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%.     

Guarded Hot-Plate (GHP) Method: Uncertainty Assessment

In civil engineering, the thermal conductivity is the most important quantity for thermal insulations and, as such, is in most cases determined with the guarded hot plate instrument in accordance with the applicable standards. These standards are to assure that uniform and reliable measurements will lead to comparable results. In addition, the quality of a measurement result essentially depends on its measurement uncertainty which, for reasons of acceptance, should also be determined according to a uniform guideline. For some time now, such a standard has been available: The ISO Guide to the Expression of Uncertainty in Measurement, often abbreviated to GUM. Its application will be demonstrated comprehensively, and in detail, by the example of a guarded hot plate instrument which can be used at working temperatures from –70 to 200°C. The terms and definitions of the GUM required for this purpose will be extended by the instrument-and-sample-specific corrections and used as a basis for establishing the uncertainty budget. As far as possible, both alternatives offered by the GUM—type A and type B methods—are used in parallel. The combination of the sensitivity coefficients and variances of the budget yields the expanded standard uncertainty of the specific guarded hot plate instrument examined. In this case, it is 1.9% at 20°C.     

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.     

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.     

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.     

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%.     

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.     

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.     

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.     

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.     

Thermal conductivity surface of argon: A fresh analysis

This paper presents a fresh analysis of the thermal conductivity surface of argon at temperatures between 100 and 325 K with pressures up to 70 MPa. The new analysis is justified for several reasons. First, we discovered an error in the compression-work correction, which is applied when calculating thermal conductivity and thermal diffusivity obtained with the transient hot-wire technique. The effect of the error is limited to low densities, i.e., for argon below 5 mol·L^–1. The error in question centers on the volume of fluid exposed to compression work. Once corrected, the low-density data agree very well with the available theory for both dilute-gas thermal conductivity and the first density coefficient of thermal conductivity. Further, the corrected low-density data, if used in conjunction with our previously reported data for the liquid and supercritical dense-gas phases, allow us to represent the thermal conductivity in the critical region with a recently developed mode-coupling theory. Thus the new surface incorporates theoretically based expressions for the dilute-gas thermal conductivity, the first density coefficient, and the critical enhancement. The new surface exhibits a significant reduction in overall error compared to our previous surface which was entirely empirical. The uncertainty in the new thermal conductivity surface is ±2.2% at the 95% confidence level.     

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.     

Uncertainty Analysis of Thermophysical Property Measurements of Solids Using Dynamic Methods

This work reports on an analysis of thermophysical properties (thermal conductivity, thermal diffusivity, and specific heat capacity) measurements of solids using dynamic methods. The influence of temperature measurement uncertainty on the parameter estimation uncertainty is studied using a least-squares procedure. The standard and difference analyses are used for optimizing the experiment with respect to the data window or time interval of measurements. The analysis is applied to the extended dynamic plane source method, and the results of numerical computations are illustrated in the form of contour plots.     

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.     

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.     

Assessment of Uncertainties for the NIST 1016 mm Guarded-Hot-Plate Apparatus: Extended Analysis for Low-Density Fibrous-Glass Thermal Insulation

An assessment of uncertainties for the National Institute of Standards and Technology (NIST) 1016 mm Guarded-Hot-Plate apparatus is presented. The uncertainties are reported in a format consistent with current NIST policy on the expression of measurement uncertainty. The report describes a procedure for determination of component uncertainties for thermal conductivity and thermal resistance for the apparatus under operation in either the double-sided or single-sided mode of operation. An extensive example for computation of uncertainties for the single-sided mode of operation is provided for a low-density fibrous-glass blanket thermal insulation. For this material, the relative expanded uncertainty for thermal resistance increases from 1 % for a thickness of 25.4 mm to 3 % for a thickness of 228.6 mm. Although these uncertainties have been developed for a particular insulation material, the procedure and, to a lesser extent, the results are applicable to other insulation materials measured at a mean temperature close to 297 K (23.9 °C, 75 °F). The analysis identifies dominant components of uncertainty and, thus, potential areas for future improvement in the measurement process. For the NIST 1016 mm Guarded-Hot-Plate apparatus, considerable improvement, especially at higher values of thermal resistance, may be realized by developing better control strategies for guarding that include better measurement techniques for the guard gap thermopile voltage and the temperature sensors.     

Surface Tensions and Thermal Conductivities of Aqueous LiBr-Based Solutions Containing n-Octanol and 2-Ethyl-1-Hexanol: Application to an Absorption Heat Pump

Surface tensions and thermal conductivities were measured for LiBr+1,3-propanediol+water and LiBr+LiI+1,3-propanediol+water. These two mixtures were chosen as one of the potential candidates for working fluids for absorption heat pumps. Surface tensions and thermal conductivities were measured by the capillary rise method equipped with a cathetometer and the transient hot wire method with a coated tantalum wire, respectively. The measured surface tension and thermal conductivity data were well correlated with a simple polynomial function of temperature and absorbent concentration. In addition, the surface tensions of LiBr+1,3-propanediol+water containing a small amount of alcohol-based surfactants, n-octanol and 2-ethyl-1-hexanol, were also measured at 298.15 K by the ring method. An increase in the surfactant concentration up to about 500 ppm leads to a gradual decrease in the mixture surface tensions.