Thermal conductivity of hydrate and effective thermal conductivity of hydrate-bearing sediment

The research on the thermal property of the hydrate has recently made great progress,including the understanding of hydrate thermal conductivity and effective thermal conductivity(ETC)of hydratebearing sediment.The thermal conductivity of hydrate is of great significance for the hydrate-related field,such as the natural gas hydrate exploitation and prevention of the hydrate plugging in oil or gas pipelines.In order to obtain a comprehensive understanding of the research progress of the hydrate thermal conductivity and the ETC of hydrate-bearing sediment,the literature on the studies of the thermal conductivity of hydrate and the ETC of hydrate-bearing sediment were summarized and reviewed in this study.Firstly,experimental studies of the reported measured values and the temperature dependence of the thermal conductivity of hydrate were discussed and reviewed.Secondly,the studies of the experimental measurements of the ETC of hydrate-bearing sediment and the effects of temperature,porosity,hydrate saturation,water saturation,thermal conductivity of porous medium,phase change,and other factors on the ETC of hydrate-bearing sediment were discussed and reviewed.Thirdly,the research progress of modeling on the ETC of the hydrate-bearing sediment was reviewed.The thermal conductivity determines the heat transfer capacity of the hydrate reservoir and directly affects the hydrate exploitation efficiency.Future efforts need to be devoted to obtain experimental data of the ETC of hydrate reservoirs and establish models to accurately predict the ETC of hydrate-bearing sediment.

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.

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.

Modelling seedling development using thermal effectiveness and photosynthetically active radiation

Seedling quality is a prerequisite for successful field performance and therefore influences crop yields. Temperature and illumination are two major factors affecting seedling quality during nursery propagation. Suboptimal temperature or light of nurseries generally result in leggy or weak seedlings and great economic loss. However, production of healthy seedlings is challenging due to the lack of knowledge in systemic management of nursery environments. In this study, we have established simulation models to predict how temperature and illumination coordinately influence the growth of tomato and cabbage seedlings. Specifically, correlation between seedling quality characteristics(root-shoot ratio, G value(growth function: defined as ratio of whole plant dry weight to days of seedling), healthy indexes) and TEP(thermal effectiveness and photosynthetically active radiation) were explored to establish the models, which were validated with independent test data. Our results suggested that the curve of healthy index 1(HI1) and TEP fitted well with high coefficient of determination(R2) in both species, indicating that the model is highly reliable. The HI1 simulation models for tomato and cabbage are HI1=0.0009e0.0308TEP-0.0015 and HI1= 0.0003e0.0671TEP-0.0003, respectively, which can be used for predicting vigors of tomato and cabbage seedlings grown under different temperature and light conditions.

INTERACTION MODELS FOR EFFECTIVE THERMAL AND ELECTRIC CONDUCTIVITIES OF CARBON NANOTUBE COMPOSITES

The present article provides supplementary information of previous works of analytic models for predicting conductivity enhancements of carbon nanotube composites. The models, though fairly simple, are able to take account of the effects of conductivity anisotropy, nonstraightness, and aspect ratio of the CNT additives on the conductivity enhancement of the composite and to give predictions agreeing well with existing experimental data. The omitted detailed derivation of this model is demonstrated in the present article with a more systematical analysis, which may help with further development in this direction. Furthermore, the effects of various orientation distributions of CNTs are reported here for the first time. The information may be useful in design or fabrication technology of CNT composites for better or specified conductivities.

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.

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 Thermal Lattice Vibration on the Effective Potential of Weak-Coupling Bipolaron in a Quantum Dot

Based on the Huybrechts' linear-combination operator,effects of thermal lattice vibration on the effective potential of weak-coupling bipolaron in semiconductor quantum dots are studied by using the LLP variational method and quantum statistical theory.The results show that the absolute value of the induced potential of the bipolaron increases with increasing the electron-phonon coupling strength,but decreases with increasing the temperature and the distance of electrons,respectively;the absolute value of the effective potential increases with increasing the radius of the quantum dot,electron-phonon coupling strength and the distance of electrons,respectively,but decreases with increasing the temperature;the temperature and electron-phonon interaction have the important influence on the formation and state properties of the bipolaron:the bipolarons in the bound state are closer and more stable when the electron-phonon coupling strength is larger or the temperature is lower;the confinement potential and coulomb repulsive potential between electrons are unfavorable to the formation of bipolarons in the bound state.

Efficiency and Effectiveness Thermal Analysis of the Shell and Helical Coil Tube Heat Exchanger Used in an Aqueous Solution of Ammonium Nitrate Solubility (<i>ANSOL</i>) with 20% H₂O and 80% <i>AN</i>

The case study is about obtaining the flow rate and saturation temperature of steam that makes it possible to heat a solution of water and ammonia nitrate (ANSOL) in a shell and helical coil tube heat exchanger, within a time interval, without that the crystallization of the ANSOL solution occurs. The desired production per batch of the solution is 5750 kg in 80 minutes. The analysis uses the concepts of efficiency and effectiveness to determine the heat transfer rate and temperature profiles that satisfy the imposed condition within a certain degree of safety and with the lowest possible cost in steam generation. Intermediate quantities necessary to reach the objective are the Reynolds number, Nusselt number, and global heat transfer coefficient for the shell and helical coil tube heat exchanger. Initially, the water is heated for a specified period and, subsequently, the ammonium nitrate is added to a given flow in a fixed mass flow rate.

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.

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.

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.

Effect of Geometry of Filler Particles on the Effective Thermal Conductivity of Two-Phase Systems

The present paper deals with the effect of geometry of filler particles on the effective thermal conductivity for polymer composites. In the earlier models, less emphasis has been given on the shape of filler particles. In this paper, expressions for effective thermal conductivity has been derived using the law of minimal thermal resistance and equal law of the specific equivalent thermal conductivity for three different shapes i.e. spherical, elliptical and hexagonal of filler particles respectively. Calculated values of effective thermal conductivity for various samples using the derived expressions then compared with experimental data available and other models developed in the literature. The results calculated are in good agreement with the earlier experimental data and the deviation, is least in our expressions showing the success of the model.

Non-Linear Effect of Volume Fraction of Inclusions on The Effective Thermal Conductivity of Composite Materials: A Modified Maxwell Model

In this paper, non-linear dependence of volume fraction of inclusions on the effective thermal conductivity of composite materials is investigated. Proposed approximation formula is based on the Maxwell’s equation, in that a non-linear term dependent on the volume fraction of the inclusions and the ratio of the thermal conductivities of the polymer continuum and inclusions is introduced in place of the volume fraction of inclusions. The modified Maxwell’s equation is used to calculate effective thermal conductivity of several composite materials and agreed well with the earlier experimental results. A comparison of the proposed relation with different models has also been made.

Effect of residual interface stress on effective thermal expansion coefficient of particle-filled thermoelastic nanocomposite

The surface/interface energy theory based on three configurations proposed by Huang et al. is used to study the effective properties of thermoelastic nanocomposites. The particular emphasis is placed on the discussion of the influence of the residual inter- face stress on the thermal expansion coefficient of a thermoelastic composite filled with nanoparticles. First, the thermo-elastic interface constitutive relations expressed in terms of the first Piola-Kirchhoff interface stress and the Lagrangian description of the gen- eralized Young-Laplace equation are presented. Second, the Hashin＇s composite sphere assemblage （CSA） is taken as the representative volume element （RVE）, and the residual elastic field induced by the residual interface stress in this CSA at reference configuration is determined. Elastic deformations in the CSA from the reference configuration to the current configuration are calculated. Prom the above calculations, analytical expressions of the effective bulk modulus and the effective thermal expansion coefficient of thermoelastic composite are derived. It is shown that the residual interface stress has a significant effect on the thermal expansion properties of thermoelastic nanocomposites.

Effective Thermal Conductivity for 3D Five-Directional Braided Composites Based on Microstructural Analysis

A method for predicting effective thermal conductivities(ETCs) of three-dimensional five-directional(3D5D) braided composites is presented. The effective thermal conductivity prediction method contains a digital image processing technology. Multiple scanning electron microscopy(SEM)images of composites are analyzed to obtain actual microstructural features. These actual microstructural features of 3D5D braided composites are introduced into representative volume element(RVE) modeling. Apart from applying actual microstructural features,compression effects between yarns are considered in the modeling of RVE,making the RVE more realistic. Therefore,the ETC prediction method establishes a representative unit cell model that better reflects the true microstructural characteristics of the 3D5D braided composites. The ETCs are predicted with the finite element method. Then thermal conductivity measurements are carried out for a 3D5D braided composite sample.By comparing the predicted ETC with the measured thermal conductivity, the whole process of the ETC prediction method is proved to be effective and accurate,where a relative error of only 2.9 % is obtained.Furthermore,the effects of microstructural features are investigated,indicating that increasing interior braiding angles and fiber fill factor can lead to higher transverse ETCs. Longitudinal ETCs decrease with increasing interior braiding angles,but increase with increasing fiber fill factor. Finally,the influence of variations of microstructure parameters observed in digital image processing are investigated. To explore the influence of variations in microstructural features on variations in predicted ETCs,the actual probability distributions of microstructural features obtained from the 3D5D braided composite sample are introduced into the ETC investigation. The results show that,compared with the interior braiding angle,variations in the fiber fill factor exhibit more significant effects on variations in ETCs.

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.

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.

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.

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.