Direct Measurement Of Thermal Conductivity Research Articles

Use of distributed temperature sensing (DTS) coupled to ground source heat exchangers for geological thermo-stratigraphic correlation

The thermal characterisation of a geosonde field, consisting of four boreholes at the ENEA-Casaccia Research Centre (Rome, Italy), was carried out by processing the temperature values measured by DTS (Distributed Temperature Sensing) fibre optics positioned vertically in each well. By correlating the vertical temperature profiles, it was possible to estimate the thermal conductivity of each stratigraphic level and the contribution of the groundwater on the heat exchange between ground and geothermal probes. The theoretical model has been confirmed by the experimental data obtained through direct measurement of thermal conductivity on soil/rock samples collected at different depths.In the first 10 m of depth, temperature variations are influenced by seasonal climatic fluctuations, the amplitude of which decreases with depth, to regularise and assume a linear trend, compatible with the movement of groundwater.The work carried out has shown that the area investigated is affected by the upwelling of hydrothermal fluids from the deep aquifer, which infiltrate the fractured lavas reaching the most superficial layers of the subsurface. The results of this research could be useful for estimating the geothermal potential of the areas within the ‘Cesano geothermal field’, whose lithotypes belong to the Sabatini volcanic province.

Direct measurement of thermal conductivity of gold nanowires and nanoribbons at ambient room temperature and 100 °C

Direct measurements are reported of the thermal conductivity (κ) for gold nanowires and nanoribbons fabricated on a support substrate. Two thickness values of 50 and 100 nm are investigated with lateral dimensions ranging from 74 to 720 nm, thereby spanning the nanowire to nanoribbon scales. Average polycrystalline grain sizes were 27 ± 5 nm for thickness 50 nm and 35 ± 4 nm for 100 nm thickness. Systematic decrease in κ is observed as film thickness is reduced and, for given thickness, as width decreases. At large lateral width studied here, corresponding to the microscale, κ values at room temperature are 280 and 200 W/m K for thicknesses of 100 and 50 nm, respectively. These are to be compared with the accepted value of κ = 317 W/m K for bulk gold. For the smallest case investigated, 50 nm in thickness and 74 nm in width, a value of κ = 56 W/m K is obtained. A small decrease is observed for κ when measured with ambient temperature 100 °C. The systematic dependence on width, for each thickness and both ambient temperatures studied, followed a simple exponential dependence with a characteristic length parameter of ∼150 nm. This length parameter exceeds the accepted electron mean-free path (∼40 nm), the grain sizes, and the film thicknesses. The decrease in κ with diminishing size was examined based on the Boltzmann transport equation (BTE) methods. Agreement and limitations of the BTE are discussed.

Indirect Methods for Validating Shallow Geothermal Potential Using Advanced Laboratory Measurements from a Regional to Local Scale—A Case Study from Poland

This paper presents a broad overview of laboratory methods for measuring thermal properties and petrophysical parameters of carbonate rocks, and analytical methods for interpreting the obtained data. The investigation was conducted on carbonate rock samples from the Kraków region of Poland in the context of shallow geothermal potential assessment. The measurement techniques used included standard macroscopic examinations; petrophysical investigations (porosity, density); analysis of mineral composition thermal conductivity (TC) and specific heat measurements; and advanced investigations with the use of computed tomography (CT). Various mathematical models, such as layer model, geometric mean, and spherical and non-spherical inclusion models, were applied to calculate thermal conductivity based on mineralogy and porosity. The aim of this paper was to indicate the optimal set of laboratory measurements of carbonate rock samples ensuring sufficient characterization of petrophysical and thermal rock properties. This concerns both the parameters directly characterizing the geothermal potential (thermal conductivity) and other petrophysical parameters, e.g., porosity and mineral composition. Determining the quantitative relationship between these parameters can be of key importance in the case of a shortage of archival thermal conductivity data, which, unlike other petrophysical measurements, are not commonly collected. The results clearly show that the best correlations between calculated and measured TC values exist for the subgroup of samples of porosity higher than 4%. TC evaluation based on porosity and mineral composition correlation models gives satisfactory results compared with direct TC measurements. The methods and results can be used to update the existing 3D parametric models and geothermal potential maps, and for the preliminary assessment of geothermal potential in the surrounding area.

Mediate relation between electrical and thermal conductivity of soil

Thermal conductivity is a key parameter for many soil applications, especially for dimensioning shallow and very shallow geothermal systems based on the possible heat extraction rate and for modelling heat transfer processes around high voltage underground cables. Due to the limited purview of direct thermal conductivity measurements, for an investigation of extensive areas, usually other geophysical methods like electrical resistivity tomography measurements are applied. To derive thermal conductivity of soil from geoelectrical measurements a relation between electrical and thermal conductivity is needed. Until now only few approaches worked on a direct correlation between both conductivities. Due to the difficulties of a direct relation, within this study a modular approach of a mediate correlation between electrical and thermal conductivity was investigated. Therefore, a direct relationship between a corrected electrical conductivity and water content as well as the standard and simple thermal conductivity model of Kersten (Bull of the Univ Minnesota 28:1–227, 1949) was used. To develop this concept soil types of sand, silt loam and clay were investigated where different saturation steps and pressure loads were applied. For each configuration electrical and thermal conductivity as well as water content and bulk density was determined. To refine the results of the calculated water content a corrective factor was applied. Furthermore, bulk density as an inlet parameter of the Kersten equation was also derived based on electrical conductivity. The suggested proceeding enables the determination of thermal conductivity solely based on electrical conductivity without prior soil property information.

High temperature measurements and condensed matter analysis of the thermo-physical properties of ThO2

Values are presented for thermal conductivity, specific heat, spectral and total hemispherical emissivity of ThO2 (a potential nuclear fuel material) in a temperature range representative of a nuclear accident - 2000 K to 3050 K. For the first time direct measurements of thermal conductivity have been carried out on ThO2 at such high temperatures, clearly showing the property does not decrease above 2000 K. This could be understood in terms of an electronic contribution (arising from defect induced donor/acceptor states) compensating the degradation of lattice thermal conductivity. The increase in total hemispherical emissivity and visible/near-infrared spectral emissivity is consistent with the formation of donor/acceptor states in the band gap of ThO2. The electronic population of these defect states increases with temperature and hence more incoming photons (in the visible and near-infrared wavelength range) can be absorbed. A solid state physics model is used to interpret the experimental results. Specific heat and thermal expansion coefficient increase at high temperatures due to the formation of defects, in particular oxygen Frenkel pairs. Prior to melting a gradual increase to a maximum value is predicted in both properties. These maxima mark the onset of saturation of oxygen interstitial sites.

Technique for direct measurement of thermal conductivity of elastomers and a detailed uncertainty analysis

High thermal conductivity thermal interface materials (TIMs) are needed to extend the life and performance of electronic circuits. A stepped bar apparatus system has been shown to work well for thermal resistance measurements with rigid materials, but most TIMs are elastic. This work studies the uncertainty of using a stepped bar apparatus to measure the thermal resistance and a tensile/compression testing machine to estimate the compressed thickness of polydimethylsiloxane for a measurement on the thermal conductivity, keff. An a priori, zeroth order analysis is used to estimate the random uncertainty from the instrumentation; a first order analysis is used to estimate the statistical variation in samples; and an a posteriori, Nth order analysis is used to provide an overall uncertainty on keff for this measurement method. Bias uncertainty in the thermocouples is found to be the largest single source of uncertainty. The a posteriori uncertainty of the proposed method is 6.5% relative uncertainty (68% confidence), but could be reduced through calibration and correlated biases in the temperature measurements.

Direct measurement of thermal conductivity in solid iron at planetary core conditions.

The conduction of heat through minerals and melts at extreme pressures and temperatures is of central importance to the evolution and dynamics of planets. In the cooling Earth's core, the thermal conductivity of iron alloys defines the adiabatic heat flux and therefore the thermal and compositional energy available to support the production of Earth's magnetic field via dynamo action. Attempts to describe thermal transport in Earth's core have been problematic, with predictions of high thermal conductivity at odds with traditional geophysical models and direct evidence for a primordial magnetic field in the rock record. Measurements of core heat transport are needed to resolve this difference. Here we present direct measurements of the thermal conductivity of solid iron at pressure and temperature conditions relevant to the cores of Mercury-sized to Earth-sized planets, using a dynamically laser-heated diamond-anvil cell. Our measurements place the thermal conductivity of Earth's core near the low end of previous estimates, at 18-44 watts per metre per kelvin. The result is in agreement with palaeomagnetic measurements indicating that Earth's geodynamo has persisted since the beginning of Earth's history, and allows for a solid inner core as old as the dynamo.

Transport Properties of Bulk Thermoelectrics: An International Round-Robin Study, Part II: Thermal Diffusivity, Specific Heat, and Thermal Conductivity

For bulk thermoelectrics, improvement of the figure of merit ZT to above 2 from the current values of 1.0 to 1.5 would enhance their competitiveness with alternative technologies. In recent years, the most significant improvements in ZT have mainly been due to successful reduction of thermal conductivity. However, thermal conductivity is difficult to measure directly at high temperatures. Combined measurements of thermal diffusivity, specific heat, and mass density are a widely used alternative to direct measurement of thermal conductivity. In this work, thermal conductivity is shown to be the factor in the calculation of ZT with the greatest measurement uncertainty. The International Energy Agency (IEA) group, under the implementing agreement for Advanced Materials for Transportation (AMT), has conducted two international round-robins since 2009. This paper, part II of our report on the international round-robin testing of transport properties of bulk bismuth telluride, focuses on thermal diffusivity, specific heat, and thermal conductivity measurements.

Thermal Conductivity of Industrial $\hbox{Nb}_{3} \hbox{Sn}$ Wires Fabricated by Various Techniques

We have developed a new experimental setup specifically designed for measuring thermal conductivity on technical superconductors in the range of temperatures 3-330 K in magnetic fields up to 21 T. Three Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn wires, produced by the powder-in-tube technique, the bronze route, and the internal tin restacked-rod process, respectively, have been investigated. We show that, due to the complexity of the architecture of these wires, direct measurement of thermal conductivity is required for a correct estimation of thermal stability in superconducting magnets.

Evaluation System for Figure of Merit of Thermoelectric Devices

The apparatus for evaluation of the figure of merit (ZT) of thermoelectric devices has been developed in order to investigate the performance of the thermoelectric devices. ZT value is comprised of three physical quantities, Seebeck coefficient, electrical conductivity, and thermal conductivity. In this study, we present new apparatus developed for evaluating the ZT and power generation efficiency of devices by direct measurement of thermal conductivity using guarded hot plate (GHP) method. The measured ZT values and power generation efficiency of the thermoelectric devices are presented.

A combined experimental and numerical method for extracting temperature-dependent thermal conductivity of gypsum boards

This paper proposes a hybrid numerical–experimental method for extracting thermal conductivity of various gypsum board products at elevated temperatures. Gypsum board is ubiquitously used in fire resistant construction, yet there is wide variability in reported values of thermal conductivity of gypsum at high temperatures. Given the effects of porosity, moisture and non-linear temperature distribution in gypsum under heating, direct measurement of thermal conductivity, e.g. by using the hot plate method, is not an easy task. This paper proposes a thermal conductivity model for gypsum at high temperatures, treating gypsum as a porous material consisting of solid and pores and takes into consideration the effects of radiation at high temperatures. This enables the gypsum thermal conductivity–temperature relationship to be described as a function of two variables: reduction in thermal conductivity from its value at ambient temperature to that of dried gypsum, and effective spherical void size. To enable these two parameters to be quantified, a hybrid experimental–numerical method is proposed. This hybrid model uses a validated one-dimensional Finite Difference heat conduction program and high temperature test results on small samples of gypsum boards. Through a clearly defined trial and error procedure, the water evaporation induced drop in the thermal conductivity, and the void size that gives the best agreement between numerical prediction and high temperature tests are obtained to quantify the gypsum thermal conductivity–temperature relationship.

Diamond overgrown InAlN/GaN HEMT

In this work the technology and characterization of nanocrystalline diamond (NCD) films directly grown on InAlN/GaN HEMTs is presented. Optimization of GaN based HEMT process steps including metallization stacks is discussed. A fully processed InAlN/GaN HEMT structure with 7 nm barrier has been overgrown in a temperature range of 750 °C to 800 °C with a 500 nm thick nanocrystalline diamond film in a Hot Filament CVD system. First results of semi-enhancement mode of DC and RF HEMT operation are reported. The grown NCD films were characterized by SEM, TEM, and Raman spectroscopy. Although no direct thermal conductivity measurements are conducted yet; the performed experiments shows the compatibility of growing high quality NCD films, several microns thick, on InAlN/GaN HEMTs as a potential material for heat extraction purposes.

Thermal conductivity in metallic nanostructures at high temperature: Electrons, phonons, and the Wiedemann-Franz law

The Boltzmann transport equation is used to calculate thermal and electrical conductivity of metal nanostructures with characteristic dimensions in the 25--500 nm range, near to and above the Debye temperature. Thermal conductivity contributions from phonons and electrons are considered. The intrinsic effects of electron-phonon, phonon-phonon, and phonon-electron scattering, and grain boundary and surface interactions are addressed. Excellent agreement is found between model results and available data reporting direct measurements of thermal conductivity of nanowires, ribbons, and thin films in Al, Pt, and Cu, respectively. The Wiedemann-Franz (W-F) law and Lorenz factor are examined with decreasing size; their applicability is found to degrade in nanowires due mainly to increased relative phonon contribution. The effect of differences in the electron mean-free path for thermal gradient versus electrical field is also examined. A modified version of W-F is presented, corrected for these two factors and valid from macroscale to nanoscale provided characteristic sizes exceed the phonon mean-free path.

The thermal conductivity of meteorites: New measurements and analysis

We have measured the thermal conductivity at low temperatures (5–300 K) of six meteorites representing a range of compositions, including the ordinary chondrites Cronstad (H5) and Lumpkin (L6), the enstatite chondrite Abee (E4), the carbonaceous chondrites NWA 5515 (CK4 find) and Cold Bokkeveld (CM2), and the iron meteorite Campo del Cielo (IAB find). All measurements were made using a Quantum Design Physical Properties Measurement System, Thermal Transport Option (TTO) on samples cut into regular parallelepipeds of ∼2–6 mm dimension. The iron meteorite conductivity increases roughly linearly from 15 W m −1 K −1 at 100 K to 27 W m −1 K −1 at 300 K, comparable to typical values for metallic iron. By contrast, the conductivities of all the stony samples except Abee appear to be controlled by the inhomogeneous nature of the meteorite fabric, resulting in values that are much lower than those of pure minerals and which vary only slightly with temperature above 100 K. The L and CK sample conductivities above 100 K are both about 1.5 W m −1 K −1, that of the H is 1.9 W m −1 K −1, and that of the CM sample is 0.5 W m −1 K −1; by contrast the literature value at 300 K for serpentine is 2.5 W m −1 K −1 and those of enstatite and olivine range from 4.5 to 5 W m −1 K −1 (which is comparable to the Abee value). These measurements are among the first direct measurements of thermal conductivity for meteorites. The results compare well with previous estimates for meteorites, where conductivity was derived from diffusivity measurements and modeled heat capacities; our new values are of a higher precision and cover a wider range of temperatures and meteorite types. If the rocky material that makes up asteroids and provides the dust to comets, Kuiper Belt objects, and icy satellites has the same low thermal conductivities as the ordinary and carbonaceous chondrites measured here, this would significantly change models of their thermal evolution. These values would also lower their thermal inertia, thus affecting the Yarkovsky and YORP evolution of orbits and spin for solid objects; however, in this case the effect would not be as great, as thermal inertia only varies as the square root of the conductivity and, for most asteroids, is controlled by the dusty nature of asteroidal surfaces rather than the conductivity of the material itself.

Direct measurement of thermal conductivity of aluminum nanowires

A nanofabricated electrothermal test structure is reported for directly measuring the thermal conductivity of aluminum nanowires near room temperature. Interdigitated nanowires perturb an otherwise symmetric heater-sensor structure analogous to an electrical bridge circuit. Nanowires studied are 100 nm thick with 75, 100, and 150 nm widths. Finite element simulation accounts for complex device geometry. Thermal conductivity and electrical resistivity vary significantly with nanowire dimensions. Electron transport equation models which adequately describe the resistivity data consistently underestimate the thermal conductivity. Incorporating a phonon contribution of ∼21 W/m K to the total thermal conductivity is found to accurately describe the measured values.

Thermophysical Properties of a Chromium–Nickel–Molybdenum Steel in the Solid and Liquid Phases

Numerical simulation of vacuum arc re-melting, pressurized or protective electro-slag re-melting, and ingot casting have become quite important in the metal industry. However, a major drawback of these simulation techniques is the lack of accurate thermophysical properties for temperatures above 1,500 K. Heat capacity, heat of fusion, density, and thermal conductivity are important input parameters for the heat transfer equation. Since, direct measurements of thermal conductivity of alloys in the liquid state are almost impossible, its estimation from electrical conductivity using the Wiedemann–Franz law is very useful. The afore-mentioned thermophysical properties of several steels are investigated within the context of an ongoing project. Here, we present a full set of thermophysical data for the chromium–nickel–molybdenum steel meeting the standard DIN 1.4435 (X2CrNiMo18-14-3); these values will be used by our partner to simulate various re-melting and solidification processes. Wire-shaped samples of the steel are resistively volume-heated, as part of a fast capacitor discharge circuit. Time-resolved measurements with sub-μs resolution of current through the specimen are performed with a Pearson probe. The voltage drop across the specimen is measured with knife-edge contacts and ohmic voltage dividers, the temperature of the sample with a pyrometer, and the volumetric expansion of the wire with a fast acting CCD camera. These measurements enable the heat of fusion, the heat capacity, and the electrical resistivity to be determined as a function of temperature in the solid and liquid phases. The thermal conductivity and thermal diffusivity are estimated via the Wiedemann–Franz law.

Thermophysical properties of the Ni-based alloy Nimonic 80A up to 2400 K, II

Numerical simulation of fluid flow, heat transfer, solidification or thermal induced stresses have gained a tremendous significance in steel working industry branches. With the advent of adequate computing power, full three-dimensional calculation of the determining physical equations have become possible. A major drawback of these simulation techniques is the lack of accurate thermophysical properties. By the means of a fast pulse heating technique thermophysical data for the solid and liquid material required for the simulations can be measured. Important input parameters for the heat transfer equation are heat capacity, heat of fusion, density and thermal conductivity. Since direct measurements of thermal conductivity of alloys in the liquid state are almost impossible, its estimation from the electrical conductivity using the Wiedemann–Franz law is very useful.

Recommended values for the thermal conductivity of aluminium of different purities in the cryogenic to room temperature range, and a comparison with copper

The thermal conductivity of pure aluminium at cryogenic temperatures varies by many orders of magnitude depending on purity and treatment, and there is little information in the literature on the likely values to be obtained for samples of a given purity. A compilation of measurements from the literature has been assembled and used to provide recommended ranges of values for aluminium of different purities (4N, 5N and 6N) in the normal (non superconducting) state. The number of direct thermal conductivity measurements is too limited to be used alone. Electrical resistivity measurements have thus also been used by converting to thermal conductivity using the Wiedemann–Franz law, which is shown to be valid. Since low temperature measurements can easily be extrapolated to higher temperatures, the results cover the range from 1.2 K (the superconducting transition temperature) to room temperature. Values for 5N purity copper have also been examined in a similar manner, to allow a comparison between the two materials. The main application of these results is in the design of cryogenic thermal links; a discussion of the advantages and disadvantages of both materials for this use is given. The use of silver is also investigated briefly. Trends in the behaviour of the conductivity of aluminium in the superconducting state (to temperatures as low as 50 mK) are also discussed.

Direct measurements of the thermal conductivity of various pyrolytic graphite samples (PG,TPG) used as thermal dissipation agents in detector applications

We performed model measurements on heat conduction in graphite-based structures, using several configurations. We describe our method for the direct measurement of thermal conductivity both in-plane and out-of-plane, for TPG and PG samples. Our results for the in-plane thermal conductivity coefficient, K ab were obtained with two different sets of boundary conditions; they are in good mutual agreement. Those for the transverse coefficient, K c, differ by a significant factor from the values published by the producers of the material.

Thermal conductivity of a self-frequency-doubling laser crystal measured by use of optical methods

We present a new all-optical technique to measure the thermal conductivity of laser crystals. This technique can be used for crystals that are too small for direct measurement of thermal conductivity. We used this technique to measure the thermal conductivities of Nd:LYAB, with the result of 44 +/- 6% compared with that of Nd:YAG thermal conductivity.