Thermal conductivity by a pulse-heating method: Theory and experimental apparatus

A new dynamic technique for the measurement of thermal conductivity at high temperatures has been developed at the IMGC. The specimen is brought to high temperatures with a current pulse; during cooling the heat content is dissipated by radiation and by conduction. The differential equation describing this process contains terms related to the heat capacity, the hemispherical total emittance, and the thermal conductivity of the material. If the first two properties are determined using the same specimen during subsecond pulse heating experiments, thermal conductivity may be evaluated by accurate measurements of the round-shaped temperature profiles established on the specimen during cooling. High-speed scanning pyrometry makes possible accurate measurements of temperatures and of temperature derivatives (with respect to space and time), which enables the differential equation describing the power balance at each point of the specimen to be transformed into a linear equation of the unknown thermal conductivity. A large overdetermined system of linear equations is solved by least-squares techniques to obtain thermal conductivity as a function of temperature. The theory underlying the technique is outlined, the experimental apparatus is described, and details of the measurement technique are given.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.     

Temperature oscillation techniques for simultaneous measurement of thermal diffusivity and conductivity

Simple temperature ocillation techniques are described for the last measurement of thermal dill'usivity and conductivity of liquids. The liquid specimen is a slab bounded above and below by a reference material. Two Peltier elements mounted on the outer Surfaces of the reference layers generate temperature ocillationS of these surfaces. Temperature waves propagate tluough the reference layers into the specimen. The thermal dilhusivity of the specimen is deduced by measuring all evaluating the amplitude attenuation and or the phase shift between the fundamental temperature oscillations at the surface of the liquid specimen and at a well-defined position inside the specimen. If the thermal diffusivity of the specimen is known. the thermal conductivity is determined by the measured amplitude attenuation and or the phase shill between the fundamental temperature oscillations at the surface of the reference layer and at the surface of the specimen. Slab and semi-infinite body geometries are considered. Measurement cells are designed and experiments are carried out with water, ethanol. heptane. monane. and glycerine. The results of the measurements of thermal dilhusivity asree very well, and those of thermal conductivity reasonably well, with the data obtained from the literature.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19-24, 1994, Boulder, Colorado, U.S.A.Author to whom correspondence should be addressed.     

A new dynamic technique for the measurement of hemispherical total emittance

A new dynamic technique for the measurement of thermal conductivity under development at the IMGC requires accurate values of heat capacity and of hemispherical total emittance at high temperature. Until recently, these data were provided by subsecond pulse heating experiments performed on the same specimens in the same apparatus. The pulse heating technique is the most accurate method for the determination of heat capacity at high temperatures, but because of various experimental problems, the accuracy of hemispherical total emittance determinations is limited to 5%. A new method for a more accurate determination of hemispherical total emittance is proposed, which uses the same experimental data available from thermal conductivity experiments. An analysis of the temperature profiles measured during the free cooling indicates that regions with high-temperature gradients (toward the ends of the specimen) are the best regions for thermal conductivity measurements, while regions with low-temperature gradients (at the center of the specimen) are the best regions for hemispherical total emittance determinations. The new measurement method and some preliminary results are presented and discussed.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Conventional Simultaneous Measurement of Specific Heat Capacity and Thermal Conductivity by Thermal Radiation Calorimetry

Thermal radiation calorimetry has been applied to measure the thermal conductivity and the specific heat capacity of an isolated solid specimen simultaneously. The system, in which a disk-shaped specimen and a flat heater are mounted in a vacuum chamber with the specimen heated on one face by irradiation, is presented. A theoretical formulation of the simultaneous measurement at quasi-steady state is described in detail. Noncontact temperature measurement of both specimen surfaces has been performed using pyrometers and a thermocouple set in the gap between the heater and the specimen. Pyroceram 9609 specimens, whose surfaces were blackened with colloidal graphite, were used in the measurement. The largest error involved in the noncontact temperature measurement is ±2°C in the range from 450 to 650°C. The resultant values of the specific heat capacity and the thermal conductivity deviate by about 10% from the recommended values for the Pyroceram specimen.     

一种新的测量半球全波发射率的动态技术

本章介绍了一种用于半球全波发射率测量的动态技术 .它需要已知热容量和热传导率的准确的资料 .对在自然冷却过程中所测量的样品的温度分布的分析表明 ,高温度梯度区域 (样品的两端部分 )是测量热传导率的最好区域 ,而低温度梯度区域 (样品的中间部分 )是测量半球全波发射率的最佳范围 .讨论了这种新的测量方法及一些初步的实验结果 .     

A hybrid finite element/method of moment formulation for singlefrequency eddy current inversion

Eddy-current inverse techniques using single-frequency currents have been applied with limited success to the reconstruction of crack width and thickness profiles primarily for one-dimensional and axisymmetric geometries. Because of the diffusive nature of the induced low-frequency eddy currents, the reconstruction process differs from high-frequency wave propagation methods. On the physical basis that both diffusive and wave phenomena can be described by the same Green's function with either a complex or real wave number, an integral formulation for the low-frequency magnetic vector potential is presented. By employing an iterative Born approximation algorithm and the method of moments, a reconstruction method for the conductivity profile in a metallic specimen is developed. To make this formulation amenable to complex geometries, finite-element analysis techniques are utilized to compute the integral kernel. The inversion process is tested with synthetic data generated by the numerical solution of a generic embedded flaw in a full-space and a surface-breaking defect     

Thermal conductivity measurements at low temperatures

We describe briefly the experimental facilities developed for the measurement of thermal conductivity of solids in the temperature range 10K–300K. Different techniques have been used for the determination of thermal conductivity, depending on the relaxation time of the system under investigation. Measurements on stainless steel 304, using steady state and non-steady state methods are presented. Values of thermal conductivity obtained by both these methods agree to each other and are consistent with those reported earlier. Paper presented at the poster session of MRSI AGM VI, Kharagpur, 1995     

基于岩土轴向分层垂直地埋管换热模型分析

当埋管周围岩土轴向分层热物性相差较大时,传统均匀介质模型忽略了岩土分层、热物性变化和地下水流动的综合影响,往往会带来偏差。本文通过对南京某一地埋管换热器现场实验,分析了岩土分层和地下水流动特性,建立了地埋管换热器岩土轴向分层数值模型,并进行验证分析。对比分析轴向数值模型与传统的有限长纯导热模型(FLS)和渗流有限长线热源模型MFLS均匀介质模型,结果表明:连续加热60 d后轴向分层模型的埋管出水温度比FLS模型低约0. 5℃,比MFLS模型高0. 3℃,且轴向分层模型不同深处温度响应差别较大。并对不同距离不同加热时间下,埋管轴向温度的分布特性进行了研究探讨。     

Mathematical Models for Pulse-Heating Experiments

Accurate measurements of thermophysical properties at high temperatures (above 1000 K) have been obtained with millisecond pulse-heating techniques using tubular specimens with a blackbody hole. In the recent trend toward applications, simpler specimens in the form of rods or strips have been used, with simultaneous measurement of the normal spectral emissivity using either laser polarimetry or integrating sphere reflectometry. In these experiments the estimation of the heat capacity and of the hemispherical total emissivity is based on various computational methods that were derived assuming that the temperature was uniform in the central part of the specimen (long thin-rod approximation). The validity of this approach when using specimens with large cross sections (rods, strips) and when measuring temperature on the specimen surface must be verified. The application of the long thin-rod approximation to pulse-heating experiments is reconsidered, and an analytical solution of the heat equation that takes into account the temperature dependence of thermophysical properties is presented. A numerical model that takes into account the temperature variations across the specimen has been developed. This model can be used in simulated experiments to assess the magnitude of specific phenomena due to the temperature gradient inside the specimen, in relation to the specimen geometry and to the specific thermophysical properties of different materials.     

铝硅合金热疲劳过程的应力应变分析

对铝硅合金进行了热疲劳模拟实验和应力、应变分析。铝硅合金的导热系数高,高温弹性模量低,温度涨落过程产生的宏观热应力低于同一温度下合金的屈服应力和疲劳极限;而铝、硅热膨胀系数的差异将在铝硅相界等局部区域产生远大于宏观热应力的微观热应力,并因此萌生热疲劳裂纹。通过变质工艺改变硅相形态,可改善合金的抗热疲劳性能。     

An apparatus for noncontact measurement of thermal conductivity by thermal radiation heating

Thermal radiation calorimetry was applied to measure the thermal conductivity of insulating solid specimens. We consider the system in which a disk-shaped specimen and a flat heater are mounted in a vacuum chamber with the specimen heated on one face by irradiation. A temperature difference between two faces was observed at elevated temperatures under steady-state conditions. An apparatus was developed using a thin graphite sheet as the heater element. Disk-shaped Pyrex glass and Pyroceram specimens, whose surfaces were blackened with colloidal graphite, were used in the measurements. Noncontact temperature measurement was performed using pyrometers and a thermocouple set in the gap between the heater and the specimen. Deviations of the estimated thermal conductivities from the recommended values were about 5% in the temperature range 250 to 800°C. Paper presented at the Fourth Asian Thermophysical Properties Conference, September 5–8, 1995, Tokyo, Japan.     

Thermophysical Properties of Diorites along with the Prediction of Thermal Conductivity from Porosity and Density Data

The main focus of this paper involves the use of models to predict the thermophysical properties of diorites. For the prediction of thermal conductivity, an existing mixing law and empirical models have been used. Due to the porosity dependence in all the existing models, ASTM (American Society for Testing and Materials) standard methods have been applied to measure the density, porosity, and specific gravity of diorite rocks taken from the Shewa-Shahbaz Garhi volcanic complex near Mardan, Pakistan. The chemical composition of these samples has been analyzed using the X-ray florescence technique. The theoretically calculated values of specific gravity and the density of the specimen based on the chemical composition and porosity are in good agreement with those obtained from experimental measurements at ambient conditions. The thermal conductivity and thermal diffusivity of these rocks have been measured simultaneously using the transient plane source (TPS) technique at room temperature. The effective thermal conductivity calculated from various models is in agreement with the experimental data within 15%. Simple correlations between estimated density and porosity and between the effective thermal conductivity and porosity are also established.     

Thermal Conductivity of Cobalt-Based Catalyst for Fischer–Tropsch Synthesis

In this study, the thermal conductivity of cobalt-based catalyst specimens in the temperature range from 160 ^◦C to 255 ^◦C are measured via a steady-state apparatus. The apparatus and procedures are applied to several specimens of cobalt-based catalyst powder compacts. Specimens with different degrees of porosity are produced by pressing cobalt-based catalyst powder with a particle size of (80 to 360) mesh. The thermal conductivity of cobalt-based catalyst powder compacts is investigated as functions of temperature, specimen density, porosity, and powder size. The results indicate that the thermal conductivity of the catalyst specimens increases linearly with temperature and density and is practically independent of the particle size of the powder in an atmosphere of air, while the porosity dependence of the thermal conductivity is inverse to that of density. In addition, the effects of some measuring factors on the thermal conductivity show that the reliability of the thermal conductivity measurements of cobalt-based catalyst specimens are influenced easily by parallelism, specimen roughness, and moisture content, whereas the specimen thickness and water bath temperature have only a slight effect on the reliability.     

Thermal conductivity of additively colored MgO

The thermal conductivity of MgO additively colored in magnesium vapor has been measured in the temperature range 1–55 K. These measurements have been compared to the pure crystal thermal conductivity data. There is a “dip” in the thermal conductivity vs. temperature curve of the additively colored specimen near 20 K, where the thermal conductivity is depressed to one-fifth of the pure crystal value. The “dip” is attributed to resonant phonon scattering associated with quasilocalized modes of theF center. After UV irradiation, resulting in partialF →F ⁺ conversion, the thermal conductivity “dip” was found to be much weaker. The increase in thermal conductivity of the bleached sample is attributed to a relaxation of neighboring ions due to the different charge state of the defect. A successful fit to the thermal conductivity data has been made using the Debye model of solids and a defect scattering rate consisting of a resonance expression plus Rayleigh scattering term. A good fit can be made to the data of the bleached specimen by varying only the parameter associated with concentration ofF centers.     

Establishment of accuracy limits and standards for comparative thermal conductivity measurements

New techniques have been developed for reducing thermal conductivity data from thermal comparative measurements. The first of these techniques is based on making a Taylor-series expansion of the stack centerline temperature profile. The result is an expression giving the ratio of sample to reference conductivities at any temperature as a function of measured quantities, the stack thermocouple readings and stack element thicknesses. The conventional formula presently used to reduce comparative conductivity data is shown to be a special result of the general analysis. A second technique involves the use of linear least-squares (LS) techniques to derive both the sample and the reference conductivities from the measured data. The LS technique provides the coefficients for a polynomial temperature expansion of the reference and sample conductivities directly. Use of the new techniques is illustrated in a reduction of some comparative data on the conductivities of Pyrex 7740 and Pyroceram 9606. It is shown that a highly self-consistent pair of conductivity functions can be derived for these two commonly used reference materials if the conductivity vs temperature relation for Pyrex is modified slightly from its recommended value. The Pyroceram conductivity results from the comparative measurements are in good agreement with a conductivity derived from pulse diffusivity and differential scanning calorimetry measurements and also in good agreement with the recommended Pyroceram conductivity function.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Evaluation of Thermophysical Properties of Functionally Graded Materials

In this work, by considering four-layered functionally graded material (FGM) specimens of Cu/Ni and PSZ/NiCrAlY, the transient characteristics and homogeneity of heat conduction media have been studied. The thermal diffusivities of the considered specimens have been measured by the laser flash method. As the temperature response curve of a FGM is very similar to that of a homogeneous material, it is difficult to distinguish a FGM from a homogeneous material by the shape of the temperature responses. Therefore, the thermal diffusivity obtained from the half-time method is usually taken as the corresponding value of the thermal diffusivity. The apparent thermal conductivity, obtained from the corresponding value of the thermal diffusivity and the average of the heat capacity of each layer, is different from the effective thermal conductivity, obtained from the sum of the heat resistances of each layer. As the values of the heat capacity of materials exist over a certain range, and the heat capacity distribution can be predicted when the materials in a FGM are known, the amount of error that will be caused when the effective thermal conductivity is replaced by the apparent value can be determined. Also, the heterogeneity of a FGM, based on an evaluation of thermophysical properties, has been discussed.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui,P. R. China.     

Stability and thermal conductivity enhancement of carbon nanotube nanofluid using gum arabic

This experimental study reports on the stability and thermal conductivity enhancement of carbon nanotubes (CNTs) nanofluids with and without gum arabic (GA). The stability of CNT in the presence of GA dispersant in water is systematically investigated by taking into account the combined effect of various parameters, such as sonication time, temperature, dispersant and particle concentration. The concentrations of CNT and GA have been varied from 0.01 to 0.1?wt% and from 0.25 to 5?wt%, respectively, and the sonication time has been varied in between 1 and 24?h. The stability of nanofluid is measured in terms of CNT concentration as a function of sediment time using UV-Vis spectrophotometer. Thermal conductivity of CNT nanofluids is measured using KD-2 prothermal conductivity meter from 25 to 60°C. Optimum GA concentration is obtained for the entire range of CNT concentration and 1–2.5?wt% of GA is found to be sufficient to stabilise all CNT range in water. Rapid sedimentation of CNTs is observed at higher GA concentration and sonication time. CNT in aqueous suspensions show strong tendency to aggregation and networking into clusters. Stability and thermal conductivity enhancement of CNT nanofluids have been presented to provide a heat transport medium capable of achieving high heat conductivity. Increase in CNT concentrations resulted in the non-linear thermal conductivity enhancement. More than 100–250% enhancement in thermal conductivity is observed for the range of CNT concentration and temperature.     

绝热材料低温热导率测试装置

针对被测试样聚氨脂塑料硬泡沫的低温性能,采用平板热导仪[1],用稳态法测量其低温热导率.以液氮和液氦作为冷源,用真空绝热、控制冷热板温度,可以获得不同温度下的微分热导率和平均热导率.     

High-Temperature Thermal Conductivity Measurement Apparatus Based on Guarded Hot Plate Method

An alternative calibration procedure has been applied using apparatus built in-house, created to optimize thermal conductivity measurements. The new approach compared to those of usual measurement procedures of thermal conductivity by guarded hot plate (GHP) consists of modified design of the apparatus, modified position of the temperature sensors and new conception in the calculation method, applying the temperature at the inlet section of the specimen instead of the temperature difference across the specimen. This alternative technique is suitable for eliminating the effect of thermal contact resistance arising between a rigid specimen and the heated plate, as well as accurate determination of the specimen temperature and of the heat loss at the lateral edge of the specimen. This paper presents an overview of the specific characteristics of the newly developed “high-temperature thermal conductivity measurement apparatus” based on the GHP method, as well as how the major difficulties are handled in the case of this apparatus, as compared to the common GHP method that conforms to current international standards.     

The effect of variable properties on the helical flow and heat transfer of power law fluids

Summary Laminar flow and forced convection heat transfer of the time independent non–Newtonian fluid obeying power law stress-strain relation have been investigated numerically in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder rotates about the common axis with constant angular velocity and the outer cylinder is at rest. The viscosity of the fluid and thermal conductivity are assumed to vary with the temperature. The outer surface of the annulus is considered to be adiabatic, while the inner surface has a uniform temperature. The tangential and axial momentum equations and energy equation have been solved iteratively by using a finite difference method. For the steady fully developed flow, the velocity distributions, temperature profiles, the volumetric flow rate, torque and the average Nusselt number have been obtained for different values of the radius ratio and model parameters.