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%.     

Quasi-Steady State Method: Uncertainty Assessment

The newly developed quasi-steady state (QSS) method to measure the thermal conductivity combines characteristic advantages of transient and steady-state techniques but avoids their major drawbacks. Based upon a transient hot strip setup, the QSS technique can be realized by adding only two temperature sensors at different radial distances from the strip. After a short settling time, the QSS output signal which is the measure for the thermal conductivity is constant in time as it is for steady-state instruments. Moreover, in contrast to transient techniques, the QSS signal is not altered by homogeneous boundary conditions. Thus, there is no need to locate a time window as has to be done with the transient hot wire or transient hot strip techniques. This paper describes the assessment of the QSS standard uncertainty of thermal conductivity according to the corresponding ISO Guide. As has already been done in previous papers on the uncertainty of the transient hot wire and transient hot strip techniques, first, the most significant sources of error are analyzed and numerically evaluated. Then the results are combined to yield an estimated overall uncertainty of 3.8%. Simultaneously, the present assessment is used as an aid in planning an experiment and in designing a QSS sensor to achieve minimal uncertainty. Such a sensor is used to verify the above mentioned standard uncertainty from a run on the candidate reference material polymethyl methacrylate.     

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.     

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.     

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.     

Use of the Transient Plane Source Technique for Rapid Multiple Thermal Property Measurements

This paper describes work at NPL to evaluate the capability of the transient plane source (TPS) technique using various sensor sizes and different types of materials that include solids (Perspex, alumina, extruded polystyrene, agar gel, and ice) and liquids (water and silicone oil). The aim of the present work is to investigate use of the TPS technique on materials where probe size, contact, and internal specimen convection are potentially important issues. Following validation of the technique on the NPL solid reference materials, measurements were carried out on ice using TPS and the NPL guarded hot plate (GHP) to illustrate the probe-to-sample thermal contact resistance issue. Measurements on silicone oil were compared to GHP and the NPL transient hot wire (THW) technique where the probe size/short times are crucial. In addition, measurements on water and agar gel were made to illustrate the influence of natural convection. Although the TPS is a multi-property technique, the focus of this work was on thermal conductivity.     

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.     

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.     

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%.     

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.     

Transient Hot Strip (THS) Method: Uncertainty Assessment

The transient hot strip (THS) method can be used to measure simultaneously the thermal conductivity and diffusivity a of dielectrics within a few minutes. However, although the method has been known for 20 years, there is no complete assessment of its uncertainty. First, the underlying complex mathematical model makes any error analysis a tedious and complicated task. Secondly, the ISO Guide to the Expression of Uncertainty in Measurement does not apply directly because of the classical model's implicit character. In the present paper, the combined standard uncertainty u of the THS method has been determined by applying two different models. First, we start from the classical nonlinear model. The major sources of errors are analyzed, namely, the ideal model errors, the evaluation errors, and the measurement errors. Next, a newly developed numerical procedure combines all the components in a way that the resultant standard uncertainties of the nonlinear model, u()/=2.6% and u(a)/a=11%, comply as closely as possible with the principles of the ISO Guide. Second, we start from the recently presented linear expression of the THS mathematical model that is briefly discussed. Since this approximation is explicit in both measurands, the uncertainties, u()/=2.5% and u(a)/a=11%, are determined in full accordance with the ISO guide. The uncertainty in thermal conductivity is experimentally assessed against the standard reference CRM 039 (Pyrex). The results obtained are in excellent agreement with the theoretical values.     

The thermal conductivity and heat capacity of gaseous argon

This paper presents new absolute measurements of the thermal conductivity and of the thermal diffusivity of gaseous argon obtained with a transient hot-wire instrument. We measured seven isotherms in the supercritical dense gas at temperatures between 157 and 324 K with pressures up to 70 MPa and densities up to 32 mol · L^–1 and five isotherms in the vapor at temperatures between 103 and 142 K with pressures up to the saturation vapor pressure. The instrument is capable of measuring the thermal conductivity with an accuracy better than 1% and thermal diffusivity with an accuracy better than 5%. Heat capacity results were determined from the simultaneously measured values of thermal conductivity and thermal diffusivity and from the density calculated from measured values of pressure and temperature from an equation of state. The heat capacities presented in this paper, with a nominal accuracy of 5%, prove that heat capacity data can be obtained successfully with the transient hot wire technique over a wide range of fluid states. The technique will be invaluable when applied to fluids which lack specific heat data or an adequate equation of state.     

An Oscillating Boundary Temperature Method for the Determination of Transient Thermal Conductivity and Internal Heat Generation with a Comparison to a Transient Hot-Wire Method

An oscillating boundary temperature (OBT) method is proposed to simultaneously determine transient thermal properties including thermal conductivity, thermal diffusivity, internal heat generation, and volumetric heat capacity for exothermic solids and semi-solids over a narrow, controlled temperature range by using internal temperature measurements of the thermal wave. A comparison of this method and a transient hot-wire (THW) method is conducted in the presence of heat generation using physical properties which change over time. The advantages and disadvantages of both methods are discussed. The OBT method is potentially useful for the analysis of exothermic solid or semi-solid materials such as hydrating (freshly mixed) cement and concrete, polymers and composites undergoing polymerization reactions, and biological tissues.     

A New Transient Two-Wire Method for Measuring the Thermal Diffusivity of Electrically Conducting and Highly Corrosive Liquids Using Small Samples

The transient hot-wire (THW) technique is widely used for measurements of the thermal conductivity of most fluids, and some attempts have also been carried out for simultaneous measurements of the thermal diffusivity with the same hot wire. However, for some particular liquids like concentrated nitric acid solutions or similar nitric mixtures, for which the thermal properties are important for industrial or security applications, this technique may be difficult to use, because of possible technological incompatibilities between measurement probe materials and highly electrically conducting and corrosive liquids. Moreover, the possible highly energetic (explosive) character of these liquids requires minimum volume liquid samples and safety measurement devices and processes. It is the purpose of this paper to report on a modified THW technique (previously used for thermal-diffusivity measurements in soils), which is associated with a specific patented double-wire probe and is shown to be valid for direct thermal-diffusivity measurements in liquids. This method responds to the previous requirements and allows automatic and quasi-simultaneous thermal-conductivity and thermal-diffusivity measurements to be made safely on liquids compatible with the tantalum technology, with liquid sample volumes < 2 cm³. Low uncertainties are found for the thermal-diffusivity data when relative measurements are carried out with reference liquids like water or toluene.     

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.     

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     

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.     

The Thermal Conductivity, Thermal Diffusivity, and Specific Heat of Liquid n-Pentane

The thermal conductivity and thermal diffusivity of liquid n-pentane have been measured over the temperature range from 293 to 428 K at pressures from 3.5 to 35 MPa using a transient hot-wire instrument. It was determined that the results were influenced by fluid thermal radiation, and a new expression for this effect is presented. The uncertainty of the experimental results is estimated to be better than ±0.5% for thermal conductivity and ±2% for thermal diffusivity. The results, corrected for fluid thermal radiation, are correlated as functions of temperature and density with a maximum uncertainty of ±2% for thermal conductivity and ±4% for thermal diffusivity. Derived values of the isobaric specific heat are also given.     

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.