities of each layer.In the second step of homogenization,the generalized self-consistent method is used to obtain the effective thermal conductivities of all the concentric cylinder layers.The accuracy of the developed model is validated by comparing with the local and full-field FE simulation.Finally,the effects of the twist pitch on the effective thermal conductivities of twisted multi-filamentary superconducting strand are studied.

Effects of Substrate Temperature on Properties for Transparent Conducting ZnO:A1 Films on Organic Substrate Deposited by r.f. Sputtering

This paper presents the substrate temperature dependence of opto-electrical properties for transparent conducting Al-doped ZnO films prepared on polyisocyanate (PI) substrates by r f sputtering. Polycrystalline ZnO:Al films with good adherence to the substrates having a (002) preferred orientation have been obtained with resistivities in the range from 4.1×10-3to 5.3×104 Ωcm, carrier densities more than 2.6×1020 cm-3 and Hall mobilities between 5.78 and 13.11 cm2/V/s for films. The average transmittance reaches 75% in the visible spectrum. The quality of obtained films depends on substrate temperature during film fabrication.

A Prediction Model of Effective Thermal Conductivity for Metal Powder Bed in Additive Manufacturing

In current research,many researchers propose analytical expressions for calculating the packing structure of spherical particles such as DN Model,Compact Model and NLS criterion et al.However,there is still a question that has not been well explained yet.That is:What is the core factors affecting the thermal conductivity of particles?In this paper,based on the coupled discrete element-finite difference(DE-FD)method and spherical aluminum powder,the relationship between the parameters and the thermal conductivity of the powder(ETC_(p))is studied.It is found that the key factor that can described the change trend of ETC_(p) more accurately is not the materials of the powder but the average contact area between particles(a_(ave))which also have a close nonlinear relationship with the average particle size d_(50).Based on this results,the expression for calculating the ETC_(p) of the sphere metal powder is successfully reduced to only one main parameter d_(50)and an efficient calculation model is proposed which can applicate both in room and high temperature and the corresponding error is less than 20.9%in room temperature.Therefore,in this study,based on the core factors analyzation,a fast calculation model of ETC_(p) is proposed,which has a certain guiding significance in the field of thermal field simulation.

Study of the generalized mixture rule for determining effective conductivity of two-phase stochastic models

The generalized mixture rule （GMR） is usually applied in determining mechanical properties such as the rheological property and Young’s modulus of multi-phase rocks. However, it is rarely used to determine electrical conductivity of multi-phase rocks presently. In this paper, we calculate the effective conductivity using the 3D finite element method for a large number of two-phase medium stochastic models. The GMR is then employed as an effective conductivity model to fit the data. It shows a very close relationship between the parameter J of GMR and the ratio of conductivities of the two phases. We obtain the equations of the parameter J with the ratio of conductivity of two phases for the first time. On this basis, we can quickly predict （or calculate） the effective conductivity of any twophase medium stochastic model. The result is much more accurate than two other available effective conductivity models for the stochastic medium, which are the random model and effective medium theory model, laying a solid base for detailed evaluation of oil reservoirs.

A Novel Approach for the Effective Thermal Conductivity of Porous Ceramics

A new approach in combination of the effective medium theory with the equivalent unit in numerical simulation was developed to study the effective thermal conductivity of porous ceramics. The finite element method was used to simulate the heat transfer process which enables to acquire accurate results through highly complicated modeling and intensive computation. An alternative approach to mesh the material into small cells was also presented. The effective medium theory accounts for the effective thermal conductivity of cells while the equivalent unit is subsequently applied in numerical simulation to analyze the effective thermal conductivity of the porous ceramics. A new expression for the effective thermal conductivity, allowing for some structure factors such as volume fraction of pores and thermal conductivity, was put forward, and the results of its application was proved to be close to those of the mathematical simulation.

Random checkerboard based homogenization for estimating effective thermal conductivity of fully saturated soils

This paper proposes homogenization scheme for estimating the effective thermal conductivity of fully saturated soils. This approach is based on the random checkerboard-like microstructure. Two modeling scales and two modeling approaches are distinguished and used, i.e. microscale and mesoscale and 1-step and 2-step homogenizations, respectively. The 2-step homogenization involves sequential averaging procedure, i.e. first, at microscale, a mineralogical composition of soil skeleton is considered and averaging process results in estimation of the skeleton effective thermal conductivity, and then, at mesoscale, a random spatial packing of solid skeleton and pores via random checkerboard microstructure is modeled and leads to evaluation of the soil overall thermal conductivity. The 1-step homogenization starts directly at the mesoscale and homogenization procedure yields evaluation of the overall soil thermal conductivity. At the mesoscale, the distinct nature of soil skeleton, as composed of soil separates,is considered and random variability of soil is modeled via enriched random checkerboard-like structure.Both approaches, i.e. 1-step and 2-step homogenizations, interrelate mineralogical composition with the soil texture characterized by the volume fractions of soil separates, i.e. sand, silt and clay. The probability density functions(PDFs) of thermal conductivity are assumed for each of the separates. The soil texture PDF of thermal conductivity is derived taking into consideration the aforementioned functions. Whenever the random checkerboard-like structure is used in averaging process, the Monte Carlo procedure is applied for estimation of homogenized thermal conductivity. Finally, the proposed methodology is tested against the laboratory data from our measurements as well as those available from literature.

Conductivity effects during the transition from collisionless to collisional regimes in cylindrical inductively coupled plasmas

A numerical model is developed to study the conductivity effects during the transition from collisionless to collisional regimes in cylindrical inductively coupled argon plasmas at pressures of 0.1-20 Pa.The model consists of electron kinetics module,electromagnetics module,and global model module.It allows for self-consistent description of non-local electron kinetics and collisionless electron heating in terms of the conductivity of homogeneous hot plasma.Simulation results for non-local conductivity case are compared with predictions for the assumption of local conductivity case.Electron densities and effective electron temperatures under non-local and local conductivities show obvious differences at relatively low pressures.As increasing pressure,the results under the two cases of conductivities tend to converge,which indicates the transition from collisionless to collisional regimes.At relatively low pressures the local negative power absorption is predicted by non-local conductivity case but not captured by local conductivity case.The two-dimensional(2D)profiles of electron current density and electric field are coincident for local conductivity case in the pressure range of interest,but it roughly holds true for non-local conductivity case at very high pressure.In addition,an effective conductivity with consideration of non-collisional stochastic heating effect is introduced.The effective conductivity almost reproduces the electron density and effective electron temperature for the non-local conductivity case,but does not capture the non-local relation between electron current and electric field as well as the local negative power absorption that is observed for nonlocal conductivity case at low pressures.

Thermal performance analysis of borehole size effect on geothermal heat exchanger

Thermal performance was the most important factor in the development of borehole heat exchanger utilizing geothermal energy. The thermal performance was affected by many different design parameters, such as configuration type and borehole size of geothermal heat exchanger. These eventually determined the operation and cost efficiency of the geothermal heat exchanger system. The main purpose of this work was to assess the thermal performance of geother^nal heat exchanger with variation of borehole sizes and numbers of U-tubes inside a borehole. For this, a thermal response test rig was established with line-source theory. The thermal response test was performed with in-line variable input heat source. Effective thermal conductivity and thermal resistance were obtained from the measured data. From the measurement, the effective thermal conductivity is found to have similar values for two- pair type （4 U-tubes） and three-pair type （6 U-tubes） borehole heat exchanger systems indicating similar heat transfer ability. Meanwhile, the thermal resistance shows lower value for the three-pair type compared to the two-pair type. Measured data based resistance have lower value compared to computed result from design programs. Overall comparison finds better thermal performance for the three-pair type, however, fluctuating temperature variation indicates complex flow behavior inside the borehole and requires further study on flow characteristics.

Effects of lime treatment on the microstructure and hydraulic conductivity of Héricourt clay

This study aims at evidencing the effects of lime treatment on the microstructure and hydraulic conductivityof a compacted expansive clay, with emphasis put on the effect of lime hydration and modification.For this purpose, evolutions of hydraulic conductivity were investigated for both lime-treatedand untreated soil specimens over 7 d after full saturation of the specimens and their microstructureswere observed at the end. Note that for the treated specimen, dry clay powder was mixed with quicklimeprior to compaction in order to study the effect of lime hydration. It is observed that lime hydration andmodification did not affect the intra-aggregate pores but increased the inter-aggregates pores size. Thisincrease gave rise to an increase of hydraulic conductivity. More precisely, the hydraulic conductivity oflime-treated specimen increased progressively during the first 3 d of modification phase and stabilisedduring the next 4 d which correspond to a short period prior to the stabilisation phase. The microstructureobservation showed that stabilisation reactions took place after 7 d. Under the effect of stabilisation,a decreasing hydraulic conductivity can be expected in longer time due to the formation ofcementitious compounds. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A Fractal Model for the Effective Thermal Conductivity of Granular Flow with Non—uniform Particles

The equipartition of energy applied in binary mixture of granular flow is extended to granular flow withnon-uniform particles. Based on the fractal characteristic of granular flow with non-uniform particles as well as energyequipartition, a fractal velocity distribution function and a fractal model of effective thermal conductivity are derived.Thermal conduction resulted from motions of particles in the granular flow, as well as the effect of fractal dimension oneffective thermal conductivity, is discussed.

A THEORY OF EFFECTIVE THERMAL CONDUCTIVITY FOR MATRIX-INCLUSION-MICROCRACK THREE-PHASE HETEROGENEOUS MATERIALS BASED ON MICROMECHANICS

The effective thermal conductivity of matrix-inclusion-microcrack three-phase heterogeneous materials is investigated with a self-consistent micromechanical method (SCM) and a random microstructure finite element method(RMFEM). In the SCM, microcracks are assumed to be randomly distributed and penny-shaped and inclusions to be spherical, the crack effect is accounted for by introducing a crack density parameter, the effective thermal conductivity is derived which relates the macroscopic behavior to the crack density parameter. In the RMFEM, the highly irregular microstructure of the heterogeneous media is accurately described, the interaction among the matrix-inclusion-microcracks is exactly treated, the inclusion shape effect and crack size effect are considered. A Ni/ZrO2 particulate composite material containing randomly distributed, penny-shaped cracks is examined as an example. The main results obtained are: (1) the effective thermal conductivity is sensitive to the crack density and exhibits essentially a linear relationship with the density parameter: (2) the inclusion shape has a significant effect on the effective thermal conductivity and a polygon-shaped inclusion is more effective in increasing or decreasing the effective thermal conductivity than a sphere-shaped one; and (3) the SCM and RMFEM are compared and the two methods give the same effective property in the case in which the matrix thermal conductivity A, is greater than the inclusion one lambda(2). In the inverse case of lambda(1) < lambda(2), the two methods as the as the inclusion volume fraction and crack density are low and differ as they are high. A reasonable explanation for the agreement and deviation between the two methods in the case of lambda(1) < lambda(2) is made.

Effects of Metal Absorber Thermal Conductivity on Clear Plastic Laser Transmission Welding

In our previous study, metals have been used as absorbers in the clear plastic laser transmission welding. The effects of metal thermal conductivity on the welding quality are investigated in the present work. Four metals with distinctly different thermal conductivities, i.e., titanium, nickel, molybdenum, and copper, are selected as light absorbers. The lap welding is conducted with an 808 nm diode laser and simulation experiments are also conducted. Nickel electroplating test is carried out to minimize the side-effects from different light absorptivities of different metals. The results show that the welding with an absorber of higher thermal conductivity can accommodate higher laser input power before smoking, which produces a wider and stronger welding seam.The positive role of the higher thermal conductivity can be attributed to the fact that a desirable thermal field distribution for the molecular diffusion and entanglement is produced from the case with a high thermal conductivity.

Numerical Predictions of the Effective Thermal Conductivity of the Rigid Polyurethane Foam

A reconstruction method is proposed for the polyurethane foam and then a complete numerical method is developed to predict the effective thermal conductivity of the polyurethane foam. The finite volume method is applied to solve the 2D heterogeneous pure conduction. The lattice Boltzmann method is adopted to solve the 1D homogenous radiative transfer equation rather than Rosseland approximation equation. The lattice Boltzmann method is then adopted to solve 1D homogeneous conduction-radiation energy transport equation considering the combined effect of conduction and radiation. To validate the accuracy of the present method, the hot disk method is adopted to measure the effective thermal conductivity of the polyurethane foams at different temperature. The numerical results agree well with the experimental data. Then, the influences of temperature, porosity and cell size on the effective thermal conductivity of the polyurethane foam are investigated. The results show that the effective thermal conductivity of the polyurethane foams increases with temperature; and the effective thermal conductivity of the polyurethane foams decreases with increasing porosity while increases with the cell size.

Analytical design of effective thermal conductivity for fluid-saturated prismatic cellular metal honeycombs

A comparative optimal design of fluid-saturated prismatic cellular metal honeycombs （PCMHs） having different cell shapes is presented for thermal management applications. Based on the periodic topology of each PCMH, a unit cell （UC） for thermal transport analysis was selected to calculate its effective thermal conductivity. Without introducing any empirical coefficient, we modified and extended the analytical model of parallel-series thermal-electric network to a wider porosity range （0.7 ~ 0.98） by considering the effects of two-dimensional local heat conduction in solid ligaments inside each UC. Good agreement was achieved between analytical predictions and numerical simulations based on the method of finite volume. The concept of ligament heat conduction efficiency （LTCE） was proposed to physically explain the mechanisms underlying the effects of ligament configuration on effective thermal conductivity （ETC）. Based upon the proposed theory, a construct strategy was developed for designing the ETC by altering the equivalent interaction angle with the direction of heat flow： relatively small average interaction angle for thermal conduction and relatively large one for thermal insulation.

Effective Thermal Conductivity with Convection and Radiation in Packed Bed

Effective thermal conductivity with convection and radiation is analyzed by the homogenization method. This method can precisely represent the microstructure of a packed bed. In this study, the effects of parameters such as the radiation emissivity, temperature, contact area and particle size of the packed bed on the conductivity have been estimated. For example, heat transfer by radiation does not dominate if the material has voids of less than l mm in size. Moreover, the effects of contact area and pressure on effective thermal conductivity are negligible for thermal radiation. By considering the microscopic behavior of a packed bed, the homogenization method is thus a powerful tool for estimating the bed＇s effective thermal conductivity.

Effective thermal conductivity of wire-woven bulk Kagome sandwich panels

Thermal transport in a highly porous metallic wire-woven bulk Kagome （WBK） is numerically and analytically modeled. Based on topology similarity and upon introducing an elongation parameter in thermal tortuosity, an idealized Kagome with non-twisted struts is employed. Special focus is placed upon quanti- fying the effect of topological anisotropy of WBK upon its effective conductivity. It is demonstrated that the effective conductivity reduces linearly as the poros- ity increases, and the extent of the reduction is significantly dependent on the orientation of WBK. The governing physical mechanism of anisotropic thermal transport in WBK is found to be the anisotropic thermal tortuosity caused by the intrinsic anisotropic topology of WBK.

Characteristic analysis of bleeding effect on standing column well (SCW) type geothermal heat exchanger

Thermal performance is the most important factor in the development of a borehole heat exchanger utilizing geothermal energy.The thermal performance is affected by many different design parameters and different operating conditions such as bleeding.This eventually determines the operation and cost efficiency of the borehole heat exchanger system.The thermal performance of an open standing column well (SCW) type geothermal heat exchanger was assessed under the influence of bleeding.For this,a thermal response test rig was established with line-source theory.The test rig also had a bleeding function by releasing fluid while taking additional underground water through the heat exchanger.The thermal response test was performed with an additional constant input heat source.Effective thermal conductivity and thermal resistance were obtained from the measured data.From the measurement,the effective thermal conductivity is found to have 1.47 times higher value when bleeding is applied.The thermal resistance also increases by 1.58 times compared to a non-bleeding case.This trend indicates enhanced heat transfer in the SCW type heat exchanger with a bleeding function.Bleeding,therefore,could be an effective method of achieving a high heat transfer rate in the SCW type heat exchanger with sufficient underground water supply.

Calculating the effective thermal conductivity of gray cast iron by using an interconnected graphite model

A new theoretical model of gray cast iron taking into account a locally interconnected structure of flake graphite was designed,and the corresponding effective thermal conductivity was calculated using the thermal resistance network method.The calculated results are obviously higher than that of the effective medium approximation assuming that graphite is distributed in isolation.It is suggested that the interconnected structure significantly enhances the overall thermal conductivity.Moreover,it is shown that high anisotropy of graphite thermal conductivity,high volume fraction of graphite,and small aspect ratio of flake graphite will cause the connectivity effects of graphite to more obviously improve the overall thermal conductivity.Higher graphite volume fraction,lower aspect ratio and higher matrix thermal conductivity are beneficial to obtain a high thermal conductivity gray cast iron.This work can provide guidance and reference for the development of high thermal conductivity gray cast iron and the design of high thermal conductivity composites with similar locally interconnected structures.

Achieving thermal magnification by using effective thermal conductivity

thermal magnification device is proposed by using effective thermal conductivity. Different fromtransformation optics method, the magnification design is realized analytically by enforcingequality of effective thermal conductivity on the magnification device and the reference case inspecified domains. The validity of theoretical analysis is checked by numerical simulation results,which demonstrates the magnifying effects of the proposed design. The device only needsisotropic and homogeneous materials that are easy to obtain in nature. It is also shown that theobtained magnifying conditions are the same as those derived by separation of variables. But theproposed method proves more flexible for multilayered materials and simpler for non-sphericalobjects under non-uniform thermal fields. It can also be extended to other fields and applicationsgoverned by Laplace equation.