Transient Hot Wire (THW) Method: Uncertainty Assessment

The standard method for measuring thermal transport properties of dielectric solids such as ceramics and refractories is the transient hot wire (THW) technique. In its simplest arrangement, a thin wire is embedded between two sample halves, where it acts simultaneously as a resistive heat source and a thermometer. From its temperature signal, the thermal conductivity and the thermal diffusivity of the dielectric can be derived. Up to now, there is no uncertainty assessment for this technique strictly following the ISO Guide to the Expression of Uncertainty in Measurement. Here we analyze the ISO standard uncertainty of the THW technique in the same way as in a previous paper on the uncertainty of the closely related transient hot strip (THS) technique. The two papers provide a comprehensive comparison of the most important advantages and disadvantages of these two transient techniques. The results obtained here for the uncertainty (5.8% for the thermal conductivity and 30% for the thermal diffusivity) are nearly the same as those for the THS method. Experiments on a Pyrex standard-reference sample confirm the results.     

A Quasi-Steady State Technique to Measure the Thermal Conductivity

A new method is developed for the measurement of thermal conductivity. It combines characteristic advantages of steady-state and transient techniques but avoids major drawbacks of both these classes of methods. On the basis of a simple transient hot wire (THW) or transient hot-strip (THS) arrangement, a direct indicating thermal-conductivity meter is realized by adding only one temperature sensor. After a short settling time during which all transients die out, the instrument operates under quasi-steady state conditions. No guard heaters are required because outer boundaries are free to change with time. The instrument's uncertainty is provisionally estimated to be 3%.     

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.     

Absolute Steady-State Thermal Conductivity Measurements by Use of a Transient Hot-Wire System

A transient hot-wire apparatus was used to measure the thermal conductivity of argon with both steady-state and transient methods. The effects of wire diameter, eccentricity of the wire in the cavity, axial conduction, and natural convection were accounted for in the analysis of the steady-state measurements. Based on measurements on argon, the relative uncertainty at the 95 % level of confidence of the new steady-state measurements is 2 % at low densities. Using the same hot wires, the relative uncertainty of the transient measurements is 1 % at the 95 % level of confidence. This is the first report of thermal conductivity measurements made by two different methods in the same apparatus. The steady-state method is shown to complement normal transient measurements at low densities, particularly for fluids where the thermophysical properties at low densities are not known with high accuracy.     

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 Conductivity of Saturated Liquid Toluene by Use of Anodized Tantalum Hot Wires at High Temperatures

Absolute measurements of the thermal conductivity of a distilled and dried sample of toluene near saturation are reported. The transient hot-wire technique with an anodized tantalum hot wire was used. The thermal conductivities were measured at temperatures from 300 K to 550 K at different applied power levels to assess the uncertainty with which it is possible to measure liquid thermal conductivity over wide temperature ranges with an anodized tantalum wire. The wire resistance versus temperature was monitored throughout the measurements to study the stability of the wire calibration. The relative expanded uncertainty of the resulting data at the level of 2 standard deviations (coverage factor k = 2) is 0.5 % up to 480 K and 1.5 % between 480 K and 550 K, and is limited by drift in the wire calibration at temperatures above 450 K. Significant thermal-radiation effects are observed at the highest temperatures. The radiation-corrected results agree well with data from transient hot-wire measurements with bare platinum hot wires as well as with data derived from thermal diffusivities obtained using light-scattering techniques.     

A New Pulse Hot Strip Sensor for Measuring Thermal Conductivity and Thermal Diffusivity of Solids

The pulse hot strip method is a newly developed dynamic method to measure the thermal conductivity and thermal diffusivity of solids. It is based on monitoring the temperature response of a sample to a very short heat pulse liberated by a strip heat source. The instrument's uncertainty is estimated to be less than 3% for both quantities.     

Measurement of the Thermal Conductivity of Stainless Steel AISI 304L Up to 550 K

New measurements of the thermal conductivity of stainless steel AISI 304L over the temperature range 300 to 550 K are reported. To perform the measurements, the transient hot-wire technique was employed, with a new wire sensor. The sensor makes use of a soft silicone paste material and of two thin polyimide films, between the hot wires of the apparatus and the stainless steel specimen. The transient temperature rise of the wire sensor is measured in response to an electrical heating step over a period of 40 s to 2 s, allowing an absolute determination of the thermal conductivity of the solid, as well as of the polyimide film and the silicone paste. The method is based on a full theoretical model with equations solved by a two-dimensional finite-element method applied to the exact geometry. At the 95% confidence level, the standard deviation of the thermal conductivity measurements is 0.6%, while the standard uncertainty of the technique is less than 1.5%.     

The Thermal Conductivity, Thermal Diffusivity and Isobaric Heat Capacity of Toluene and Argon

This paper presents absolute measurements for the thermal conductivity and thermal diffusivity of toluene obtained with a transient hot-wire instrument employing coated wires over the density interval of 735 to 870 kgm^–3. A new expression for the influence of the wire coating is presented, and an examination of the importance of a nonuniform wire radius is verified with measurements on argon from 296 to 323 K at pressures to 61 MPa. Four isotherms were measured in toluene between 296 and 423 K at pressures to 35 MPa. The measurements have an uncertainty of less than ±0.5% for thermal conductivity and ±2% for thermal diffusivity. Isobaric heat capacity results, derived from the measured values of thermal conductivity and thermal diffusivity, using a density determined from an equation of state, have an uncertainty of ±3% after taking into account the uncertainty of the applied equation of state. The measurements demonstrate that isobaric specific heat determinations can be obtained successfully with the transient hot wire technique over a wide range of fluid states provided density values are available.     

瞬态热线法导热系数测量的数值模拟

利用有限元方法对瞬态热线法导热系数测量进行了数值模拟,对各种因素如加热功率、热线半径以及实验温度等对测量过程的影响进行了分析,并将模拟得到的温升曲线与实验测量得到的温升曲线进行了比较,结果表明:通过选择适当的参数值,模拟曲线可以与实测曲线吻合得很好,实验值与模拟值的偏差小于实验结果的不确定度.本结果的获得对进一步理解瞬态热线法导热系数测量过程,提高导热系数测量技术水平具有借鉴意义.     

Simulation of the Transient Heating in an Unsymmetrical, Coated, Hot-Strip Sensor with a Self-Adaptive Finite-Element Method (SAFEM)1

The transient heating in an unsymmetrical, coated, hot-strip sensor was simulated with a self-adaptive finite-element method (SAFEM). The first tests of this model show that it can be used to determine, with a small error, the thermal conductivity of liquids, from the transient temperature rise in the hot strip, which is deposited in a substrate and coated by an alumina spray.     

The Thermal Conductivity, Thermal Diffusivity, and Heat Capacity of Gaseous Argon

This paper presents new absolute measurements for the thermal conductivity and thermal diffusivity of gaseous argon obtained with a transient hot-wire instrument. Six isotherms were measured in the supercritical dense gas at temperatures between 296 and 423 K and pressures up to 61 MPa. A new analysis for the influence of temperature-dependent properties and residual bridge unbalance is used to obtain the thermal conductivity with an uncertainty of less than 1% and the thermal diffusivity with an uncertainty of less than 4%. Isobaric heat capacity results were derived from measured values of thermal conductivity and thermal diffusivity using a density calculated from an equation of state. The heat capacities presented here have a nominal uncertainty of 4% and demonstrate that this property can be obtained successfully with the transient hot wire technique over a wide range of fluid states. The technique will be useful when applied to fluids which lack specific heat data.     

Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7

The thermal conductivity of polymethyl methacrylate (PMMA) and borosilicate crown glass BK7 has been studied. The transient hot-wire technique has been employed, and measurements cover a temperature range from room temperature up to 350 K for PMMA and up to 500 K for BK7. The technique is applied here in a novel way that minimizes all remaining thermal-contact resistances. This allows the apparatus to operate in an absolute way and with very low uncertainty. The method makes use of a soft silicone paste material between the hot wires and the solid under test. Measurements of the transient temperature rise of the wires in response to an electrical heating step over a period of 20 μs up to 5 s allow an absolute determination of the thermal conductivity of the solid, as well as of the silicone paste. The method is based on a full theoretical model with equations solved by a two-dimensional finite-element method applied to the exact geometry. At the 95% confidence level, the standard deviations of the thermal conductivity measurements are 0.09% for PMMA and 0.16% for BK7, whereas the standard uncertainty of the technique is less than 1.5%.     

微风速标准装置的建立和热线风速仪校准方法的实验研究

中国计量科学研究院建立了微风速标准装置,基于该标准装置对热线风速仪的校准展开了实验研究。微风速标准装置基于相对法测量原理,实验通过气浮滑车搭载热线风速仪运动,由激光干涉仪测得的距离对时间微分得到标准速度,通过这种方式实现了热线风速仪的校准。滑车的运动速度可以溯源到国家计量院的时间和长度基准;此外,根据热线风速仪传感器的理论模型计算得到了热线风速仪的静态特性方程,比较理论模型与校准结果,发现二者具有良好的一致性。实验结果和不确定度分析表明:微风速标准装置的扩展不确定度U=0.82%（k=2）;热线风速仪校准结果的扩展不确定度U=2.42%（k=2）。     

Thermal Conductivity,Thermal Diffusivity,and Heat Capacity of Gaseous Argon and Nitrogen

Low-pressure thermal conductivity and thermal diffusivity measurements are reported for argon and nitrogen in the temperature range from 295 to 350 K at pressures from 0.34 to 6.9 MPa using an absolute transient hot-wire instrument. Thermal conductivity measurements were also made with the same instrument in its steady-state mode of operation. The measurements are estimated to have an uncertainty of 1% for the transient thermal conductivity, 3% for the steady-state thermal conductivity, and 4% for thermal diffusivity. The values of isobaric specific heat, derived from the measured thermal conductivity and thermal diffusivity, are considered accurate to 5% although this is dependent upon the uncertainty of the equation of state utilized.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom     

A computer-controlled instrument for the measurement of the thermal conductivity of liquids

A new instrument for the measurement of the thermal conductivity of liquids by the transient hot-wire method is described. The instrument has features in common with earlier versions but employs a novel technique for the determination of the transient temperature rise of the hot wire during the course of a measurement. New determinations of the thermal conductivity of toluene confirm the accuracy of the instrument to be better than 0.5%.     

Thermal Conductivity of Liquid Tin and Indium

The present paper reports new measurements of the thermal conductivity of liquid tin and indium. The measurements have been performed at atmospheric pressure in a range of temperatures from 450 to 750 K using a new experimental method based on the principle of the transient hot wire technique. The particular version of the technique employed for molten metals has been shown to have an accuracy in the measurement of the thermal conductivity of molten metals of ±2%. Ultimately, it is intended that the technique operate in a wide range of temperatures, from ambient up to 1200 K, and work is in progress to increase the working temperature and to extend the range of measurements. The results are compared with experimental data reported in the literature by other authors and with predictions of the Wiedemann and Franz law.     

Measurements of Thermal Conductivity and Electrical Conductivity of a Single Carbon Fiber

In this paper, the thermal conductivity of a single carbon fiber under different manufacturing conditions is measured using the steady-state short-hot-wire method. This method is based on the heat transfer phenomena of a pin fin attached to a short hot wire. The short hot wire is supplied with a constant direct current to generate a uniform heat flux, and both its ends are connected to lead wires and maintained at the initial temperature. The test fiber is attached as a pin fin to the center position of the hot wire at one end and the other end is connected to a heat sink. One-dimensional steady-state heat conduction along the hot wire and test fiber is assumed, and the basic equations are analytically solved. From the solutions, the relations among the average temperature rise of the hot wire, the heat generation rate, the temperature at the attached end of the fiber, and the heat flux from the hot wire to the fiber are accurately obtained. Based on the relations, the thermal conductivity of the single carbon fiber can be easily estimated when the average temperature rise and the heat generation rate of the hot wire are measured for the same system. Further, the electrical conductivity of the single carbon fiber is measured under the same conditions as for the thermal conductivity using a four-point contact method. The relation between the thermal conductivity and electrical conductivity is further discussed, based on the crystal microstructure.     

A new method for the evaluation of thermal conductivity and thermal diffusivity from transient hot strip measurements

The standard straight-line fit to data of a transient hot strip (THS) experiment to determine the thermal conductivity and thermal diffusivitya suffers from two major drawbacks: First, due to the statistical nature of the estimation procedure, there is no relation between the uncertainty of the measured value on one hand and the transport properties obtained on the other. Second, in order to account for he heat capacity of the strip and outer boundary conditions, two intervals of the plot must he rejected before analyzing it. So far, these intervals are selected arbitrarily. We now treat the THS working equation as a function of the four parameters concerned. a.U ₀ (initial voltage), andt ₀ (time delay). Chi-square fittings. following the Levenberg-Marquardt algorithm. are performed separately for several overlapping time intervals of the entire plot to find and a with minimal standard deviation. In the course of subsequent iterations an individual weighting factor is applied to each point to account for systematic errors. This procedure yields the "best" values of anda along with their individual errors. comprising the systematic and the statistical errors. Experimental results on Pyrex glass 7740 were taken to verify the new procedure.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder. Colorado, U.S.A.     

A Novel Instrument for the Measurement of the Thermal Conductivity of Molten Metals. Part I: Instrument’s Description

The paper reports the design and construction of a new instrument for the measurement of the thermal conductivity of molten metals and salts. The apparatus is based on the transient hot-wire technique, and it is intended for operation over a wide range of temperatures, from ambient up to 1200 K. The present experimental technique overcomes problems of convection and thermal radiation, and it is demonstrated that it operates in accord with a theoretical model. The uncertainty of the thermal conductivity results is estimated to be ±2% which is superior to that achieved in most earlier work.