In-plane Thermal Diffusivity Measurement of Thin Samples Using a Transient Fin Model and Infrared Thermography

A method for determining the in-plane thermal diffusivity of planar samples was constructed. The time-dependent temperature field of the sample heated at one edge was measured with an infrared camera. The temperature fields were averaged for different times over a narrow strip around the center line of the sample, and the temperature profiles for varying time were fitted by a solution to a corresponding one-dimensional heat equation. Heat losses by convective and radiative heat transfer were both included in the model. Two fitting parameters, the thermal diffusivity and the effective heat-loss term, were obtained from time-dependent temperature data by optimization. The ratio of these two parameters was also extracted from the steady-state temperature profile. The method was found to give good and consistent results when tested on copper and aluminum samples.     

基于激光闪光法的立式热扩散率测量装置研究

介绍了基于激光闪光法的立式热扩散率测量装置,利用脉冲激光对样品进行均匀加热,使样品内部产生一维热流,并通过红外探测器测量样品温升信号,采用立式真空加热炉控制测量温度环境,实现室温至1600℃的热扩散率测量。用该装置测量厚度为1. 1 mm,直径为10 mm的不锈钢样品,测量结果与PTB参考数据的偏差小于1%。     

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.     

Thermal Diffusivity of Sintered Steels with Flash Method at Ambient Temperature

Due to lack of reliable thermal diffusivity data of sintered steels in literature, experimental investigations were conducted on samples made of different powder types (based on prealloyed, or diffusion-bonded, or admixed powders) and under different process conditions. So the influence of pressing pressure and sintering temperature on thermal diffusivity was established. Thermal diffusivity was measured using the “flash method”: a sample in the shape of a slab is irradiated with a light pulse on one of the two surfaces, and temperature of the other surface is detected by an ambient temperature pyrometer. The value of the thermal diffusivity is obtained by a least squares regression on the entire trend of the temperature vs. time using the analytical solution of the heat conduction as regression model. Results show the increase of the thermal diffusivity with increasing density. This outcome can be explained from the mutual effect of thermal conductivity and density on thermal diffusivity in porous media. The experimental results have also permitted to verify the influence of the composition of the sintered materials and carbon contents on thermal diffusivity.     

Combined effect of thermal dispersion and radiation on free convection in a fluid saturated, optically thick porous medium

The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton–Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.     

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.     

Determination of Thermal-Diffusivity Dependence on Temperature of YAG Single Crystals with Different Concentrations of Yb<Superscript>3+</Superscript> and V<Superscript>3+</Superscript> Doping Ions

Thermal diffusivities of pure and doped yttrium aluminum garnet single crystals were measured as a function of temperature. Samples doped with rare earth ions (3 at% and 25 at% of Yb ³⁺, and 0.8 at% and 2.1 at% of V ³⁺) were investigated in the temperature range from 34 °C to 300 °C. Determination of the thermal diffusivity was based on an analysis of propagation of a thermal wave in the sample. The frequency of the thermal wave was 100 mHz. A temperature disturbance connected with the thermal wave propagating in the sample was detected using the mirage effect. The results showed that the thermal diffusivity of all investigated samples decreases with an increase of sample temperature. A drop in the thermal diffusivity is more pronounced for pure and low-doped crystals.     

Contactless method of determining the coefficient of thermal diffusivity of local domains of surface layers and thin films

A method is proposed for measuring the coefficient of thermal diffusivity of microsections of surface layers and thin films. The coefficient of thermal diffusivity is calculated from the time dependence of the heat flux emitted by the heated surface.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 2, pp. 289–294, August, 1976.     

Analysis of Two-Dimensional Effect in the Measurement of Thermal Diffusivity of Thin Films with an AC Calorimetric Method1

An ac calorimetric method for measuring the thermal diffusivity of thin-film materials has been widely applied. In the application of this method, the systematic errors caused by the heat loss effect, the edge reflection effect, etc., have been analyzed and corresponding correction methods have been developed. But when measuring films with low thermal diffusivity or with thickness comparable to the thermal diffusion length, a two-dimensional effect which will also result in a systematic error of the measurement is present. In this paper, the mechanism of two-dimensional heat conduction within a thin sample which is supplied a periodic heat flux by a chopped light beam is analyzed. A numerical analysis method is developed to study the effect of the two-dimensional heat conduction on the measured thermal diffusivity values. The relations between the measured thermal diffusivity and independent parameters such as frequency, thickness of sample, width of light spot, etc., are demonstrated to indicate the two-dimensional effect. The experimental precondition for minimizing the systematic error caused by the two-dimensional effect is determined. In addition, the analysis method presented in this paper should be useful for more difficult problems such as error estimation of the thermal diffusivity measurement of coatings or composite films.     

Celestial body irradiance determination from an underfilled satellite radiometer: application to albedo and thermal emission measurements of the Moon using CERES

The Clouds and the Earth's Radiant Energy System (CERES) is a program that measures the Earth radiation budget (ERB) from two polar orbiting satellite platforms. CERES radiometers are designed to make stable broadband measurements of scattered solar and emitted thermal radiative flux leaving Earth with an accuracy of 1% or better. Using versatile and programmable scan modes, it is also possible for every CERES instrument to view the Moon on each orbit. However, until now, it has not been possible to derive absolute measurements of lunar irradiance using CERES because the Moon's disk fills only 10% of the telescope field of view. This work presents a method of integrating CERES raster-scan data in order to obtain a measurement of the average scattered solar and emitted thermal radiance from the entire lunar disk. The technique results in excellent agreement between CERES instruments on different satellites as to lunar albedo and emitted thermal flux. The average broadband Moon albedo is measured by CERES at a value of 0.1362 (+/-2-3%) when normalized to a static lunar phase angle of 7 degrees using the U.S. Geological Survey lunar irradiance Robotic Lunar Observatory model. The method for the first time also yields very accurate measurements of the thermal irradiance emitted from the Moon. These suggest an average long-wave flux of 977 Wm(-2) (+/-2-3% at 7 degrees phase), implying an approximate mean surface temperature of around 92 degrees C. Statistical analysis on available data suggests that a CERES instrument performing monthly lunar measurements could utilize the Moon as a stability target and reduce calibration drifts to 0.3% per decade or less within an instrument's lifetime. Given the success of the technique, a solar calibration system is proposed that will allow precise tracking of an ERB instrument's optical degradation using the Sun.     

The effects of cobalt substitution on the thermal diffusivity of YBa2Cu3O7−δ superconductor

The thermal diffusivity κ(T) of the cobalt-substituted sintered YBCO system, YBa₂Cu_3?x Co _x O_7∮δ (x=0.0, 0.1), has been measured to, investigate, effects of atomic substitution and charge carrier concentration on the thermal diffusion processes. The thermal diffusivity was measured in the temperature range 35–300 K, using the transient-plane-source technique. The results show that, belowT _c , the κ(T) values of the doped (x=0.1), samples are lower than the corresponding values for the undoped (x=0.0) samples. This may be due to the difference in the free-charge carrier concentrations of the two samples. A decoupling between the conducting Cu?O planes as a result, of Co-doping in the chain sites may contribute to additional decrease in the thermal diffusivity of the doped sample. An attempt was made to explain the rise in the thermal diffusivity belowT _c by adopting a recent theoretical model based on the existence of weakly damped collective electron excitations of Bose type, with acoustic dispersion relation, (acoustic plasmons) inside the superconducting gap.     

Thermal-Diffusivity Dependence on Temperature of Gadolinium Calcium Oxoborate Single Crystals

Thermal diffusivities of pure and doped gadolinium calcium oxoborate (GdCOB) single crystals were measured as a function of the temperature along optical indicatrix axes X, Y, and Z. Three GdCOB samples were investigated, chemically pure single crystal, the one doped with 4 at% of Nd and the next one doped with 7 at% of Yb. Measurements were carried out for temperature range 40 °C to 300 °C. Determination of the thermal diffusivity based on an analysis of thermal wave propagation in the sample. For a detection of temperature disturbance propagating in the sample the mirage effect was used. Obtained results show that the thermal diffusivity decreases with the increase of sample temperature for all investigated crystals. The GdCOB single crystals reveal a strong anisotropy. The thermal diffusivity along Y direction has the highest value while values obtained in X and Z axes are much lower. Dopants cause decrease in the thermal diffusivity for all investigated directions.     

Cu2S相变过程中热扩散系数的精确测量和解析

材料发生相变时, 其结构和物理性能可能会发生剧烈的变化。采用激光闪射法测量热扩散系数时, 激光照射样品可能会伴随有光吸收/发射现象以及温度的显著升高, 导致其测量值偏离真实值。本工作以Cu₂S为研究对象, 发现激光照射样品后, 光吸收/发射的影响很小可以忽略, 但样品温度的升高则会明显影响热扩散系数的测量。通过构建具有不同石墨层厚度的石墨/Cu₂S双层结构, 利用石墨层减弱激光照射时Cu₂S样品的温度增加幅度, 成功使热扩散系数出现显著降低的起始温度接近采用DSC测量材料发生相变的起始温度。本研究进一步建立了石墨/Cu₂S双层结构样品的热流输运模型, 从石墨/Cu₂S双层结构样品的实验测试热扩散系数中解析出了Cu₂S在相变区间的本征热扩散系数。本工作对于理解和精确表征具有相变特征的离子导体热电材料、光敏、热敏材料的热扩散系数具有重要的意义。     

Simultaneous Absorptance and Thermal-Diffusivity Determination of Optical Components with Laser Calorimetry Technique

The laser calorimetry (LCA) technique is used to determine simultaneously the absorptances and thermal diffusivities of optical components. An accurate temperature model, in which both the finite thermal conductivity and the finite sample size are taken into account, is employed to fit the experimental temperature data measured with an LCA apparatus for a precise determination of the absorptance and thermal diffusivity via a multiparameter fitting procedure. The uniqueness issue of the multiparameter fitting is discussed in detail. Experimentally, highly reflective (HR) samples prepared with electron-beam evaporation on different substrates (BK7, fused silica, and Ge) are measured with LCA. For the HR-coated sample on a fused silica substrate, the absorptance is determined to be 15.4?ppm, which is close to the value of 17.6?ppm, determined with a simplified temperature model recommended in the international standard ISO11551. The thermal diffusivity is simultaneously determined via multiparameter fitting to be approximately 6.63?×?10^?7?m² · s^?1 with a corresponding square variance of 4.8?×?10^?4. The fitted thermal diffusivity is in reasonably good agreement with the literature value (7.5?×?10^?7?m² · s ^?1). Good agreement is also obtained for samples with BK7 and Ge substrates.     

An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation1

This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.     

The effects of cobalt substitution on the thermal diffusivity of YBa2Cu3O7?δ superconductor

The thermal diffusivity κ(T) of the cobalt-substituted sintered YBCO system, YBa₂Cu_3−x Co _x O_7∮δ (x=0.0, 0.1), has been measured to, investigate, effects of atomic substitution and charge carrier concentration on the thermal diffusion processes. The thermal diffusivity was measured in the temperature range 35–300 K, using the transient-plane-source technique. The results show that, belowT _c , the κ(T) values of the doped (x=0.1), samples are lower than the corresponding values for the undoped (x=0.0) samples. This may be due to the difference in the free-charge carrier concentrations of the two samples. A decoupling between the conducting Cu−O planes as a result, of Co-doping in the chain sites may contribute to additional decrease in the thermal diffusivity of the doped sample. An attempt was made to explain the rise in the thermal diffusivity belowT _c by adopting a recent theoretical model based on the existence of weakly damped collective electron excitations of Bose type, with acoustic dispersion relation, (acoustic plasmons) inside the superconducting gap.     

Estimation of thermal properties of composite materials without instrumentation inside the samples

Recent contributions of parameter estimation in the measurement of thermal properties are of great importance. In comparison with other techniques such as steady state (hot guarded plate, etc.) or transient (line source method, flash method, etc.), the use of parameter estimation provides more information and, in most cases, produces faster results. With this technique the thermal conductivity and the volumetric specific heat are estimated simultaneously and as a function of time, temperature, or position. This method requires experimental data, such as transient temperature and heat flux measurements. Previously, the temperature measurements came from thermocouples embedded in the sample. These thermocouples are introduced in the sample either by drilling holes or by molding the material around a series of thermocouples. Both operations are time-consuming and costly and are needed for each sample. In this study, temperature measurements are made only on the two sides of the samples with thin resistance thermometers. Since the sensors are not inside the material, the effect of the thermal contact conductance between sensor and sample was first investigated. The value of this thermal contact conductance was estimated by using samples of high-conductivity material. Using these values, the estimated thermal properties obtained with surface temperature measurements are compared with values provided by other methods for several low-thermal conductivity materials; agreement has been very good.     

Determination of Thermal-Diffusivity Dependence on Temperature of Transparent Samples by Thermal Wave Method

The use of a typical measuring cryostat with a standard temperature controller was proposed for investigation of the temperature dependence of the thermal diffusivity of transparent samples. The basic idea is to use the cryostat heater to control the mean sample temperature and to generate the thermal wave in it, simultaneously. Because of the relatively high thermal inertia of the system, the measurements are carried out at frequencies not exceeding 50 mHz. The periodic temperature disturbance in the sample was detected optically by the use of the mirage effect. The proposed method was used for determination of the thermal diffusivity of yttrium aluminum garnet single crystals in a temperature range from 20 °C to 200 °C.     

Measurement of thermophysical properties of molten salts: Mixtures of alkaline carbonate salts

The purpose of this study is to develop measuring methods for the thermal diffusivity, the specific heat capacity, and the density of molten salts, as well as to measure these properties of mixtures of alkaline carbonate salts. The thermal diffusivity is measured by the stepwise heating method. The sample salt is poured into a thin container, and as a result, a three-layered cell is formed. The thermal diffusivity is obtained from the ratio of temperature rises at different times measured at the rear surface of the cell when the front surface is heated by the stepwise energy from an iodine lamp. The specific heat capacity is measured using an adiabatic scanning calorimeter. The density is measured by Archimedes' principle. Thermal conductivity is determined from the above properties. Measured samples are Li₂CO₃-K₂CO₃ (42.7–57.3, 50.0-50.0, and 62.0-38.0 mol%).Invited paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Correction of Edge Effect in AC Calorimetric Method for Measuring Thermal Diffusivity of CVD Diamond Films1

In the thermal diffusivity measurement of a CVD diamond film using an ac calorimetric method, the reflection of an ac temperature wave at the edge of the film sample should be considered due to the limited length of the sample and its high thermal diffusivity, i.e., the edge effect. In this case, the measured thermal diffusivity is given as a function of frequency. The relation between the measured thermal diffusivity and the frequency is represented as an analytical expression. The real thermal diffusivity is obtained by correcting the edge effect by two means. One is an iterative method using the directly measured edge length of the sample to fit the analytical expression. The other is a parameter estimation method by which a simplex method is used to estimate the edge length and the real thermal diffusivity. Thermal diffusivities of two diamond films were measured, and data were analyzed using the above methods. The result shows that the parameter estimation method is relatively accurate and convenient in processing test data.