Determination of specific heat and true thermal conductivity of glass from dynamic temperature data

A method to determine the true specific heat and true thermal conductivity for glass and other semitransparent materials from dynamic temperature data is presented. A unique fabrication technique to obtain high quality dynamic temperature data from glass test plates employing thermocouples fused to the glass is described. The true thermal conductivity and specific heat of float glass has been measured using these techniques, and the results are compared with the scant data available in the literature. Sensitivity of the measured specific heat and thermal conductivity to sources of uncertainty is identified and these are discussed.     

考虑材料温度相关性的二维轮轨弹塑性滑动接触温升分析

轮轨滑动接触温升的准确预测对于轮轨的磨耗和疲劳研究均具有重要意义. 目前的轮轨温升解析或半解析模型通常考虑Hertz弹性接触压力分布和单一材料属性的温度相关性, 与实际的轮轨传热状态尚有一定偏差, 因此在轮轨滑动温升计算模型中考虑接触压力的塑性修正和多种材料属性的温度相关性, 有望提高温升预测结果的准确性. 基于弹塑性接触理论, 同时考虑热导率、比热容和摩擦系数的温度相关性, 通过基尔霍夫变换方法以热导率温度相关性函数的积分作为待求量, 将复杂的非线性Fourier导热方程转化成含单个变系数的简单偏微分方程形式, 从而构建了一种不限制材料温度相关性函数形式的统一隐式差分求解格式, 分别讨论了对流换热系数、法向载荷、蠕滑率以及行车速度对钢轨表面滑动温升的影响. 结果表明, 当列车高速行驶时, 对流换热系数对轮轨滑动温升的影响甚微; 蠕滑率和行车速度的增大, 均会引起摩擦功率的增大, 进而导致钢轨表面温度的升高; 钢轨表面滑动温升的峰值随法向载荷的增大而近似线性上升. 此外, 在轮轨滑动温升计算模型中考虑材料属性的温度相关性可有效避免对滑动温升的过分高估, 且摩擦系数的温度相关性对温升的影响要显著强于热导率和比热容.      

FRICTIONAL TEMPERATURE ANALYSIS OF TWO-DIMENSIONAL ELASTO-PLASTIC WHEEL-RAIL SLIDING CONTACT WITH TEMPERATURE-DEPENDENT MATERIAL PROPERTIES 1)

轮轨滑动接触温升的准确预测对于轮轨的磨耗和疲劳研究均具有重要意义. 目前的轮轨温升解析或半解析模型通常考虑Hertz弹性接触压力分布和单一材料属性的温度相关性, 与实际的轮轨传热状态尚有一定偏差, 因此在轮轨滑动温升计算模型中考虑接触压力的塑性修正和多种材料属性的温度相关性, 有望提高温升预测结果的准确性. 基于弹塑性接触理论, 同时考虑热导率、比热容和摩擦系数的温度相关性, 通过基尔霍夫变换方法以热导率温度相关性函数的积分作为待求量, 将复杂的非线性Fourier导热方程转化成含单个变系数的简单偏微分方程形式, 从而构建了一种不限制材料温度相关性函数形式的统一隐式差分求解格式, 分别讨论了对流换热系数、法向载荷、蠕滑率以及行车速度对钢轨表面滑动温升的影响. 结果表明, 当列车高速行驶时, 对流换热系数对轮轨滑动温升的影响甚微; 蠕滑率和行车速度的增大, 均会引起摩擦功率的增大, 进而导致钢轨表面温度的升高; 钢轨表面滑动温升的峰值随法向载荷的增大而近似线性上升. 此外, 在轮轨滑动温升计算模型中考虑材料属性的温度相关性可有效避免对滑动温升的过分高估, 且摩擦系数的温度相关性对温升的影响要显著强于热导率和比热容.     

A length-dependent model for the thermomechanical response of ceramics

We present a length-dependent model for the thermomechanical response of ceramics through a concurrent multiscale scheme that accounts for: (i) the locally varying values of the sub-grain thermal conductivity tensor due to the interaction of phonons with microstructural features such as grain boundaries, and (ii) a continuum model of thermal stresses that explicitly resolves the polycrystalline structure of the material. At the sub-grain level, we compute the values of the thermal conductivity tensor using the Boltzmann transport equation under the relaxation time approximation. At the continuum level, the polycrystalline structure of the specimen is resolved explicitly by a finite element mesh and the texture of the polycrystal is assumed to be given. At this level, we adopt a Fourier model of heat conduction which utilizes values of thermal conductivity obtained at the lower scale. The mechanical response of the grains is modeled as elastic and anisotropic. The capabilities of the model are demonstrated through a series of examples, which highlight the potential of our approach for designing materials with improved thermomechanical response.     

Meshless method for nonlinear heat conduction analysis of nano-composites

Carbon nanotubes (CNTs) may become ideal reinforcing materials for high-performance nano-composites due their exceptional properties. Still, much work is needed to be done before the potentials of CNT based composites can be fully realized. The evaluation of effective material properties of nano-composites is one of many difficult tasks. Simulations using continuum mechanics approach can play a significant role in the analysis of these composites. In the present work, nonlinear heat conduction analysis of CNT based composites has been carried out using continuum mechanics approach. Element free Galerkin method has been applied as a numerical tool. Thermal conductivities of nanotube and polymer matrix are assumed to vary quadratically with temperature. Picard and quasi-linearization schemes have been utilized to obtain the solution of a system of nonlinear equations. Cylindrical representative volume element has been used to evaluate the thermal properties of nano-composites. Present simulations show that the temperature dependent matrix thermal conductivity has a significant effect on the equivalent thermal conductivity of the composite, whereas temperature dependent nanotube thermal conductivity has a small effect on the equivalent thermal conductivity of the composite. The results obtained by Picard method have been found almost similar with those obtained by quasi-linearization approach.     

Response of an Elastic Body whose Heat Conduction Is Pressure Dependent

The properties of many real materials such as the viscosity, thermal and electrical conductivity, specific heat, relaxation time, as well as optical properties, depend upon the pressure to which the body is subject. For instance, the viscosity of fluids can vary by several orders of magnitude due to the variation in the pressure. In this paper we investigate the change in the response of an elastic solid due to the thermal conductivity being pressure dependent. It is well known that higher pressure leads to reduced molecular mobility, in rubber-like materials, leading in turn to higher cross-linking reaction rates. We find that the response of the solid is quite different from the classical response that is obtained by using Fourier??s law of heat conduction. The theoretical predictions according to the assumption that the thermal conductivity is pressure dependent, are in keeping with experimental results concerning the vulcanization of rubbers wherein one observes the conduction to be dependent on the pressure. To our knowledge, this is the first theoretical study that evaluates the response of non-linear elastic solids due the thermal conductivity depending on the pressure.     

Topological design of structures and composite materials with multiobjectives

This paper studies the influence of heat conduction in both structural and material designs in two dimensions. The former attempts to find the optimal structures with the maximum stiffness and minimum resistance to heat dissipation and the latter to tailor composite materials with effective thermal conductivity and bulk modulus attaining their upper limits like Hashin–Shtrikman and Lurie–Cherkaev bounds. In the part of structural topology optimization of this paper solid material and void are considered respectively. While in the part of material design, two-phase ill-ordered base materials (i.e. one has a higher Young’s modulus, but lower thermal conductivity while another has a lower Young’s modulus but higher conductivity) are assumed in order to observe competition in the phase distribution defined by stiffness and conduction. The effective properties are derived from the homogenization method with periodic boundary conditions within a representative element (base cell). All the issues are transformed to the minimization problems subject to volume and symmetry constraints mathematically and solved by the method of moving asymptote (MMA), which is guided by the sensitivities with respect to the design variables. To regularize the problem the SIMP model is explored with the nonlinear diffusion techniques to create edge-preserving and checkerboard-free results. The illustrative examples show how to generate Pareto fronts by means of linear weighting functions, which provide an in-depth understanding how these objectives compete in the topologies.     

Thermal system identification using fractional models for high temperature levels around different operating points

This work aims at the preparation of an experiment for the thermal modeling of an ARMCO iron sample (iron of the American Rolling Mill COmpany) for small temperature variations around different operating points. Fractional models have proven their efficacy for modeling thermal diffusion around the ambient temperature and for small variations. Due to their compactness, as compared to rational models and to finite element models, they are suitable for modeling such diffusive phenomena. However, for large temperature variations, thermal characteristics such as thermal conductivity and specific heat vary along with the temperature. In this context, the thermal diffusion obeys a nonlinear partial differential equation and cannot be modeled by a single linear model. In this paper, thermal diffusion of the iron sample is modeled around different operating points for temperatures ranging from 400 to 1070?K, which is above the Curie point (In physics and materials science, the Curie temperature (T _C), or Curie point, is the temperature at which a ferromagnetic or a ferrimagnetic material becomes paramagnetic.) showing that for a large range of temperature variations, a nonlinear model is required. Identification and validation data are generated by finite element methods using COMSOL Software.     

Evaluation of thermophysical characteristics on shape-stabilized paraffin as a solid-liquid phase change material

This report deals with thermophysical properties and measuring methods of shape-stabilized paraffin as a new type of latent heat storage material, which keeps the same shape in a solid state when the paraffin melts. Therefore, this type paraffin can be used in a latent heat storage system without encapsulation. A transient hot wire method, a differential scanning calorimeter (DSC), a water calorimeter and a volume expansion meter, which were developed in the present study, were used to measure effective thermal conductivity, latent heat, specific heat and density of the shape-stabilized paraffin, respectively. From the obtained data, useful correlation equations of the above-mentioned thermophysical properties of the shape-stabilized paraffin were expressed as functions of physical property and mass fraction of each constituent of the shape-stabilized paraffin.     

Periodisches Hitzdrahtverfahren zur Messung von Wärme- und Temperaturleitfähigkeit von geringen Stoffmengen

A measuring procedure for the simultaneous determination of the thermal conductivity and thermal diffusivity of small quantities is described. The procedure is suited for high-viscous fluids and for powdery material. The measuring principle is based on the transient hot-wire method. A sinusoidal alternating current flows through a thin platinum wire and heats up the wire periodically. This results in thermal waves, which penetrate into the surrounding sample. The amplitude and the phase shift of the thermal waves depend on the thermal diffusivity “a” and the thermal conductivity “λ” of the sample. The temperature oscillation in the sample is measured by means of the platinum wire, which is simultaneously applied as a resistance thermometer. The values measured for water and glycerine correspond well to those given in literature. Results of the effective thermal conductivity and the effective thermal diffusivity of zeolite powder under pressurized hydrogen are also discussed. The advantage of this measuring procedure is that only a sample of 13 ml is needed for the test.     

多相材料传热微结构的多目标优化设计

提出基于散热弱度的材料微结构热传导性能的预测方法,分别从理论和数值上验证该方法与均匀化方法的等效性;推导出微结构等效热传导系数的灵敏度计算格式,建立传热微结构拓扑优化的数学模型.以二维、三维多相材料等效热传导系数的加权组合为目标,采用凸规划对偶优化算法和二次型周长约束进行材料微结构的设计和材料分布的棋盘格控制.数值算例表明基于散热弱度的传热材料微结构设计是可行、有效的,可以为实际的材料设计提供依据.     

Determination of the surface temperature of poor heat conducting materials by radiation measurements from −60 °C to +250 °C in vacuum

The accurate measurement of the surface temperature is especially important in the determination of the radiative properties of poor heat conducting materials. Contact methods are not suitable for such materials. A radiation technique has been developed which does not require prior knowledge of the radiative properties of the material. The sample is mounted in good contact with a metallic base and surrounded by a black enclosure. A total radiation detector, at the same temperature as the enclosure, views the sample and measures the heat flux exchanged between the sample and the enclosure. When the heat flux through the sample is known, together with the thermal conductivity, the thickness, and the temperature of the sample back, measured accurately by resistance or thermoelectric thermometers, then the surface temperature can be calculated by the heat conduction equation. Measurements on visually transparent glasses, coatings and plastics have shown that accuracies of ± 0.03 °C are possible. The problems and the limitations of the technique, the reproducibility of the receiver, the thermocouples, and the resistance thermometers used in this apparatus for many years, will be discussed.

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Bestimmung der Oberflächentemperatur von schlecht wärmeleitenden Materialien mittels Strahlungsmessung von –60 °C bis +250 °C in Vakuum

Zusammenfassung Die genaue Messung der Oberflächentemperatur ist besonders wichtig bei der Bestimmung der Strahlungseigenschaften schlecht wärmeleitenden Materials. Kontaktmethoden sind bei solchen Materialien ungeeignet. Hier wird ein Verfahren entwickelt, das auf einer Strahlungsmessung beruht, aber keine vorherige Kenntnis der Strahlungseigenschaften des Materials erfordert. Die Probe befindet sich in gutem Wärmekontakt auf einem metallischen Probenhalter und ist von einer schwarzen Umhüllung umgeben. Ein auf die Probe gerichteter Gesamtstrahlungsempfänger, der die Temperatur der Umhüllung hat, mißt die Wärmestromdichte zwischen Probe und Umhüllung. Kennt man die durch die Probe gehende Wärmestromdichte, die Wärmeleitfähigkeit und die mit Widerstandsthermometern genau bestimmte Temperatur der Probenrückseite, ist die Probenoberflächentemperatur aus der Wärmeleitungsgleichung zu berechnen. Messungen an durchsichtigen Gläsern, Überzügen und Kunststoffen haben gezeigt, daß die Temperaturbestimmung mit einer Unsicherheit von ±0,03°C möglich ist. Die Grenzen dieser Technik und die Reproduzierbarkeit des benutzten Empfängers, der Thermoelemente und der Widerstandsthermometer über viele Jahre werden diskutiert.

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Publication from the Physikalisch-Technische Bundesanstalt, Braunschweig     

The effect of carbon nanotubes in enhancing the thermal transport properties of PCM during solidification

This study is aimed to prepare a novel class of nanofluid phase change material (NFPCM) by dispersing a small amount of multi-walled carbon nanotubes (MWCNT) in liquid paraffin, to enhance the heat transfer properties and examine the characteristics of the NFPCM during the solidification process. The stable NFPCMs are prepared by dispersing the MWCNT in liquid paraffin at 30°C with volume fractions of 0.15, 0.3, 0.45 and 0.6% without any dispersing agents. The rheology measurement illustrates the Newtonian fluid behavior in the shear stress range of 1–10?Pa. The differential scanning calorimetric results showed that there is no observable variation in the freezing/melting temperature of the NFPCM, and only a small observable change in the latent heat values. The thermal conductivity of various NFPCM is measured. The enhancement in thermal conductivity increases with the increased volume fraction of the MWCNT, and shows a weak dependence on the temperature. Further, for the NFPCM with a volume fraction of 0.6%, there is an appreciable increase in heat transfer with a reduction in the solidification time of 33.64%. The enhancement in the heat transfer performance would alleviate the major problems that have been encountered in the conventional phase change materials since several years.     

Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: A three-dimensional theory based on thermodynamics with internal state variables

In the vicinity of the glass transition, glass-forming materials exhibit pronounced frequency-dependent changes in the mechanical material properties, the thermal expansion behaviour and the specific heat. The frequency dependence becomes apparent under harmonic stress, strain or temperature excitations. The Prigogine-Defay ratio is a characteristic number which connects the changes in magnitude of these quantities at the glass transition. In order to represent the thermoviscoelastic properties of glass-forming materials in continuum mechanics, a three-dimensional approach which is based on the Gibbs free energy as thermodynamic potential is developed in this article. The Gibbs free energy depends on the stress tensor, the temperature and a set of internal variables which is introduced to take history-dependent phenomena into account. In the vicinity of an equilibrium reference state, the specific Gibbs free energy is approximated up to second order terms. Evaluating the Clausius-Duhem inequality, the constitutive relations for the strain tensor, the entropy and the internal variables are derived. In comparison with other approaches, the entropy, the strain tensor and the internal variables are functionals not only of the stress tensor but also of the temperature. Applying harmonic temperature- or stress-controlled excitations, complex frequency-dependent relations for the specific heat under constant stress, for the thermal expansion coefficients as well as for the dynamic mechanical compliance are obtained. The frequency-dependence of these quantities depicts the experimentally observed behaviour of glass-forming materials as published in literature. Under the assumption of isotropic material behaviour, it is shown that the developed theory is compatible with the Prigogine-Defay inequality for arbitrary values of the material parameters.     

Effective thermal conductivity of heterogeneous multi-component materials: an SPH implementation

Modeling heat transfer and fluid flow in materials with complicated micro-structures is a major challenge to numerical methods due to their multiscale and multiphysics nature. A relatively novel numerical technique—the meshless smoothed particle hydrodynamics (SPH) method has the potential of making a significant contribution to this research field. In the present SPH modeling effort, a 2D modeling system is devised for the prediction of the effective thermal conductivity in heterogeneous materials containing two or three different components. The microscopic component configuration inside the materials is constructed in the SPH methodology by randomly assigning particles as a certain component to meet the required macroscopic composition. For heterogeneous two-component materials, the effective thermal conductivity predicted by the modified effective medium theory model with the so-called “flexible” factor f equal to 4.5 agrees well with the SPH data. On the basis of a simple “step-process” concept, the effective thermal conductivity of a heterogeneous multi-component material can be derived from the corresponding “degenerate” materials which consist of fewer components.     

Measurement of Residual Stresses in Nuclear-grade Zircaloy-4(R) Tubes—Effect of Heat Treatment

Nuclear-grade Zircaloy-4(R) tubes are produced by a unique manufacturing process known as pilgering, which leaves the material in a work-hardened state containing a pattern of residual stresses. Moreover, such tubes exhibit elastic anisotropy as a result of the pilgering process. Therefore, standard equations originally proposed by Sachs (Z Met Kd, 19: 352–357, 1927; Sachs, Espey, Iron Age, 148: 63–71, 1941). for isotropic materials do not apply in this situation. Voyiadjis et al. (Exp Mech, 25: 145–147, 1985) proposed a set of equations for treating elastically anisotropic materials, but we have determined that there are discrepancies in their equations. In this paper, we present the derivation for a set of new equations for treating elastically anisotropic materials, and the application of these equations to residual stress measurements in Zr-4(R) tubes. To this end, through thickness distribution of residual stress components in as-received and heat treated (500°C) Zr-4(R) tubes was measured employing the Sachs’ boring-out technique in conjunction with electrochemical machining as the means of material removal, and our new equations. For both as-received and the heat treated materials, the axial and tangential residual stresses were significantly higher than the radial and shear residual stresses. The largest residual stress was the tangential stress component in the as-received material, showing a tensile value at the outer surface and a compressive value at the inner surface. At high values of von Mises equivalent stress, the principal directions of residual stress coincided with the principal axes of the tube for the as-received material, as well as for the material heat treated at 500°C.     

Non-linear strain rate dependent micro-mechanical composite material model for finite element impact and crashworthiness simulation

The present study aims at implementation of a strain rate dependent, non-linear, micro-mechanics material model for laminated, unidirectional polymer matrix composites into the explicit finite element code LSDYNA. The objective is to develop an accurate and simple micro-mechanical, rate dependent material model, which is computationally efficient. Within the model a representative volume cell is assumed. The stress-strain relation including rate dependent effects for the micro-model is derived for both shell elements and solid elements. Micro-failure criterion is presented for each material constituent and failure mode. The implemented model can deal with problems such as impact, crashworthiness, and failure analysis under quasi-static loads. The developed material model has a wide range of applications such as jet engine jackets, armor plates, and structural crashworthiness simulation. The deformation response of two representative composite materials with varying fiber orientation is presented using the described technique. The predicted results compare favorably to experimental values.     

纤维增强复合材料热隐身斗篷设计

基于变换热动力学原理可获得具有热隐身性能的隐身结构(隐身斗篷)所需要的材料性质的空间分布。但这种材料性质的复杂分布形式以及局部热传导性能无限大等极值性质需求,使得隐身斗篷设计的实现非常困难,需要研究基于常规材料的隐身斗篷设计。本文基于常规材料的热隐身结构实现问题,提出了基于纤维增强复合材料圆环结构的实现热隐身的结构形式。首先,基于变换热动力学原理获得热隐身所需的热传导系数沿半径方向的变化规律;进而,通过设计复合材料不同位置的纤维铺设方式(含量和铺设方向)实现热隐身对材料性能的需求。选择金属银作为纤维,空气作为基体,设计出了具有热隐身性能的复合材料圆环结构纤维含量和铺设方向沿径向的分布方案。对该设计方案进行数值仿真,结果显示所设计的隐身结构具有良好的热隐身性能。由于设计方案基于常规材料,因此具有容易实现的优点。     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading

The present paper deals with the specificities of the thermal response of rubber under cyclic mechanical loading at constant ambient temperature. This question is important, since the stabilized thermal response is used in fatigue life criteria, especially for the fast evaluation of fatigue life. For this purpose, entropic coupling in a thermo-hyperelastic framework is first used to predict the variation in the heat source produced or absorbed by the material during cyclic loading. The heat diffusion equation is then used to deduce temperature variations under adiabatic and non-adiabatic conditions. The influence of several parameters on the stabilized thermal response is studied: signal shape, frequency, minimum and maximum stretch levels, multiaxiality of the mechanical state. The results show that, in the steady-state regime, the mean value between the maximum and minimum temperature variations over a mechanical cycle is different from zero. This is due to the specific variation in the heat source, which depends on both the stretch rate and the stretch level. This result has numerous consequences, in particular for fatigue. Indeed, the stabilized mean value between the maximum and minimum temperature variations during fatigue tests does not reflect only fatigue damage, since the entropic coupling also leads to a value different from zero. This is a major difference with respect to materials exhibiting only isentropic coupling, such as metallic materials.