A Two-Dimensional Analytical Solution for the Transient Short-Hot-Wire Method

Unlike the conventional transient hot-wire method for measuring thermal conductivity, the transient short-hot-wire method uses only one short thermal-conductivity cell. Until now, this method has depended on numerical solutions of the two-dimensional unsteady heat conduction equation to account for end effects. In order to provide an alternative and to confirm the validity of the numerical solutions, a two-dimensional analytical solution for unsteady-state heat conduction is derived using Laplace and finite Fourier transforms. An isothermal boundary condition is assumed for the end of the cell, where the hot wire connects to the supporting leads. The radial temperature gradient in the wire is neglected. A high-resolution finite-volume numerical solution is found to be in excellent agreement with the present analytical solution.     

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.     

瞬态热线法导热系数测量实验数据处理方法的研究

为克服瞬态热线法导热系数测量中实验数据处理一般方法的弊端,将数值模拟引入实验数据处理过程,并通过比较理论计算曲线与实验曲线的符合程度来获得最终的实验结果。通过不同方法对实验数据处理结果的比较分析表明,所使用的方法可以更好地处理瞬态热线法导热系数测量数据,同时,与传统方法相比,采用较少的数据点即可得到正确的结果。研究结果不仅可以改进瞬态热线法导热系数实验数据的分析方法,而且对实验系统的设计与搭建也有借鉴意义。     

利用瞬态热线法测量固体导热系数

在利用瞬态热丝法测量固体与流体导热系数方法研究的基础上,对固体的导热系数进行了计算,提出了既有理论意义又包含了测量参数、既严格又简便的新表达式;分析与定量计算了模型误差、截断误差、热阻误差、热容忽视误差及测量系统的合成误差;并指出了减小误差的措施。在实验研究中,建立了试件测试台和自动化参数采集与数据处理的计算机测控系统。测量结果表明,所测得的3种固体材料的导热系数值与文献参照值相差约5％。具有一定的实用价值。     

An Improved Application of the Transient Hot-Wire Technique for the Absolute Accurate Measurement of the Thermal Conductivity of Pyroceram 9606 up to 420 K

This article describes the final refinements of a novel application of the transient hot-wire technique developed for the absolute, accurate measurements of the thermal conductivity of solids. Although the technique was originally developed five years ago, these new refinements allow a full understanding of the method and hence the performance of measurements with an absolute uncertainty of less than 1 %. New measurements of Pyroceram 9606 up to 420 K are reported. The maximum deviation of the present measurements is 0.54 %, while their standard deviation at the 95 % confidence level is 0.25 %. Since May 2007, Pyroceram 9606 is a European Commission certified thermal-conductivity reference material, designated as BCR-724, with an uncertainty of ±6.5 % at the 95 % confidence level.     

Numerical Analysis of Convective Instabilities in a Transient Short-Hot-Wire Setup for Measurement of Liquid Thermal Conductivity

Numerical simulation has been used to investigate the effects of natural convection on measurements of the thermal conductivity of fluids by transient hot-wire methods. Comparison of the numerical data with the experimental results obtained with a custom-built setup exploiting a short-wire geometry allows fixing an operationally useful time scale, where convective effects can be safely neglected.     

End Effects in the Three-Omega Method to Measure Gas Thermal Conductivity

A two-dimensional analytical solution is derived for the three-omega method for measurement of thermal conductivity of materials with a fine wire. The analytical solution includes the wire heat capacity and the effect of heat losses from the ends of the wire. To derive the solution, finite Fourier transforms are applied in the direction parallel to the wire axis. The solution is compared with a one-dimensional solution and experimental data. It is found that heat losses from the wire ends have a significant effect on the 3ω components at low frequency and tend to be less important at high frequency. Moreover, it is shown that two-dimensional effects will be severe for nano-scale wires, even if the wire length-to-diameter ratio is very large.     

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。     

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.     

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.     

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.     

An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction

In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The iterative MFS algorithm is tested for Cauchy problems related to heat conduction in two-dimensional anisotropic solids to confirm the numerical convergence, stability and accuracy of the method.     

An Analysis of the Heat Conduction Problem for Plates with the Functionally Graded Material Using the Hybrid Numerical Method

A heat conduction analysis of the functionally graded material (FGM) plates has been investigated based on the hybrid numerical method (HNM). HNM combines the layer element method with the method of Fourier transforms and proves to be efficient and reliable. The FGM plates are infinite large and the material properties vary continuously through thickness. The heat source continually acted one the FGM plates. The temperature distribution of the FGM plates is obtained in different time and different position. Some useful results for heat conduction problems are shown in figures. This article applies HNM to heat conduction firstly and provides us a new way for studying the heat conduction problems.     

An Application of DHW Algorithm for the Solution of Inverse Heat Conduction Problem

A damped heat wave (DHW) algorithm is applied for the temperature distribution calculation in a solution of a linear inverse heat conduction problem (IHCP). A nonlinear least squares algorithm is used for calculation of the unknown boundary heat flux history in a one-dimensional medium. The solution is based on the assumption that the temperature measurements are available, at least, at one point of the medium over the whole time domain. Sample calculations, for a comparison between exact heat sources and estimated ones, are made to confirm the validity of the proposed method. The close agreement between the exact and estimated values calculated for both exact and noisy data shows the potential of the proposed method for finding a relatively accurate heat source distribution in a one-dimensional homogeneous finite medium. The proposed method of solving inverse heat conduction problems is very simple and easy to implement.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.M. L?ffler: Deceased     

Thermal-Conductivity and Thermal-Diffusivity Measurements of Nanofluids by 3<Emphasis Type="Italic">ω</Emphasis> Method and Mechanism Analysis of Heat Transport

A 3ω technique is developed for simultaneous determination of the thermal conductivity and thermal diffusivity of nanofluids. The 3ω measuring system is established, in which a conductive wire is used as both heater and sensor. At first, the system is calibrated using water with known thermophysical properties. Then, the thermal conductivity and thermal diffusivity of TiO₂/distilled water nanofluids at different temperatures and volume fractions and the thermal conductivity of SiO₂ nanofluids with different carrier fluids (water, ethanol, and EG) are determined. The results show that the working temperature and the carrier fluid play important roles in the enhancement of thermal transport in nanofluids. These results agree with the predictions for the temperature dependence effect by the Brownian motion model and the micro-convection model. For SiO₂ nanofluids, the thermal-conductance enhancement becomes strong with a decrease in the heat capacity of the carrier fluids. Finally, according to our results and mechanism analysis, a corrected term is introduced to the Brownian motion model for providing better prediction of heat transport performance in nanofluids.     

Repeatability and Refinement of a Transient Hot-Wire Instrument for Measuring the Thermal Conductivity of High-Temperature Melts

The paper reports an assessment of the repeatability of a method for the measurement of the thermal conductivity of high temperature melts. The main goal is to demonstrate that a novel approach to the transient hot-wire technique can yield highly accurate results that are consistent with previous, independent measurements. The paper summarizes the modified transient hot-wire method, presents improvements in the finite-element analysis of its operation, and briefly discusses deviations from available analytical equations. The transient hot-wire instrument and experimental configuration are also described. Results from measurements on molten metals, in particular, tin and indium, in the temperature range from their melting points up to 750 K are presented. A comparison with previously measured values is given, and the accuracy and repeatability of the method are discussed.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

A New Transient Hot-Wire Instrument for Measuring the Thermal Conductivity of Electrically Conducting and Highly Corrosive Liquids using Small Samples

The transient hot-wire technique is widely used for measurements of the thermal conductivity of most fluids. However, for some particular liquids such as concentrated nitric acid solutions or similar nitric mixtures, for which the thermal properties are important for industrial or security applications, this technique can be difficult to use, which is essentially due to incompatibility 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 new patented instrument, based on tantalum short-hot-wire probe technology, which responds to the above requirements and allows safe automated thermal-conductivity measurements of concentrated acid nitric solutions and similar nitric mixtures for liquid samples less than 2 cm³, with uncertainties better than 5%.     

测定保温材料导热系数的自补偿圆管法的方法误差分析

本文对测定保温材料导热系数的自补偿圆管法的方法误差进行了分析。在００４～０１０Ｗ／（ｍ·Ｋ）导热系数范围内，固定功率补偿子方案的方法误差不超过２３％；而在００４～００６和００６～０１０Ｗ／（ｍ·Ｋ）分区域范围内则分别不超过１３％和１０％。这表明，测定保温材料导热系数的自补偿圆管法采用固定补偿因子方案在原理上是可行的。     

拓展导热逆问题原理测算物体导热系数方法的最优化问题再探讨

对拓展导热逆问题原理测算物体导热系数方法的最优化问题进行了更广泛、深入的研究，提示了敏感度系数Ｘ＾＋ｋ、Ｘ＾＋ｈ的变化规律，得到了最优化判别式和判据。实验测算中，探讨并确定了实测环境与条件、参数优选及最优化测算程序。对于导热系数ｋ值数量级为１０＾－２－１０Ｗ／（ｍ．℃）的三种不同试材测量与计算结果表明，本方法所测算的ｋ值与传统方法所测值相比，相对误差在１．５９％－４．００％之内：而本方法简单、可靠     

Evaluation of the Heat Leakage in the Thermal Diffusivity Measurement of Molten Metals by a Laser Flash Method

Evaluation of the radiative and conductive heat loss from a molten metal sample to the cell has been made in order to obtain accurate thermal diffusivities of molten metals at high temperature with a laser flash method. The results suggest that thermal diffusivity values of molten nickel can be determined in the temperature range from 1728 to 1928 K with an uncertainty of ±3% in comparison with case considering only the effect of radiative heat loss. The usefulness of a cell for a laser flash method has been confirmed by applying simulated results to evaluate the heat leakage in the thermal diffusivity measurement of molten metals.