An analytical solution of temperature response in multilayered materials for transient methods

Transient methods, such as those with pulse- or stepwise heating, have often been used to measure thermal diffusivities of various materials including layered materials. The objective of the present study is to derive an analytical solution of the temperature rise in a multilayered material, the front surface of which is subjected to pulse- or stepwise heating. The Laplace transformation has been used to obtain the analytical solution. This solution will enable us to establish the appropriate measurement method for thermophysical properties of the multilayered material. It is also shown that the present solution can be extended to functionally gradient materials (FGM), in which thermophysical properties as well as compositions change continuously.     

Effect of radiation heat transfer on thermal diffusivity measurements

Experimental data on thermal conductivity and thermal diffusivity of a semitransparent material generally include an error due to the radiation heat transfer. This error varies in accordance with the experimental conditions such as the temperature level of the sample and the measuring method. In this paper, research on the influence of radiation heat transfer on thermal diffusivity are reviewed, and as an example, the method to correct the radiation component in the apparent thermal diffusivity measured by the stepwise heating technique is presented. The transient heat transfer by simultaneous thermal conduction and radiation in a semitransparent material is analyzed when the front surface is subjected to stepwise heating. The apparent thermal diffusivity, which includes the radiation component, is calculated for various parameters.Paper presented at the Second U.S.-Japan Joint Seminar on Thermophysical Properties, June 23, 1988, Gaithersburg, Maryland, U.S.A.     

Optical measurements of thermal diffusivity of a material

The measurement of thermal diffusivity of a material (in particular, a thin film) is important for various reasons, e.g., to predict the heat transfer in the solid subjected to a thermal process, to monitor surface composition or morphology, or to detect invisible subsurface defects like delaminations. This measurement can be done in a noncontact manner using various photothermal methods. Such methods typically involve pulsed heating of the surface by small amounts using a laser source; the decay of the surface temperature after this pulsed photothermal heating is then probed to provide the thermal diffusivity. Various probing methods have been developed in the literature, including the probing of reflection, refraction, and diffraction from the pulsed heated area, infrared thermal radiometry, and surface deformation. This paper provides an overview of such techniques and some examples of their applications.     

Measurement of the Thermal Diffusivity of an Anisotropic Graphite Sheet Using a Laser-Heating AC Calorimetric Method

The thermal diffusivity of a graphite sheet having an extremely high anisotropy has been measured by a laser heating AC calorimetric method in the temperature range from 30 to 350 K. This graphite sheet has characteristics of high thermal diffusivity and high anisotropy, and it is only 100 m thick. Thus, it is difficult to apply the conventional AC technique. Therefore, we propose a simultaneous measurement method for the in-plane and out-of-plane thermal diffusivities, by analyzing the three-dimensional heat conduction process, which contains the effects of anisotropy and thermal wave reflections. This method was verified by checking with thermal diffusivity measurements of isotropic materials such as stainless steel and pure copper and was then applied to the anisotropic thermal diffusivity measurement of the graphite sheet.     

A Method for Thermal Diffusivity Determination of Thermal Insulators

A so-called “three-point” (3P) method has been developed for thermal diffusivity measurements of thermal insulating materials. One side of a cylindrical specimen, sandwiched between two thin metal plates, is subjected to intense light from an incandescent lamp to generate a thermal perturbance. The temperature response is measured in three locations along the test specimen. Thermocouples are located at the front and rear faces of the specimen, and the third is placed inside the specimen at a known location. The two outside temperatures are used as boundary conditions, and the unknown thermal diffusivity is calculated from the third temperature versus time curve. The method combines the advantages of rapid transient non-contact heating methods with the well-defined boundary conditions of steady-state methods. The results of the 3P method are compared with those from steady-state methods for a micro-porous insulation material and for a honeycomb structure.     

Suggestions regarding thermal diffusivity measurements on pyrolytic graphite and pyrolytic boron nitride by the laser pulse method

The laser pulse method can be successfully applied to the measurement of thermal diffusivity of isotropic materials subject to some assumptions. For anisotropic materials, this method is applicable to the measurement of principal thermal diffusivity only on the condition that there is no difference in direction between the principal axis and that of the temperature gradient. After analyzing the heat conduction process in an anisotropic solid, it has been shown that large errors in the measurement of thermal diffusivity would exist if the direction of the principal axis deviates inconspicuously from that of the temperature gradient. The experimental results of thermal diffusivity of highly oriented pyrolytic graphite (HOPG) samples with various deviation angles have been compared with the analytical results. The laser pulse method is not applicable to measurements on semitransparent pyrolytic boron nitride (PBN). We adopted a two-layer composite sample to measure the thermal diffusivity of PBN in the c direction and a particular graphite-PBN composite sample has been prepared which has a very low thermal resistance at the interface. The thermal diffusivity and thermal conductivity of PG (below 2300°C) and PBN (below 1000°C) are given.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Cu2S相变过程中热扩散系数的精确测量和解析

材料发生相变时, 其结构和物理性能可能会发生剧烈的变化。采用激光闪射法测量热扩散系数时, 激光照射样品可能会伴随有光吸收/发射现象以及温度的显著升高, 导致其测量值偏离真实值。本工作以Cu₂S为研究对象, 发现激光照射样品后, 光吸收/发射的影响很小可以忽略, 但样品温度的升高则会明显影响热扩散系数的测量。通过构建具有不同石墨层厚度的石墨/Cu₂S双层结构, 利用石墨层减弱激光照射时Cu₂S样品的温度增加幅度, 成功使热扩散系数出现显著降低的起始温度接近采用DSC测量材料发生相变的起始温度。本研究进一步建立了石墨/Cu₂S双层结构样品的热流输运模型, 从石墨/Cu₂S双层结构样品的实验测试热扩散系数中解析出了Cu₂S在相变区间的本征热扩散系数。本工作对于理解和精确表征具有相变特征的离子导体热电材料、光敏、热敏材料的热扩散系数具有重要的意义。     

An Experimental Study on Thermal and Electrical Properties of Packed Carbon Nanofibers

In the present study, the thermal and electrical properties of packed carbon nanofibers (P-CNFs) have been investigated. A short-hot-wire (SHW) technique was applied to determine simultaneously the thermal conductivity and thermal diffusivity of P-CNFs. In SHW measurements, a platinum wire coated with an alumina layer served as both the heating source and the thermometric sensor. A curve fitting method by matching the experimental data and numerical simulated values was proposed for determining the thermal conductivity and thermal diffusivity of P-CNFs with different packed densities. The electrical conductivities were measured by a four-terminal method where a special vessel with electrodes with circular plates was used. The results indicated that the electrical conductivity increases linearly with an increase in packed density. The thermal conductivity and thermal diffusivity also increase with an increase in packed density. The relation between the thermal conductivity and the electrical conductivity has been shown to be approximately linear. The SHW technique combined with the curve fitting method would be applicable to many kinds of materials.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China.     

Photopyroelectric Calorimetry Investigations of 8CB Liquid Crystal–Microemulsion System

In this work, the photopyroelectric technique has been used to investigate the phase transitions in a liquid crystal microemulsion by combining the simultaneous high temperature resolution thermal diffusivity measurements and optical polarization microscopy observations. It has been found that, during the conversion from the isotropic phase into the nematic one, the micelles are expelled from the nematic domains and remain confined in islands of isotropic material which survive down to the smectic temperature range. A hysteresis in the thermal diffusivity profiles between heating and cooling run over the isotropic–nematic transition temperature range has been observed which has been ascribed to the different micelles distribution into the sample volume during cooling and heating runs. Finally, the almost bulk-like behavior of the thermal diffusivity over the nematic–smectic phase transition confirms that a significant fraction of the micelles are expelled during the nucleation of the nematic phase.     

Experimental Verification to Obtain Intrinsic Thermal Diffusivity by Laser-Flash Method

There is a need to obtain highly reliable values of thermophysical properties. The thermal conductivity of solids is often calculated from the thermal diffusivity, specific heat, and density, respectively, measured by the laser-flash method, differential scanning calorimetry, and Archimedes’ method. The laser-flash method is one of the most well-known methods for measuring the thermal diffusivity of solids above room temperature. This method is very convenient to measure the thermal diffusivity without contact in a short time. On the other hand, it is considered as an absolute reference measurement method, in particular, because only measurements of basic quantities such as time, temperature, length, and electrical quantities are required, and because the uncertainty of measurement can be analytically evaluated. However, it could be difficult in some cases to obtain reliable thermal-diffusivity values. The measurement results can indeed depend on experimental conditions; in particular, the pulse heating energy. A procedure to obtain the intrinsic thermal-diffusivity value was proposed by National Metrology Institute of Japan (NMIJ). Here, “intrinsic” means unique for the material, independent of measurement conditions. In this method, apparent thermal-diffusivity values are first measured by changing the pulse heating energy at the same test temperature. Then, the intrinsic thermal diffusivity is determined by extrapolating these apparent thermal diffusivities to a zero energy pulse. In order to verify and examine the applicability of the procedure for intrinsic thermal-diffusivity measurements, we have measured the thermal diffusivity of some materials (metals, ceramics) using the laser-flash method with this extrapolation procedure. NMIJ and Laboratoire National de Metrologie et d’essais (LNE) have laser-flash thermal-diffusivity measurement systems that are traceable to SI units. The thermal diffusivity measured by NMIJ and LNE on four materials shows good agreement, although they used different measurement systems and different analysis methods of the temperature-rise curve. Experimental verification on the procedure was carried out using the measured results. Some problems and considered solutions for laser-flash thermal-diffusivity measurements are discussed.     

Evaluation of Thermophysical Properties of Functionally Graded Materials

In this work, by considering four-layered functionally graded material (FGM) specimens of Cu/Ni and PSZ/NiCrAlY, the transient characteristics and homogeneity of heat conduction media have been studied. The thermal diffusivities of the considered specimens have been measured by the laser flash method. As the temperature response curve of a FGM is very similar to that of a homogeneous material, it is difficult to distinguish a FGM from a homogeneous material by the shape of the temperature responses. Therefore, the thermal diffusivity obtained from the half-time method is usually taken as the corresponding value of the thermal diffusivity. The apparent thermal conductivity, obtained from the corresponding value of the thermal diffusivity and the average of the heat capacity of each layer, is different from the effective thermal conductivity, obtained from the sum of the heat resistances of each layer. As the values of the heat capacity of materials exist over a certain range, and the heat capacity distribution can be predicted when the materials in a FGM are known, the amount of error that will be caused when the effective thermal conductivity is replaced by the apparent value can be determined. Also, the heterogeneity of a FGM, based on an evaluation of thermophysical properties, has been discussed.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui,P. R. China.     

基于热成像的薄片材料热扩散率快速无损检测

针对传统热扩散率测量方法对热激励、边界和试样尺寸有严格要求等苛刻条件,提出一种适用于薄片材料的热扩散率测量新方法。该方法采用热成像技术采集受激光激励引起的材料表面温度场变化数据,将其通过曲线拟合对导热微分方程中的微分项进行估测,求取微分方程解析解转化为对代数方程求解以确定热扩散率值,因而无需严格控制边界条件、初始条件和热激励。通过仿真分析验证了理论模型的合理性,并对H62黄铜和304不锈钢材料进行了实测,对比文献参考值表明测量偏差均在6.0%以内,测量重复性为4.3%,可满足快速无损的测量要求。     

Thermal Diffusivity Measurements of Candidate Reference Materials by the Laser Flash Method

The National Metrology Institute of Japan (NMIJ) in AIST has investigated the laser flash method in order to establish a thermal diffusivity standard for solid materials above room temperature. A uniform pulse-heating technique, fast infrared thermometry, and a new data analysis method were developed in order to reduce the uncertainty in thermal diffusivity measurements. The homogeneity and stability of candidate reference materials such as isotropic graphite were tested to confirm their qualification as thermal diffusivity reference materials. Since graphite is not transparent to both the heating laser beam and infrared light for thermometry, the laser flash method can be applied to graphite without black coatings. Thermal diffusivity values of these specimens with different thicknesses, were measured with changing heating laser pulse energies. A unique thermal diffusivity value can be determined for homogeneous materials independent of the specimen thickness, by extrapolating to zero heating laser pulse energy on the plot of apparent thermal diffusivity values measured with the laser flash method as a function of heating laser pulse energy.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22--27, 2003, Boulder, Colorado, U.S.A.     

Failure parameters of heat-shielding materials in the nonstationary heating regime

A technique is presented for estimating the failure parameters of heat-shielding materials. The basic possibility of determining the coefficient of thermal diffusivity using the self-similar regime method in the presence of mass being carried away from the material surfaces is demonstrated. An analytic expression is proposed for calculating the times for establishing a quasistationary failure regime and heating depth.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 4, pp. 608–614, April, 1981.     

Recent development and applications of an optical method for measurements of thermophysical properties

The experimental determination of thermophysical properties has been greatly improved by the introduction of laser technology. The laser beam is used for sensing and also for heating (or exciting) the specimen. The advantage of using a laser beam is most strongly felt in the measurement of the thermal conductivity or the thermal diffusivity, which are some of the most difficult properties to measure. Interesting features of new techniques for investigating various aspects of thermal conductivity in fluids and solids are reviewed. An optical method, the so-called forced Rayleigh scattering method, or the laser-induced optical-grating method, has been developed and used extensively by the present author's group. The method is a high-speed remote-sensing method which can also quantitatively detect anisotropy, namely, direction dependence of heat conduction in the material. It was used for determination of the thermal diffusivity and its anisotropic behavior for high-temperature materials such as molten salts, liquid crystals, extended polymer samples, and flowing polymer melts under shear. Interesting applications of the method were demonstrated also for thermal diffusivity mapping and microscale measurement.Invited paper presented at the Twelfth symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

An Investigation of the Bias Caused by Surface Coatings on Material Loss Evaluation by Quantitative Thermography

The effect of a surface coating on the response of a metallic substrate to pulsed thermal excitation is examined with the view to assessing its impact on the efficacy of quantitative thermographic evaluation as applied to the problem of material loss evaluation. An analytical model describing the response of a layered structure to a surface thermal excitation has been developed and its predictions are shown to be in excellent qualitative agreement with experimental observations. The results indicate that for materials with high thermal diffusivity, a surface paint layer bears important influence on the development of the surface thermal response and should be taken into account when undertaking quantitative assessments of thermographic data.     

Thermal Conductivity during Phase Transitions

Thermal conductivity is a very basic property that determines how fast a material conducts heat, which plays an important and sometimes a dominant role in many fields. However, because materials with phase transitions have been widely used recently, understanding and measuring temperature‐dependent thermal conductivity during phase transitions are important and sometimes even questionable. Here, the thermal transport equation is corrected by including heat absorption due to phase transitions to reveal how a phase transition affects the measured thermal conductivity. In addition to the enhanced heat capacity that is well known, it is found that thermal diffusivity can be abnormally lowered from the true value, which is also dependent on the speed of phase transitions. The extraction of the true thermal conductivity requires removing the contributions from both altered heat capacity and thermal diffusivity during phase transitions, which is well demonstrated in four selected kinds of phase transition materials (Cu₂Se, Cu₂S, Ag₂S, and Ag₂Se) in experiment. This study also explains the lowered abnormal thermal diffusivity during phase transitions in other materials and thus provides a novel strategy to engineer thermal conductivity for various applications.     

基于复合相变材料的梯级组合蓄热特性研究

针对潜热蓄热装置内部相变材料(PCM)导热系数偏小,蓄热速率过低的问题,对基于复合相变材料的两级串联式梯级蓄热装置的相变过程进行了数值研究。通过对不同热物性PCM工况的对比与分析,得到了装置在不同工况下的蓄热特性。结果表明:PCM存在最佳的热扩散系数使固定熔点的PCM实现"均匀等速相变"。同时,增大PCM的热扩散系数可以有效降低加热面温度,但随着热扩散系数的增大,加热面温度降低幅度减小。通过分析Stefan数,得到了装置最佳的参数,使工况蓄热效果最佳。最后通过Stefan数为2. 88时的实验工况验证了相关规律的正确性。     

Integro-differential method of solving the inverse coefficient heat conduction problem

On the basis of differential transformations, a stable integro-differential method of solving the inverse heat conduction problem is suggested. The method has been tested on the example of determining the thermal diffusivity on quasi-stationary fusion and heating of a quartz glazed ceramics specimen.     

Analysis of Two-Dimensional Effect in the Measurement of Thermal Diffusivity of Thin Films with an AC Calorimetric Method1

An ac calorimetric method for measuring the thermal diffusivity of thin-film materials has been widely applied. In the application of this method, the systematic errors caused by the heat loss effect, the edge reflection effect, etc., have been analyzed and corresponding correction methods have been developed. But when measuring films with low thermal diffusivity or with thickness comparable to the thermal diffusion length, a two-dimensional effect which will also result in a systematic error of the measurement is present. In this paper, the mechanism of two-dimensional heat conduction within a thin sample which is supplied a periodic heat flux by a chopped light beam is analyzed. A numerical analysis method is developed to study the effect of the two-dimensional heat conduction on the measured thermal diffusivity values. The relations between the measured thermal diffusivity and independent parameters such as frequency, thickness of sample, width of light spot, etc., are demonstrated to indicate the two-dimensional effect. The experimental precondition for minimizing the systematic error caused by the two-dimensional effect is determined. In addition, the analysis method presented in this paper should be useful for more difficult problems such as error estimation of the thermal diffusivity measurement of coatings or composite films.