Bounds on the effective thermal conductivity of composites with imperfect interface

A new model is developed to bound the effective thermal conductivity of composites with thermal contact resistance between spherical inclusions and matrix. To construct the trial temperature and heat flux fields which satisfy the necessary interface conditions, the transition layer for each spherical inclusion is introduced. For the upper bound, the trial temperature field needs to satisfy the thermal contact resistance conditions between spherical inclusions and transition layers and the continuous interface conditions between transition layers and remnant matrix. For the lower bound, the trial heat flux field needs to satisfy the continuous interface conditions between different regions. It should be pointed out that the continuous interface conditions mentioned above are absolutely necessary for the application of variational principles, and the thermal contact resistance conditions between spherical inclusions and transition layers are suggested by the author. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with imperfect interfaces are rigorously derived. The effects of the size and distribution of spherical inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and does not need to calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides an entirely different way to bound the effective thermal conductivity of composites with imperfect interface, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds are finite when the thermal conductivity of spherical inclusions tends to ∞ and 0, respectively.     

Rigorous bounds on the effective thermal conductivity of composites with ellipsoidal inclusions

A new method is developed to derive the bounds of the effective thermal conductivity of composites with ellipsoidal inclusions. The transition layer for each ellipsoidal inclusion is introduced to make the trial temperature field for the upper bound and the trial heat flux field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides a powerful way to bound the effective thermal conductivity of composites, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds still are finite when the thermal conductivity of ellipsoidal inclusions tends to ∞ and 0, respectively.     

Automatic FEM model generation for evaluating thermal conductivity of composite with random materials arrangement

A new modeling method has been developed to generate FEM model of composite with complicated materials arrangement, especially random arrangement. The structure of a composite is considered to be composed of some very simplified basic models. For each basic model, the dispersions are assumed to have the same geometry and with one of the following three types of orientation: one dimensional, two dimensional random and three dimensional random. When the geometry, orientation type and number of dispersion are given, the computer randomly generates the position and orientation for each dispersion, and creates the geometrical model and FEM mesh. The effective thermal conductivity of composite has been calculated based on the models generated with this method and compared to the values obtained by analytical method and experimental measurement. The influence of some factors such as model size and mesh refinement on the reproducibility and accuracy of calculation is discussed.     

颗粒弥散复合材料等效导热系数的估算

等效热导率是热障功能梯度材料的重要热物理性能,本文采用小最小热阻力法则和比等效导热系数相等法则,推导出了热障型陶瓷／金属复赤道儿热导系数的普通式。并研究了Ni-ZrO2系复合材料的等效热导率随成分变化的规律,将理论值和实测值进行了比较。结果表明该理论对热障功能梯度材料的设计具有指导意义。     

探针法测量低温下猪主动脉导热系数研究

低温下导热系数测定对生物器官的低温保存、低温外科医学及数值模拟计算至关重要.在分析探针法测量原理的基础上,用探针法对低温下猪主动脉的导热系数进行了测量研究.实验表明探针在用甘油和蒸馏水进行标定后,可以方便准确地测量-90～-35℃温区下猪主动脉的导热系数.     

A Kansa-type MFS scheme for two-dimensional time fractional diffusion equations

In this paper, an efficient Kansa-type method of fundamental solutions (MFS-K) is extended to the solution of two-dimensional time fractional sub-diffusion equations. To solve initial boundary value problems for these equations, the time dependence is removed by time differencing, which converts the original problems into a sequence of boundary value problems for inhomogeneous Helmholtz-type equations. The solution of this type of elliptic boundary value problems can be approximated by fundamental solutions of the Helmholtz operator with different test frequencies. Numerical results are presented for several examples with regular and irregular geometries. The numerical verification shows that the proposed numerical scheme is accurate and computationally efficient for solving two-dimensional fractional sub-diffusion equations.     

含非均匀界面相纤维增强复合材料热传导性能预测的递推公式

研究了含非均匀界面相纤维增强复合材料的宏观等效传热性能。将热导率沿径向连续变化的界面相离散为多个热导率均匀的同心圆柱层,采用广义自洽法和复变函数理论,推导了复合材料宏观等效热导率的解析递推公式,并由递推公式给出了均匀界面相和理想零厚度界面的封闭公式。理想零厚度界面复合材料的热导率与已有理论结果一致。理想零厚度界面和非均匀界面相模型的计算结果与实验数据比较表明,当纤维体积分数较小时,2种模型的预测结果与实验数据吻合均较好,当体积分数较大时,与实验数据相比,非均匀界面相模型的精度大大高于理想零厚度界面模型的精度。本文中给出的递推公式亦可用于计算多涂层纤维增强复合材料的热导率。     

A theoretical model for effective thermal conductivity (ETC) of particulate beds under compression

Thermal conductivity of particulate beds is an important property for many industrial handling processes as well as for storage of particulate materials. This paper presents a new theoretical model that is based on heat transfer between particles in three modes: heat conduction through contact area, heat conduction through voids and radiation through voids. The model is further adjusted in order to obtain effective thermal conductivity of a particulate bed by using empirical augmentation factors for the heat transfer coefficient of each one of the heat transfer mechanisms. Comparison of the results predicted by the semi-empirical model to our experimental results show good agreement. The theoretical model was investigated to examine the effect of various parameters (such as: particle elasticity and surface roughness, particle and gas thermal conductivity and particle diameter), on the effective thermal conductivity of various particulate beds. Our results show the significant effect of the contact area (that is a clear function of the compression load) between particles on the effective thermal conductivity.     

复合材料热传导性能的变分渐近均匀化细观力学模型

为准确预测非均质复合材料的有效热导率和局部温度场分布,采用单胞变分渐近均匀化方法构建了一种新的细观力学模型。首先从非均质连续体热传导变分问题入手,使用变分渐近法将其细观力学模型转换为约束条件下泛函的最小化——取驻值问题;使用有限元法(FEM)推导了离散形式能量泛函的最小化求解过程;根据宏观性能(如全局温度及相应的梯度和波动函数)重构单胞的局部温度场和热通量。采用多个二元复合材料算例验证了所构建理论和程序的有效性和准确性。     

复合材料热传导系数均匀化计算的实现方法

均匀化理论可以有效预测周期性结构复合材料的等效热传导系数,然而其控制方程的载荷项形式特殊,通用有限元软件中没有对应的载荷形式,难以直接求解.提出一种本构关系及场变量的类比方法,证明了在此类比下等效热传导系数均匀化方程与等效弹性模量均匀化方程是等价的.根据求解等效弹性模量均匀化方程的热应变法,提出一种新的等效热传导系数均匀化方程数值求解方法.以ABAQUS为平台,预测单向纤维复合材料以及金属蜂窝夹芯板的等效热传导系数,计算结果与参考值吻合良好.该方法为基于通用有限元软件的复合材料等效热传导系数的均匀化计算提供了简便途径.     

Micro-structure of composites with randomly distributed particles on the impact of the effective thermal conductivity parameters

结合建立的颗粒随机分布复合材料的微结构模型和基于均匀化理论统计的双尺度计算方法,针对氮化硼颗粒增强高密度聚乙烯（BN/HDPE）复合材料,研究了颗粒形状、体积分数和空间分布参数等微结构特征对复合材料有效热传导系数的影响。结果表明：颗粒体积分数的增加将导致有效热传导系数升高;球形颗粒的位置参数、长椭球颗粒的取向程度都对有效热传导系数有重要影响。数值试验表明,材料的微结构特征对复合材料的有效热传导系数具有极大影响。     

周期性复合材料等效传热系数预测的渐进均匀化新算法及其实现

渐进均匀化方法具有严格的数学基础,预测周期性复合材料的等效热传导系数具有较高的计算精度。本文提出了基于渐进均匀化方法预测周期性复合材料等效热传导系数的新算法。相比原有的算法具有两个优点：它的实现与代表体元方法一样简单,新的算法以现有的有限元商业软件为黑箱,通过简单的几个分析步骤,即可以获得复合材料的等效热传导系数;可以利用商业软件提供的多种单元类型去离散同一个单胞,在处理复杂几何单胞结构时,可以节约大量的计算费用。通过几个典型的算例,验证了方法的有效性。该工作对于推广渐进均匀化方法在预测复合材料等效热传导系数的广泛应用具有积极作用。     

Numerical calculations of effective thermal conductivity of porous ceramics by image-based finite element method

The effective thermal conductivity of heterogeneous or composite materials is an essential physical parameter of materials selection and design for specific functions in science and engineering.The eff...     

Measurement of the effective thermal conductivity of agricultural products

This paper reports new measurements of the effective thermal conductivity of agricultural materials such as grains by means of the transient heat flow method using a line heat source. The effect of a probe diameter used for the transient heat flow method on the effective thermal conductivity was studied using standard spherical particles and some grains. It was concluded that the transient heat flow method can be applied to the measurement of the effective thermal conductivity of agricultural materials such as grains provided that the ratio of the probe diameter to the diameter of the particles of the specimen is greater than unity.Nomenclature A Area of heating surface - d Diameter of particles of the specimen - d _e Hydrodynamic diameter of particles of the specimen - E Error - H Distance between hot and cold walls - L Probe length - M Moisture content - N Number of contact points of particles of the speciment to the probe surface - Q Net heat flux - q Heat flux per probe length added to probe - R Probe radius - r Radial distance - T Temperature - T _h Surface temperature of the hot wall - T _c Surface temperature of the cold wall - t Time - _a Thermal conductivity of air - _eff Effective thermal conductivity - _s Thermal conductivity of a single kernel - Thermal diffusivity - _s Thermal diffusivity of a single kernel - Porosity - Euler constant (=0.5775...) - Angle Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

AlN/橡胶复合材料等效热导率数值计算

利用计算机生成不同的AlN/橡胶复合材料等效结构单元,基于三维格子玻尔兹曼模型计算了复合材料的等效热导率。实验制备了AlN/橡胶复合材料,并测定了不同填充量下复合材料的热导率,用以验证模型的有效性。将LBM计算结果与实验结果及Maxwell、Bruggeman、Nielsen等模型进行了比较,发现本文数值计算结果与Maxwell模型吻合较好,相比较于Bruggeman模型与Nielsen模型更加接近实验值。研究了AlN颗粒尺寸及分布方式对复合材料导热性能的影响。结果表明,一定体积分数范围内,粒径较小的AlN颗粒填充橡胶复合材料的等效热导率较大,当体积分数增大到20%,粒径较大的复合材料内先开始形成导热网络,大大提高了热导率;随机分布比均匀分布方式下的复合材料的等效热导率大,不同的粒子空间分布结构是影响复合材料热导率的关键因素。     

The thermal conductivity of talc as a function of pressure and temperature

Talc is a commonly used pressure-transmitting and gasket material for high-temperature and -pressure applications. The thermal conductivity of talc at high pressures and temperatures is therefore valuable in the design of high-pressure experiments and apparatus. In this paper measurements of the thermal conductivity of fired and unfired talc are presented. Measurements were made at pressures ranging from 0 to 2.5 GPa and temperatures from 150 to 900 K. The thermal conductivity was measured with the hotwire technique. The thermal conductivity results for both the fired and the unfired talc show a slight increase with increasing pressure. The absolute value of the thermal conductivity of talc is lower in the fired material than in the unfired material. In both cases, the thermal conductivity varied less than 15% over the temperature range studied. X-Ray diffraction studies have shown talc to be highly disordered. The results are shown to be consistent with those expected for a disordered crystal.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

国产石墨薄膜低温导热系数测量

在90-350K温度范围内,设计了1套实验装置,用以测量一种国产石墨薄膜的导热系数.介绍了实验装置的结构和原理,以及相关的数据处理方法.最终利用该装置得出了石墨薄膜导热系数与温度的关系.结果表明,该石墨薄膜在低温下可以作为铜的理想替代材料.     

膨胀石墨/石蜡相变复合材料有效导热系数的数值计算

通过膨胀石墨粉与石蜡混合制备相变复合材料可有效提高该储能材料的传热性能。为研究膨胀石墨/石蜡相变复合材料的导热机制,提出了膨胀石墨粉与石蜡混合后的3尺度层次固体有效导热系数计算方法。然后,通过数值模拟计算得到了具有不同体积分数和不同导热系数的膨胀石墨导热颗粒的膨胀石墨/石蜡相变复合材料的有效导热系数。结果表明:膨胀石墨能够有效地提高石蜡的导热性能,当膨胀石墨的体积分数为10%时,膨胀石墨/石蜡相变复合材料的有效导热系数是纯石蜡的9倍。此外,提高底层尺度的石墨片与石蜡的混合程度及降低底层尺度石墨的体积分数都能有效提高膨胀石墨/石蜡相变复合材料的有效导热系数。所得结论为探究膨胀石墨粉提高相变复合材料导热系数的机理奠定了基础。     

预报纤维增强复合材料有效热导率的随机微结构胞元模型

发展了能预报复合材料有效性质的随机微结构胞元模型以预测单向纤维增强复合材料横向热导率。研究了能反映宏观有效性质的模型最小化问题, 探讨了微结构影响宏观有效热传导性能的机制。结果表明: 通过对模型指定周期边界条件并且以多个合适的小规模模型计算的平均值取代大模型计算, 可大大改进收敛性并提高计算效率, 从10×10个到30×30个子胞的模型, 所得有效热导率计算结果的最大相对变化量仅为0.6%。不同纤维排列引起热流穿过热阻大的基体的路径长度改变, 造成有效热导率不同; 纤维热导率远大于基体热导率时, 纤维随机分布造成纤维偏聚, 部分纤维接触形成"热流通道", 使得有效热导率增大, 揭示了某一体积分数下有效热导率急剧增加是由"热流通道"贯通引起。与实验结果的比较说明了微结构随机性研究的必要性和本文工作的实用价值。