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 electric...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.展开更多
As the size of transistors shrinks and power density increases,thermal simulation has become an indispensable part of the device design procedure.However,existing works for advanced technology transistors use simplifi...As the size of transistors shrinks and power density increases,thermal simulation has become an indispensable part of the device design procedure.However,existing works for advanced technology transistors use simplified empirical models to calculate effective thermal conductivity in the simulations.In this work,we present a dataset of size-dependent effective thermal conductivity with electron and phonon properties extracted from ab initio computations.Absolute in-plane and cross-plane thermal conductivity data of eight semiconducting materials(Si,Ge,GaN,AlN,4H-SiC,GaAs,InAs,BAs)and four metallic materials(Al,W,TiN,Ti)with the characteristic length ranging from 5 nm to 50 nm have been provided.Besides the absolute value,normalized effective thermal conductivity is also given,in case it needs to be used with updated bulk thermal conductivity in the future.展开更多
Electronic components are normally assembled to printed circuit boards (PCBs). Such components generate heat in operation which must be conducted away efficiently from the small mounting areas to frames where the PCB ...Electronic components are normally assembled to printed circuit boards (PCBs). Such components generate heat in operation which must be conducted away efficiently from the small mounting areas to frames where the PCB is fixed. The temperature of the component depends on heat dissipation rate, technology and parameters of mounting, component placement and finally effective thermal conductivity (keff) of the board. The temperature of some components may reach significant magnitudes over 100°C while the PCB frame is kept at near-ambient temperature. The reliability of electronic components is directly related to operating temperature;?so the thermal project should be able to provide a correct temperature prediction of all PCB components under the hottest operational condition. In space applications, the main way to spread and reject heat of electronic equipment is by thermal conduction once there is no air available to apply convection-based cooling techniques. The PCB keff is an important parameter for the electronics thermal analysis when the PCB is modeled as a simplified homogeneous board with a unique thermal conductivity. In this paper, an intrinsic uncertainty of such approach is firstly reveled and its magnitude is evaluated for a real space use PCB. The simulation uses SINDA/FLUINT Thermal Desktop and aims to determine the keff of the PCB by comparison between a detailed multi-layered anisotropic model and an equivalent homogeneous single-layer model. The model was validated using available data for two-layered FR4-copper PCB. Multiple simulations are performed with different dissipating component position and mounting area.展开更多
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...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.展开更多
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 ...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.展开更多
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 th...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.展开更多
We present an empirical model for the effective thermal conductivity (ETC) of a polymer composite that includes dependency on the filler size distribution-chosen as the Rosin-Rammler distribution. The ETC is determine...We present an empirical model for the effective thermal conductivity (ETC) of a polymer composite that includes dependency on the filler size distribution-chosen as the Rosin-Rammler distribution. The ETC is determined based on certain hypotheses that connect the behavior of a real composite material A, to that of a model composite material B, filled with mono-dimensional filler. The application of these hypotheses to the Maxwell model for ETC is presented. The validation of the new model and its characteristic equation was carried out using experimental data from the reference. The comparison showed that by using the size distribution law a very good fit between the equation of the new model (the size distribution model for the ETC) and the reference experimental results is obtained, even for high volume fractions, up to about 50%.展开更多
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...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.展开更多
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 meth...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.展开更多
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...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.展开更多
thermal magnification device is proposed by using effective thermal conductivity. Different fromtransformation optics method, the magnification design is realized analytically by enforcingequality of effective ther...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.展开更多
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 appli...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.展开更多
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 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.展开更多
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 s...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.展开更多
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...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.展开更多
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, ma...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.展开更多
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 res...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.展开更多
The article presents the results of calculations of the effective thermal conductivity kef for bundles of steel rectangular sections obtained for a few analytical models. This coefficient expresses the ability of the ...The article presents the results of calculations of the effective thermal conductivity kef for bundles of steel rectangular sections obtained for a few analytical models. This coefficient expresses the ability of the bundles to heat transfer. The knowledge about the values of the kef coefficient of the section bundles is essential to correctly identify the parameters of their heat treatment process. The quality of the Calculation results were verified by the experimental measurement data. These measurements were performed in the guarded hot plate apparatus. It should be noted, that none of the eleven analyzed models of effective thermal conductivity is suitable for evaluation of thermal properties of the section bundles.展开更多
Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells （SOFC） and lithium-ion batteries （LIB）. For this, the porous electrode structures of both SOFC and LIB a...Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells （SOFC） and lithium-ion batteries （LIB）. For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB： the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete el- ement approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the con- nectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, es- pecially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of cal- endering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.展开更多
For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodi...For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method （EEVM）based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented, which is convenient for engineering application. The numerical results show a good convergency of the presented method,even though the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.展开更多
基金sponsored by National Natural Science Foundation of China (Grant No. 40874034)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX2-YW-QN508)
文摘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.
基金Project supported by the National Key R&D Project from Ministry of Science and Technology of China(Grant No.2022YFA1203100)the National Natural Science Foundation of China(Grant No.52122606)the funding from Shanghai Polytechnic University.
文摘As the size of transistors shrinks and power density increases,thermal simulation has become an indispensable part of the device design procedure.However,existing works for advanced technology transistors use simplified empirical models to calculate effective thermal conductivity in the simulations.In this work,we present a dataset of size-dependent effective thermal conductivity with electron and phonon properties extracted from ab initio computations.Absolute in-plane and cross-plane thermal conductivity data of eight semiconducting materials(Si,Ge,GaN,AlN,4H-SiC,GaAs,InAs,BAs)and four metallic materials(Al,W,TiN,Ti)with the characteristic length ranging from 5 nm to 50 nm have been provided.Besides the absolute value,normalized effective thermal conductivity is also given,in case it needs to be used with updated bulk thermal conductivity in the future.
基金support of the Space Mechanics and Control Division-DMC of ETE(General Coordination of Engineering and Space Technology)of the National Institute for Space Research-INPE.
文摘Electronic components are normally assembled to printed circuit boards (PCBs). Such components generate heat in operation which must be conducted away efficiently from the small mounting areas to frames where the PCB is fixed. The temperature of the component depends on heat dissipation rate, technology and parameters of mounting, component placement and finally effective thermal conductivity (keff) of the board. The temperature of some components may reach significant magnitudes over 100°C while the PCB frame is kept at near-ambient temperature. The reliability of electronic components is directly related to operating temperature;?so the thermal project should be able to provide a correct temperature prediction of all PCB components under the hottest operational condition. In space applications, the main way to spread and reject heat of electronic equipment is by thermal conduction once there is no air available to apply convection-based cooling techniques. The PCB keff is an important parameter for the electronics thermal analysis when the PCB is modeled as a simplified homogeneous board with a unique thermal conductivity. In this paper, an intrinsic uncertainty of such approach is firstly reveled and its magnitude is evaluated for a real space use PCB. The simulation uses SINDA/FLUINT Thermal Desktop and aims to determine the keff of the PCB by comparison between a detailed multi-layered anisotropic model and an equivalent homogeneous single-layer model. The model was validated using available data for two-layered FR4-copper PCB. Multiple simulations are performed with different dissipating component position and mounting area.
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(U19B2005,21808238,U20B6005,22127812)the State Key Laboratory of Heavy Oil Processing,China University of Petroleumthe National Key Research and Development Program of China(2021YFC2800902)
文摘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.
基金Project (No. 71-088/2007) supported by Program "Partnerships in Priority Areas", the Romanian Ministry of Education and Research
文摘We present an empirical model for the effective thermal conductivity (ETC) of a polymer composite that includes dependency on the filler size distribution-chosen as the Rosin-Rammler distribution. The ETC is determined based on certain hypotheses that connect the behavior of a real composite material A, to that of a model composite material B, filled with mono-dimensional filler. The application of these hypotheses to the Maxwell model for ETC is presented. The validation of the new model and its characteristic equation was carried out using experimental data from the reference. The comparison showed that by using the size distribution law a very good fit between the equation of the new model (the size distribution model for the ETC) and the reference experimental results is obtained, even for high volume fractions, up to about 50%.
文摘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.
基金the National Natural Science Foundation of ChinaChinese"863"High-Tech.Program
文摘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.
基金supported by the National 111 Project of China(B06024)the National Basic Research Program of China(2011CB610305)
文摘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.
基金supported by the National Natural Science Foundation of China (11732002,11672089, 11325210, and 11421091)
文摘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.
基金Funded by Key Project of International Joint Research of National Natural Science Foundation of China(No.51320105004)
文摘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.
基金supported by the National Natural Science Foundation of China(51506160,11472208,11472209)China Post-Doctoral Science Foundation Project(2015M580845)+1 种基金the Fundamental Research Funds for Xi’an Jiaotong University(xjj2015102)the Beijing Key Lab of Heating,Gas Supply,Ventilating and Air Conditioning Engineering(NR2016K01)
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No.51975459)Shaanxi Provincial Natural Science Foundation of China (Grant No.2017JM5046)。
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51764046 and 52160013)the Inner Mongolia Autonomous Region Postgraduate Research Innovation Project of China (Grant No. S20231165Z)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region of China (Grant Nos. 2023RCTD016 and 2024RCTD008)。
文摘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.
基金the National Natural Science Foundation of China(Grant No.51371104)。
文摘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.
文摘The article presents the results of calculations of the effective thermal conductivity kef for bundles of steel rectangular sections obtained for a few analytical models. This coefficient expresses the ability of the bundles to heat transfer. The knowledge about the values of the kef coefficient of the section bundles is essential to correctly identify the parameters of their heat treatment process. The quality of the Calculation results were verified by the experimental measurement data. These measurements were performed in the guarded hot plate apparatus. It should be noted, that none of the eleven analyzed models of effective thermal conductivity is suitable for evaluation of thermal properties of the section bundles.
基金supported by the Helmholtz Portfolio "elektrochemische Speicher",particularly the work related to lithium-ion batteriespartially supported as part of the HeteroFoam Center,an Energy Frontier Research Center funded by the U.S.Department of Energy,Office of Science, Basic Energy Sciences(DE-SC0001061)+1 种基金support from the Center for Scientific Computing at the CNSI and MRL:an NSF MRSEC(DMR-1121053) and NSF (CNS-0960316)Australian Research Council Grant DE130101639
文摘Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells （SOFC） and lithium-ion batteries （LIB）. For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB： the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete el- ement approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the con- nectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, es- pecially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of cal- endering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.
基金National Natural Science Foundation of China(90716002)The Open Fund of LNM
文摘For steady-state heat conduction,a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method （EEVM）based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented, which is convenient for engineering application. The numerical results show a good convergency of the presented method,even though the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.
