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.     

Measurement of the Thermal Conductivity and Thermal Diffusivity of Liquids. Part I: “Pure Conduction and an Example of a Solution”

The measurement of the thermal conductivity of liquids is rather complicated due to the nature of the fluid. To the conduction, which has to be characterized, are added the natural convection, the radiative transfer, and the perturbations caused by the presence of enclosure walls. The goal of this work, composed of two parts, is to implement an experimental bench allowing the measurement of the thermal diffusivity and thermal conductivity of liquids. The first part (Part I) presented here, is about pure conduction and focuses on several aspects involved in this measurement, which will lead one, based on theoretical and practical considerations, to choose a pulse method in a one-dimensional (1D) and cylindrical geometry to solve the problem. In the second section of this part, the problem of the parameters estimation is investigated with the presence of the walls of the measuring cell and this will allow us to define the characteristics of the walls (thickness and thermophysical properties). The entire problem is treated through the thermal quadrupoles method. Finally, in a last section, a setup at room temperature is described. The second part (Part II) of this work that is presented in another paper will show how it is possible to get rid of the convection by a judicious choice of the extension of the measuring cell and how the radiation effects can be taken into account to perform measurements at high temperatures (up to 500°C).Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China.     

Thermal Diffusivity Measurement of Two-Layer Optical Thin-Film Systems Using Photoacoustic Effect1

In this study, we designed and developed two-layer antireflection (AR) optical coating samples on glass substrates, using different evaporation conditions of coating rates and substrate temperatures for two dielectric materials, MgF₂ and ZnS, with different refractive indices. The through-plane thermal diffusivity of these systems was measured using the photoacoustic effect. The optical thicknesses of MgF₂ and ZnS layers were fixed at 5/4 (=514.5 nm) and , respectively, and the thermal diffusivities of the samples were obtained from the measured amplitude of the photoacoustic signals by changing the chopping frequency of the Ar⁺ laser beam. The results demonstrated that the thermal diffusivity of the sample fabricated under the conditions of 10Å·s^–1 and 150°C had the maximum value and that the results were directly related to the microstructure of the film system.     

Measurement of the In-plane Thermal Diffusivity of Materials by Infrared Thermography

A transient method using the Laplace transform for estimation of the in-plane thermal diffusivity of low conductive materials is presented. The temperature field of the sample is measured by infrared thermography. The main interest of the technique proposed here is to not require a knowledge of the stimulation and boundary conditions by using two reference temperature profiles. The parameter estimation is implemented in the time domain by an inverse technique using numerical Laplace inversion and convolution products. A sensitivity study has been carried out to optimize the choice of the two reference profiles. The effect of a space varying heat transfer coefficient on the estimated values of the unknown parameters has also been evaluated. Finally, the apparatus is described and experimental results obtained for a low conductive material like a vitroceramic are shown.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom.     

Viscosity Measurements of Liquid Toluene at Low Temperatures Using a Dual Vibrating-Wire Technique

A recently developed dual vibrating-wire technique has been used to perform viscosity measurements of liquid toluene in the temperature range 213 KT298 K, and at pressures up to approximately 20 MPa. The results were obtained by operating the vibrating-wire sensor in both forced and free decay modes. The estimated precision of the viscosity measurements, in either mode of operation, is ±0.5%, for temperatures above or equal to 273 K, increasing with decreasing temperature up to ±1% at 213 K. The corresponding overall uncertainty is estimated to be within ±1% and ±1.5%, respectively.     

Measurements of Thermal Diffusivity for Thin Slabs by a Converging Thermal Wave Technique

The measurement of thermal diffusivity for thin slabs by a converging thermal wave technique has been studied. Temperature variation at the center of the heat source ring that is produced by a pulsed high-power laser is detected by an infrared detector. A computer program based on the finite difference method is developed to analyze the thermal diffusivity of the slabs. Materials of both high thermal diffusivity (CVD diamond wafer) and low thermal diffusivity (stainless-steel foil) have been used for the measurements. The measurements have been performed by varying the size and the thickness of specimen. The converging thermal wave technique has proved to be a good method to measure the thermal diffusivity of a CVD diamond without breaking the wafer into small specimens. The technique can be applied for a small slab if the diameter of the slab is two times larger than that of the heat source ring. The sensitivity of thickness in measuring the thermal diffusivity is low for ordinary CVD diamond. The use of the converging thermal wave technique for nonhomogeneous, nonuniform, and anisotropic materials has been accomplished by applying the finite difference method.     

Measurement of the Thermal Diffusivity of Solids with an Improved Accuracy

A photothermal radiometry technique is being developed at the NPL with the goal of improving the accuracy of thermal diffusivity measurements. The principle is to perform a laser-induced thermal experiment while simultaneously making accurate measurements of the experimental boundary conditions. A numerical three-dimensional heat diffusion model based on thermal transfer functions has been developed to account for the measured boundary conditions. The thermal diffusivity is determined from the experimental data by a nonlinear, least-squares fit to the model. Experiments carried out on pure metals at 900 K demonstrate good agreement between the theoretical predictions and experimental data, and uncertainties of about 1.5% for the thermal diffusivities of platinum, titanium, and germanium were obtained.     

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%.     

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     

Effect of the Response Delay of the Measuring System on Thermal Diffusivity Measurement Using the Flash Method1

This work investigates the effect of the response delay of a measuring system on a thermal diffusivity measurement. A model of an m th-order delay in the measuring system is introduced, and a general expression for the output of the system with temperature response as input is derived. The effect on the temperature response caused by such a system is discussed. As a practical example, a third-order measuring system is considered. The measured temperature responses of stainless steel foils are compared with those calculated with the model of a third-order delay system. Good agreement between the two results is shown.     

Thermal Diffusivity Measurement of Diamond Films1

This paper discusses the short-pulse-flash method developed for thermal diffusivity measurements on thin films. Two kinds of CVD diamond film have been prepared, and their thermal diffusivity in the perpendicular direction has been measured with this method. The measurement errors caused by the surface coating are discussed.     

基于脉冲涡流热成像的面内方向性热扩散率测量

针对导电材料面内方向性热扩散率的测量,提出脉冲涡流热成像法这一新方法。该方法采用感应式脉冲线激励源,在导电试件表面形成沿一定方向的感应涡流,实现局部热激励,在非稳态条件下实现了材料面内方向热扩散率的测量;简单调节试件与线感应激励线圈的角度,就可以快速无损非接触地测量试件在垂直线圈方向上的热扩散率值。对感应线激励下面内热传导及高斯温度分布进行了分析,分别对AISI304不锈钢、纯铁、纯镍3种材料的热扩散率进行了测量,测量结果与手册值相符,偏差小于9.0%,相对扩展不确定度分别为3.18%,3.72%,3.70%。     

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.     

Measurement of Thermal Diffusivity of Thermal Control Coatings by the Flash Method Using Two-Layer Composite Sample1

The thermal diffusivity of brittle coatings cannot be measured by the flash method directly because of the difficulty of preparing free-standing samples. Adopting the flash method using a two-layer composite sample, it is possible to measure thermal diffusivity if the radiant pulse is well defined and good thermal contact on the interface of the composite sample can be ensured. Using an equilateral trapezoidal pulse of an Nd-glass laser measuring the dimensionless temperature history of the rear face of the sample, we determined the thermal diffusivity of thermal control coatings in the temperature range of 80 to 200°C. The results for different thicknesses of substrate showed that the thermal contact resistance of the interface can be neglected.     

应用光声技术测定薄型材料导温系数的研究

本文报导了用光声技术测试和研究薄型试样导温系数的结果,建立了该方法的理论模型,介绍了实验装置和数据处理的方法。用本装置对三种标准和亚标准试样的测试结果表明,实测值和文献推荐值相当吻合。本文的基本理论和实验方法同样也适用于其它有机、无机等薄型材料。     

Measurement of the Thermal Diffusivity of an Anisotropic Graphite Sheet Using a Laser-Heating AC Calorimetric Method

The thermal diffusivity of a graphite sheet having an extremely high anisotropy has been measured by a laser heating AC calorimetric method in the temperature range from 30 to 350 K. This graphite sheet has characteristics of high thermal diffusivity and high anisotropy, and it is only 100 m thick. Thus, it is difficult to apply the conventional AC technique. Therefore, we propose a simultaneous measurement method for the in-plane and out-of-plane thermal diffusivities, by analyzing the three-dimensional heat conduction process, which contains the effects of anisotropy and thermal wave reflections. This method was verified by checking with thermal diffusivity measurements of isotropic materials such as stainless steel and pure copper and was then applied to the anisotropic thermal diffusivity measurement of the graphite sheet.     

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.     

Thermal Diffusivity Measurement of Polyamide Mesh by Temperature Wave Analysis1

The thermal diffusivity of a polyamide mesh having plane wave structure was determined by a temperature wave analysis method developed in our laboratory. The measured thermal diffusivity of the polyamide mesh represents the combined result for the polyamide fiber part and the open space of the mesh. The polyamide mesh was measured in air and liquid paraffin conditions. Its effective thermal diffusivity was obtained as a function of the volume content of the surrounding material. A unit-cell model was applied to the polyamide mesh structure and shows good correspondence with the experimental results.     

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.