Determining Thermal Conductivity and Thermal Diffusivity of Low-Density Gases Using the Transient Short-Hot-Wire Method

The transient short-hot-wire method for measuring thermal conductivity and thermal diffusivity makes use of only one thermal-conductivity cell, and end effects are taken into account by numerical simulation. A search algorithm based on the Gauss–Newton nonlinear least-squares method is proposed to make the method applicable to high-diffusivity (i.e., low-density) gases. The procedure is tested using computer-generated data for hydrogen at atmospheric pressure and published experimental data for low-density argon gas. Convergence is excellent even for cases where the temperature rise versus the logarithm of time is far from linear. The determined values for thermal conductivity from experimental data are in good agreement with published values for argon, while the thermal diffusivity is about 10 % lower than the reference data. For the computer-generated data, the search algorithm can return both thermal conductivity and thermal diffusivity to within 0.02 % of the exact values. A one-dimensional version of the method may be used for analysis of low-density gas data produced by conventional transient hot-wire instruments.     

Measurement of the In-plane Thermal Diffusivity of Materials by Infrared Thermography

A transient method using the Laplace transform for estimation of the in-plane thermal diffusivity of low conductive materials is presented. The temperature field of the sample is measured by infrared thermography. The main interest of the technique proposed here is to not require a knowledge of the stimulation and boundary conditions by using two reference temperature profiles. The parameter estimation is implemented in the time domain by an inverse technique using numerical Laplace inversion and convolution products. A sensitivity study has been carried out to optimize the choice of the two reference profiles. The effect of a space varying heat transfer coefficient on the estimated values of the unknown parameters has also been evaluated. Finally, the apparatus is described and experimental results obtained for a low conductive material like a vitroceramic are shown.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom.     

Contactless method of determining the coefficient of thermal diffusivity of local domains of surface layers and thin films

A method is proposed for measuring the coefficient of thermal diffusivity of microsections of surface layers and thin films. The coefficient of thermal diffusivity is calculated from the time dependence of the heat flux emitted by the heated surface.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 2, pp. 289–294, August, 1976.     

Thermal diffusivity of solids with a low expansion coefficient: A dilatometric technique

A dilatometric method is presented, suitable to obtain both thermal diffusivity and conductivity of low-conducting solids with a low expansion coefficient. The repeatibility of the measurements of thermal conductivity is 3%, whereas that for diffusivity is 5 %. Data for fused silica at room temperature are given, consistent with those reported in the literature. Since the method is based on detecting the thermal expansion of a copper disk in thermal contact with the specimen, its range of applicability is linked to the sensitivity by which the dilation of copper can be measured: no difficulty arises between liquid nitrogen and 1000°C.     

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。     

Contribution to the Sensitivity Coefficients Analysis in the Extended Dynamic Plane Source (EDPS) Method

This work reports on a method for measuring thermophysical properties (thermal conductivity and diffusivity) of materials. The theory of the dynamic plane source method and experimental apparatus is described. The contribution of this work is the determination of the time interval within which the fitting procedure should be applied. A new algorithm for sensitivity coefficient analysis is presented, and the results are compared with those of a difference analysis of experiment modelling.     

Thermal Transport Properties of Layered Materials: Identification by a New Numerical Algorithm for Transient Measurements

Transient methods are widely used to determine thermal transport properties. In some situations they can be used for homogeneous media to measure several properties either simultaneously or separately. In this context an analytic model is available and a well-posed inverse problem of parameter identification has to be solved. The examination of composite media is more complicated. The algorithm proposed here allows simultaneous determination of the thermal conductivity and thermal diffusivity of layered dielectrics by transient measurements. It is based on a plane source that acts both as a resistive heater and temperature sensor. For the technique to be successful two essential aspects have to be considered: firstly, the mathematical modeling of the measured data (the forward problem) and secondly, the problem of ill-posedness of the inverse problem. For the proposed measurement configuration, a new fast data analysis algorithm based on an analytic solution for the forward problem is presented. In principle, a numerical solution such as an FEM solution of the heat conduction equation can be used instead of the analytical one, but the computational effort is much greater. The inverse problem is formulated as an output-least-squares problem, which leads to a transcendent algebraic system of equations. The method was successfully tested for different situations.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22--27, 2003, Boulder, Colorado, U.S.A.     

Determination of the Thermal Diffusivity of Electrically Non-Conductive Solids in the Temperature Range from 80 K to 300 K by Laser-Flash Measurement

The adoption of the popular laser-flash method at temperatures far below 300 K is restricted by the weak signal-to-noise ratio and the limited spectral bandwidth of the commonly used mercury cadmium tellurite (MCT) infrared (IR) detector used as a non-contacting temperature probe. In this work, a different approach to measure the temperature rise in pulse heating experiments is described and evaluated. This method utilizes the change of the temperature-dependent electrical resistance of a thin strip of sputtered gold for the detection of a temperature rise as it was proposed by Kogure et al. The main advantage of this method at lower temperatures is the significantly higher signal-to-noise ratio compared to the commonly used IR detectors. A newly developed laser-flash apparatus using this detection method for the determination of the thermal diffusivity in the temperature range from 80 K to 300 K is presented. To test the accuracy of the new detection method, the thermal diffusivity of a borosilicate crown glass (BK7) specimen at 300 K was determined and compared to results derived with a MCT detector. Good agreement of the derived thermal diffusivity values within 3 % was found. The thermal diffusivity of BK7 and polycrystalline aluminum nitride (AlN) was measured at temperatures between 80 K and 300 K by a laser-flash method to test the functionality of the apparatus. Finally, the thermal conductivity was calculated using values for the specific heat capacity determined by temperature modulated differential scanning calorimetry (MDSC). Comparisons with literature data confirm the reliability of the experimental setup.     

Uncertainty of Thermal Diffusivity Measurements by Laser Flash Method

The laser-pulse method is a well-established nonsteady-state measurement technique for measuring the thermal diffusivity, a, of solid homogeneous isotropic opaque materials. BNM-LNE has developed its own bench based on the principle of this method in which the thermal diffusivity is identified according to the “partial time moments method.” Uncertainties of thermal diffusivity by means of this method have been calculated according to the ISO/BIPM “Guide to the Expression of Uncertainty in Measurement.” Results are presented for several cases (Armco iron, Pyroceram 9606) in the temperature range from 20 to 800°C. The relative expanded (k = 2) uncertainty of the thermal diffusivity determination is estimated to be from ±3 to ±5%, depending on the material and the temperature. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal Diffusivity Measurement of High-Conductivity Materials by Dynamic Grating Radiometry

A new apparatus based on dynamic grating radiometry (DGR) to measure the thermal diffusivity of high-conductivity materials such as graphite and diamond has been developed. In the DGR method, a sample surface is heated by interference of two pulsed laser beams, and the decay of temperature at a spot on the thermal grating is monitored by an infrared detector. In the ideal case where the grating period is much smaller than the light absorption length, the thermal diffusivity parallel to the surface can be determined from the decay constant and the grating period. This paper describes a procedure to extract the thermal diffusivity parallel to the plane while eliminating the effect of anisotropy and gives results for a preliminary measurement using Zr foil. A quadratic dependence of the time constant on fringe space has been observed in the fringe space change. Data are also presented for a 0.1-mm-thick graphite sheet. The results indicate the capability of DGR to measure anisotropic high-conductivity materials.     

Nichtlineares inverses Wärmeleitungsproblem bei der Überwachung von Wärmespannungen

A new method to solve the problem of transient heat conduction in cylindrical bodies is presented. This method allows transient temperature and thermal stress distribution to be determined from interior temperature histories. The thermal stresses at the inner surface can be estimated by a temperature sensor placed only at the outer surface. The problem of inverse heat conduction was solved using the least squares method with the following stabilizing techniques: smoothing of the temperature-time curves, regularization of the inverse algorithm, future time steps. Two examples are shown to demonstrate the influence of the number of temperature sensors on the accuracy of the calculation. In a third example, the developed method is used to calculate the temperature coefficient and thermal stresses at the inner surface of a thick-walled cylinder using temperature histories from three locations on the outer surface.     

Analytical study for the estimation of thermal properties of processed meat based on hyperbolic heat conduction model

This study proposes an analytical method in conjunction with existing experimental temperature to estimate the unknown relaxation time and thermal diffusivity of processed meat based on the hyperbolic heat conduction model. This analytical method is a combination of the Laplace transform and least squares methods. The thermal contact resistance at the interface between adjacent samples at different temperatures is assumed to be negligible. The relaxation time is estimated from the temperature jump at a specific measurement location. The thermal diffusivity is determined from the definition of the dimensionless spatial coordinate and the resulting relaxation time. The results show that the relaxation time and thermal diffusivity obtained are in good agreement with the existing results. The obtained dimensionless temperature history at a specific measurement location is close to the experimental temperature data. This means that the Cattaneo–Vernottee (CV) model can be suitable for this study. The proposed analytical inverse method can be applied to determine a more accurate estimate of such problems. A comparison of the estimate obtained from CV and dual phase lag models is made.     

Combined effect of thermal dispersion and radiation on free convection in a fluid saturated, optically thick porous medium

The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton–Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.     

Measurement of thermal diffusivity by the flash method for a two-layer composite sample in the case of triangular pulse

A method for measuring thermal diffusivity in one of the layers of a two-layer composite sample has been described. The heat transfer problem of a two-layer sample associated with pulse thermal diffusivity measurements has been analyzed for two cases: exponential and square-wave pulses. According to our measurements, a triangular heat-pulse function approximates reasonably well the output of the Nd-glass laser. In this paper, an expression is derived for the temperature transient at the rear face of two-layer sample being subjected to a triangular heat-pulse input on the front face. The analytical solution of the problem forms the basis of our method of data reduction. This solution has been programmed for computer processing of the data. The method described here has been successfully tested by limited measurements on copper and iron.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Application of the Thermal Quadrupoles Method to Semitransparent Solids

In this study, the thermal quadrupoles method is extended to semitransparent layered solids. Using this method, the surface temperature of semitransparent multilayered materials is calculated as a function of the optical and thermal properties of each layer. This result eventually leads to determination of the thermal diffusivity, thermal resistance, and/or optical absorption coefficient of layered materials using photothermal techniques. The thermal quadrupoles method is applied to determine the thermal contact resistance in glass stacks.     

基于热成像的材料热扩散率测量方法研究

将一种基于热成像的薄片材料热扩散率测量方法的理论模型由二维拓展到三维,以适用于更大厚度材料的热扩散率测量。指出该方法适用的特征条件为:Z向空间导数值与材料表面和周围环境的温度差值为线性关系。仿真分析了传热距离与激励时间对特征条件的影响以及相关的信噪比问题,并在304不锈钢材料实测实验中依照仿真分析设置传热距离和激励时间以满足特征条件,结果显示厚度为1 mm和2 mm的不锈钢材料测量偏差均在3.0%以内,厚度为5 mm的不锈钢材料测量的偏差为4.1%,从而扩大了该测量方法的适用范围。     

Laser-produced plasma measurement of thermal diffusivity of molten metals

We have shown that a laser-produced plasma plume which is representative in elemental composition of the condensed phase target can be reproducibly generated if the movement of the surface due to evaporation is kept in pace with the thermal diffusion front propagating into the bulk. The resulting mass loss is then strongly controlled by the thermal diffusivity of the target matter, and this relationship has been exploited to measure the thermal diffusivity of metallic alloys. We have developed a novel RF Ievitator-heater as a contamination-free molten metal source to be used as a target for LPP plume generation. In order to determine the mass loss due to LPP excitation, a new high-sensitivity transducer has been constructed for measurement of the resulting impulse imparted on the specimen. The impulse transducer is built onto the specimen holder within the levitation-assisted molten metal source. The LPP method has been fully exercised for measurement of the thermal diffusivity of a molten specimen relative to the value for its room temperature solid. The results for SS304 and SS316 are presented, together with a critique of the results. A numerical modeling of the specimen heating in the molten metal source and the physical basis of the new method are also presented.Paper presented at the Fourth International Workshop on Subsecond Thermophysics, June 27–29, 1995, Köln, Germany.     

Theoretical considerations of the effects of rapid heating of solids on their apparent thermal properties

The conditions are investigated for thermal properties to change from their normal values when solids are heated very rapidly. The properties considered are specific heat, thermal expansion, thermal conductivity, and thermal diffusivity. Over times which may be as long as a microsecond, the heated solid is unable to expand: the appropriate values of specific heat and thermal conductivity are then those at constant volume rather than constant pressure. In those alloys where thermal equilibrium requires diffusion, its establishment is delayed, and if solids do not have time to expand, the diffusion coefficient is reduced. For heating times below nanoseconds, the electrons and the lattice may be at different temperatures, particularly if the energy is initially imparted to the electrons. The temperature of the electron gas of metals may then approach the degenerary temperature. The apparent specific heat of a decoupled system departs from the steady-state value in a manner which depends on how temperature is measured. In such a decoupled system the concepts of thermal conductivity and thermal diffusivity must be used with care.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.     

Mass Diffusion and Thermal Diffusivity of the Decane-pentane Mixture Under High Pressure as a Ground-based Study for SCCO Project

Thermodiffusion experiments on isomassic binary mixture of decane and pentane in the liquid phase have been performed between 25 ^°C and 50 ^°C and for pressures from 1MPa until 20MPa. By dynamic analysis of the light scattered by concentration non-equilibrium fluctuations in the binary mixture we obtained the mass diffusion coefficients of the mixture at each temperature and pressure. For the first time we were able to apply similar analysis to thermal fluctuations thus getting a simultaneous measurement of the thermal diffusivity coefficient. While mass diffusion coefficients decrease linearly with the pressure, thermal diffusivity coefficients increase linearly. In principle the proposed method can be used also for measuring the Soret coefficients at the same time. However, for the present mixture the intensity of the optical signal is limited by the optical contrast factor. This affects our capability of providing a reliable estimate of the Soret coefficient by means of dynamic Shadowgraph. Therefore the mass diffusion coefficients measurements would need to be combined with independent measurements of the thermodiffusion coefficients, e.g. thermogravitational column, to provide Soret coefficients. The obtained values constitute the on-ground reference measurements for one of the mixture studied in the frame of the project SCCO-SJ10, which aims to measure the Soret coefficients of multicomponents mixtures under reservoir conditions. Microgravity experiments will be performed on the Chinese satellite SJ10 launched in April 2016.     

Measurement of the thermal diffusivity of molten KCl up to 1000°C by the forced Rayleigh scattering method

This paper describes measurement of the thermal diffusivity of molten KCl in the temperature range from 804 to 1030°C by the forced Rayleigh scattering method. In this contact-free optical measuring technique for the thermal diffusivity of liquids, a sample needs to be colored by the admixture of a dye for suitable absorption of a heating laser beam. The dye substances employed are CoCl₂ and NiCl₂, which were chosen through the experimental evaluation. The accuracy is estimated to be ±7% for molten KCl colored with NiCl₂. The results converted to thermal conductivity show one of the smallest values among other previous data; the difference is a factor of four. The present study demonstrates the promising applicability of the forced Rayleigh scattering method to the measurement of high-temperature molten salts, which has never be attained by other conventional methods.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.