Measurement of Thermal Transport Properties with an Improved Transient Plane Source Technique

The transient plane source (TPS) technique has been revised with the aim of developing a simple and fast system to measure the thermal transport properties of materials at low temperatures, especially high-T _c superconductors. To ensure reliable results, any new system should be tested with known samples. Fused silica, 0.9% carbon steel (215/3), and halide crystals (silver chloride) were studied with the new setup to check its performance. Data were taken from room temperature down to liquid nitrogen temperature. The assembly was designed for cryogenic (79 to 300 K) measurements in an atmosphere free of humidity. Dry nitrogen gas was used as a heat transfer medium around the sample holder assembly. The measured values for thermal conductivity and thermal diffusivity of these samples are in excellent agreement with values reported earlier. The thermal conductivity and thermal diffusivity for silver chloride crystals are extended down to 80 K although recommended data were available only down to 220 K. A Ba-doped, Bi-based, high-T _c superconductor was prepared by a solid-state reaction method. The nominal composition used was Bi_1.6Pb_0.4Sr_1.6Ba_0.4Ca₂Cu₃O_y. Large-sized samples (diameter 28mm and length 11mm) are investigated for thermal transport properties.     

Simultaneous Measurements of the Thermal Conductivity and Thermal Diffusivity of Molten Salts with a Transient Short-Hot-Wire Method

A transient short-hot-wire technique has been successfully used to measure the thermal conductivity and thermal diffusivity of molten salts (NaNO₃, Li₂CO₃/K₂CO₃, and Li₂CO₃/Na₂CO₃) which are highly corrosive. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a short wire with the same length-to-diameter ratio and boundary conditions as those used in the actual experiments. In the present study, the wires are coated with a pure Al₂O₃ thin film by using a sputtering apparatus. The length and radius of the hot wire and the resistance ratio of the lead terminals and the entire probe are calibrated using water and toluene with known thermophysical properties. Using such a calibrated probe, the thermal conductivity and thermal diffusivity of molten nitrate are measured within errors of 3 and 20%, respectively. Also, the thermal conductivity of the molten carbonates can be measured within an error of 5%, although the thermal diffusivity can be measured within an error of 50%.     

Thermophysical Properties of Heterogeneous Structures Measured by Pulse Transient Method

This paper discusses differences in thermophysical parameters (thermal conductivity λ, thermal diffusivity a, and specific heat c) that can be found when experimental methods with different measuring regimes are used. Two classes of methods are compared, namely, classical methods using steady-state, equilibrium, and dynamic measuring regimes and transient methods. The data consistency formula λ = acρ gives a picture on data reliability when single-parameter methods are used. Results of analysis are verified on published, recommended, and measured data by transient methods considering homogenous materials (stainless steel A 310, BK 7, Perspex) and heterogeneous materials (composite C/C–SiC, aerated autoclaved concrete). Satisfactory agreement on data for the thermophysical parameters was found on homogenous materials only. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal Diffusivity Measurements of Liquid Silicate Melts

The effect of structure on the thermal diffusivities/conductivities for liquid silicates have been summarized based on recent experimental work carried out by the Royal Institute of Technology, Stockholm and the Tokyo Institute of Technology using the laser-flash and the hot-wire methods, respectively. In the former case, the effective thermal diffusivity was measured by a three-layer method. The relationship proposed by Mills that the thermal conductivity of silicates increases with a decrease in the ratio of NBO/T (number of non-bridging oxygens per tetrahedrally coordinated atom) has been well supported by the effective thermal diffusivity data for the liquid CaO-Al₂O₃-SiO₂ slags. However, it has been shown that for the slags having a higher CaO/Al₂O₃ ratio, the effective thermal diffusivity is roughly constant independent of the ratios of NBO/T. It has been concluded that when the silicate network is largely broken down, the phonon mean free path is not affected by the structure. It has been found by the hot-wire method that the magnitudes of thermal resistivity are in the hierarchy Li₂O-SiO₂2O-SiO₂2O-SiO₂ despite their similar values of NBO/T. It has been concluded that the ionicity of non-bridging oxygen ions is also a factor controlling the thermal conductivity of silicates as well as the number of broken bridges in the silicate network. The effective thermal diffusivity was measured for the CaO-Al₂O₃-SiO₂-FeO system to elucidate the radiation contribution to the effective thermal diffusivity. It has been found that the effective thermal diffusivity increases with an increase in FeO content. It can be considered that the strong absorption and emission within the liquid slag films caused by the Fe²⁺ ions enhances the photon heat transfer.     

New Transient Hot-Bridge Sensor to Measure Thermal Conductivity, Thermal Diffusivity, and Volumetric Specific Heat

A high sensitivity thermoelectric sensor to measure all relevant thermal transport properties has been developed. This so-called transient hot bridge (THB) decidedly improves the state of the art for transient measurements of the thermal conductivity, thermal diffusivity, and volumetric specific heat. The new sensor is realized as a printed circuit foil of nickel between two polyimide sheets. Its layout consists of four identical strips arranged in parallel and connected for an equal-ratio Wheatstone bridge. At uniform temperature, the bridge is inherently balanced, i.e., no nulling is required prior to a run. An electric current makes the unequally spaced strips establish an inhomogeneous temperature profile that turns the bridge into an unbalanced condition. From then on, the THB produces an offset-free output signal of high sensitivity as a measure of the properties mentioned of the surrounding specimen. The signal is virtually free of thermal emf’s because no external bridge resistors are needed. Each single strip is meander-shaped to give it a higher resistivity and, additionally, segmented into a long and short part to compensate for the end effect. The THB closely meets the specific requirements of industry and research institutes for an easy to handle and accurate low cost sensor. As the key component of an instrument, it allows rapid thermal-conductivity measurements on solid and fluid specimens from 0.02 to 100 W· m⁻¹·K⁻¹ at temperatures up to 250°C. Measurements on some reference materials and thermal insulations are presented. These verify the preliminary estimated uncertainty of 2% in thermal conductivity.     

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.     

Multidimensional Flash Diffusivity Measurements of Orthotropic Materials

A generalization of the radial flash technique is presented whereby the thermal diffusivity of an orthotropic solid is measured in directions parallel and perpendicular to the flash source. The theoretical formulation is based on a Green's function approach which assumes a general orthotropic solid with three mutually orthogonal thermal diffusivities (or conductivities). Using this approach, a solution to this problem is presented which can be used to develop solutions for arbitrary pulse waveforms and incident geometries. Analytical and numerical results are presented for two-dimensional and three-dimensional cases of finite and semiinfinite solids. Characteristic equations which describe the ratio of the temperatures at two points along a principal axis are given. The equations show excellent agreement with numerical predictions as well as experimental results. A parameter estimation approach is given which improves on the accuracy of the radial flash technique in the determination of thermal diffusivity from experimental data.     

Thermal Diffusivity of Semitransparent Materials Determined by the Laser-Flash Method Applying a New Analytical Model

We have developed an analytical model to determine the thermal diffusivity of nonscattering materials from samples with low optical thickness and opaque boundaries with arbitrary emissivities. The paper outlines the new analytical model and describes measurements on two samples: a microscope slide glass and a high-grade fused quartz plate. Results show that the new model applied to measurements on gold- or graphite-coated samples leads to the same results as if a conventional model is used on gold-coated samples.     

Thermal Transport Properties of Water and Ice from One Single Experiment

For the first time, the transient hot wire (THW) and the transient hot strip (THS) techniques were used to measure the thermal conductivity and thermal diffusivity of ice and the thermal conductivity of liquid water simultaneously in one run. With the additional knowledge of the thermal diffusivity of water from a subsequent single-phase run, the latent heat of melting can be determined as well as the time dependent position of the interface between both phases during an experiment. The results of the dual-phase measurements are compared with those obtained in the single-phase experiments using the same simple setup. The composite THS and THW signals are interpreted based on the underlying phase-change-theory of Stefan and Neumann, as outlined briefly in the text.     

Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method

In this paper, the thermal conductivity and thermal diffusivity of four kinds of polymer melts were measured by using the transient short-hot-wire method. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a wire with the same length-to-diameter ratio and boundary conditions as those in the actual experiments. The present method is particularly suitable for measurements of molten polymers where natural convection effects can be ignored due to their high viscosities. The results have shown that the present method can be used to measure the thermal conductivity and thermal diffusivity of molten polymers within uncertainties of 3 and 6%, respectively. Further, the thermal conductivity and thermal diffusivity of solidified samples were also measured and discussed.     

Measurements of the Thermal Conductivity of Molten Lead Using a New Transient Hot-Wire Sensor

The paper reports new measurements of the thermal conductivity of molten lead at temperatures from 600 to 750 K. The measurements have been carried out with an updated version of a modified transient hot-wire (THW) method, where the hot-wire sensor is embedded within an insulating substrate with a planar geometry. However, unlike previous sensors of the same type, the updated sensor works with the hot-wire divided into three thermally isolated parts. The operation of this sensor has been modeled theoretically using a finite-element (FE) analysis and has subsequently been confirmed by direct observation. The new sensor is demonstrated to have a higher sensitivity and a better signal-to-noise ratio than earlier sensors. Molten lead is used as the test fluid. It has the lowest thermal conductivity of any material we have yet studied. This allows us to probe the limits of our sensor system for the thermal conductivity of high-temperature melts. It is estimated that the uncertainty of the measurements is 3% over the temperature range studied. The results are used to examine the application of the Wiedemann–Franz (W-F) relationship.     

A High-Temperature Transient Hot-Wire Thermal Conductivity Apparatus for Fluids

A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-power-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the response of the primary wire. Both hot wires are 12.7 µm diameter platinum wire and are simultaneously used as electrical heat sources and as resistance thermometers. A microcomputer controls bridge nulling, applies the power pulse, monitors the bridge response, and stores the results. Performance of the instrument was verified with measurements on liquid toluene as well as argon and nitrogen gas. In particular, new data for the thermal conductivity of liquid toluene near the saturation line, between 298 and 550 K, are presented. These new data can be used to illustrate the importance of radiative heat transfer in transient hot-wire measurements. Thermal conductivity data for liquid toluene, which are corrected for radiation, are reported. The precision of the thermal conductivity data is ± 0.3% and the accuracy is about ±1%. The accuracy of the thermal diffusivity data is about ± 5%. From the measured thermal conductivity and thermal diffusivity, we can calculate the specific heat, C_p, of the fluid, provided that the density is measured, or available through an equation of state.     

电阻瞬态法测定材料的传热性能

利用导体的电阻温度关系,讨论了精确测定导体的电阻,实现瞬态测定材料传热性能的理论和方法。利用这种方法,可以精确测量从金属到热的不良导体等众多固体材料的传热性能。     

A Transient Heating Technique for Measuring the Thermal Diffusivity of Metals

A transient heating technique, improving the constant-rate-heating technique for the measurements of thermal diffusivities of metals, is proposed. For a physical model of a specimen to be measured, the transient heat-conduction equation was solved with some boundary conditions, and the solution obtained was used as the principle of the present transient heating technique for determining the thermal diffusivity of the specimen. Additionally, a thermal analysis was made to satisfy a boundary condition involved in the principle, that is, the condition of radiative thermal insulation at the two end surfaces of the specimen. To verify the validity of the present technique, the thermal diffusivity of iron, whose thermophysical properties are well-known, was measured with the same apparatus as used in our previous work, and the experimental results are discussed. Moreover, thermal diffusivities of thermocouple materials, namely, constantan, chromel, and alumel, were measured by the technique in the temperature range of 360 to 680 K.     

瞬态热传导问题的修正变分原理及其数值算法

本文采用拉格朗日乘子将本征边界条件引入到瞬态热传导问题的泛函方程,通过变分原理得到了其修正泛函.采用Galerkin无网格法在空间域内进行离散,得到瞬态热传导问题的半离散方程;在时间域上通过与Romberg积分相结合的精细积分法求解,并且推导了瞬态热传导方程中精细积分的普遍适应的公式,结合数值算例对方法的有效性和精确性进行了验证.     

Thermophysical Parameters of Optical Glass BK 7 Measured by the Pulse Transient Method

This paper is focused on the pulse transient method. The theory of the method and the measuring regime (time window) are analyzed. The results of the analysis are verified on borosilicate crown glass BK7, which is a candidate for a standard for thermal conductivity. Thermal contact and surface effects affect the length of the time window in which the evaluation procedure is applied. The one-point evaluation technique is compared with the results of the fitting procedure that uses the time window found by difference analysis. The values of the thermal conductivity, thermal diffusivity, and specific heat were found to be 1.05 W· m^–1 · K^–1, 0.548 × 10^–6m ^{– 2} · s^–1, and 767 J· kg^–1 · K^–1, respectively, using the one-point evaluation technique.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom.     

Thermal Conductivity Measurements of Liquid Mercury and Gallium by a Transient Hot-Wire Method in a Static Magnetic Field

The transient hot-wire method, incorporating a static magnetic field, has been developed to measure thermal conductivities of liquid mercury and gallium. Prior to the measurements, the effect of an alumina-coated hot wire on the measurements has been evaluated. Natural convection in the liquid metals has been effectively suppressed by the Lorentz force acting on the liquid metals in a static magnetic field. The thermal conductivities of liquid mercury and gallium have been determined to be 7.9 W.m ⁻¹.K ⁻¹ at 291 K and 24 W.m ⁻¹.K ⁻¹ at 302.9 K, respectively.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

The Transient Hot-Wire Technique: A Numerical Approach

The measurement of the thermal conductivity of a fluid by means of the transient hot-wire technique so far has made use of an analytical solution of the energy conservation equation for an ideal model, coupled with a set of approximate analytical corrections to account for small departures from the model. For this solution to be valid, constraints were always imposed on the experimental conditions and the construction of the apparatus, resulting in an inability to measure the thermal conductivity of high-thermal diffusivity fluids. In this paper, the set of energy conservation equations describing the transient hot-wire apparatus is solved using the numerical finite-element method. Because no approximate solutions are involved, this provides a much more general treatment of the heat transfer processes taking part in the real experiment, removing all the aforementioned constraints. In the case of the measurement of the thermal conductivity of liquids (fluids with low thermal-diffusivity values), the numerical solution fully agrees with the existing analytical solution. In the case of the measurement of the thermal conductivity of gases, the present solution allows the extension of the application of the transient hot-wire technique to experimental conditions where the value of the thermal diffusivity of the fluid is high.     

Estimation of the Mean Thermal Conductivity of Anisotropic Materials

An estimation method of the plane directional thermal conductivity of fibrous insulations using the cyclic heat method and the transient hot-wire method is proposed. By assuming that the thermal conductivity _h of anisotropic materials measured by the transient hot-wire method is equivalent to that of the isotropic materials which have the same bulk density and specific heat c as the anisotropic materials, the thermal conductivity _h is shown to be equal to , which is a geometrical mean of the thermal conductivities in the direction of the plane _x and the thickness _y of the anisotropic materials. For an alumina silica blanket (=125 kg·m^–3), the thermal conductivities _h , _x , and _y were measured in the temperature range between –140 and 300°C using the transient hot-wire method for _h and the cyclic heat method for _x and _y . In the same way, the thermal conductivities _h , _x , and _y of a rock wool (=121 kg·m^–3) insulation were also measured in the temperature range, 100 to 600°C. From a comparison of the measured results with the estimated values of _x , it is confirmed that the proposed method can estimate the measured values reasonably well.     

The Development of a Standard for Contact Transient Methods of Measurement of Thermophysical Properties

Contact transient methods, some of which are available as commercial forms, are now widely used worldwide for thermal properties measurements on broad ranges of materials used in physical, chemical, and medical applications. However, in many cases the claimed measurement uncertainty has not been substantiated while in others – especially for the multiproperty techniques – internal inconsistencies in measured and/or derived values are clearly apparent. Following recommendations of participants of two workshops held on the subject in Würzburg (1999) and Cambridge, Massachussetts (2001), NPL agreed to coordinate a task to develop a standard test-method for these techniques. This involved using inputs provided by a small group of individuals from organizations in several European countries and also taking note of comments from other interested parties via the internet during the course of the development. Details are provided on the resulting document, which takes the form of a generic standard containing appropriate details and related information common to all techniques. These sections include the scope, theory, summaries of method, basic apparatus and experiment, the influencing factors, specimen requirements, procedure, and recommended approach for analysis of the experiment and calculation of the results. In addition, there are six annexes, each of which contains additional information that applies to a specific technique. Finally, the document proposes a recommended approach for verification of a technique together with a list of appropriate reference materials having known values for one or more properties. The status of intercomparison studies will also be reported. Paper presented as the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder.