Measurement Of Thermal Properties Research Articles

Measurement and modelling of thermal and physical properties of wood construction materials

Construction materials exposed to fire conditions may decompose resulting in a loss of strength as well as contributing to the growth and size of the fire. Predicting the behavior of timber and other construction materials during a fire exposure requires accurate thermal modeling of the material considering both the effects of elevated temperature and material decomposition state (virgin to char) on the thermal and physical properties. This paper evaluates the use of different techniques to measure the porosity, permeability and thermal diffusivity of wood construction materials at different levels of decomposition due to a high temperature exposure. The porosity and thermal diffusivity values of wood exhibit similar changes with decomposition level. It was found that virgin and char material properties can be used in conjunction with thermogravimetric data to estimate material properties at intermediate decomposition levels. The findings can be used to reduce the number of experiments required to characterize other materials. Permeability was observed to be dependent on the structure and composition of the material. Scanning electron microscopy images revealed that decomposition increased the space between the otherwise compact-arranged elements (grain, particles), resulting in an increase in permeability. Consequently, permeability should be measured at different decomposition levels and direction to quantify the material changes due to a high temperature exposure.

Thermal properties of wood measured by the hot-disk method: comparison with thermal properties measured by the steady-state method

The hot-disk method is a transient method for the measurement of thermal properties. This method can measure both the thermal conductivity and thermal diffusivity in a short time for isotropic materials. To establish a method for measuring the thermal properties of wood by the hot-disk method, the relationship between the thermal properties of wood obtained by the hot-disk method and those obtained by the steady-state method was investigated. The thermal properties were measured by the hot-disk method using small pieces of kiri (Paulownia tomentosa), sugi (Cryptomeria japonica), hinoki (Chamaecyparis obtusa), yachidamo (Fraxinus mandshurica), and buna (Fagus crenata) when the hot-disk sensor was in contact with the cross section, radial section, and tangential section. The thermal conductivities in the longitudinal, radial, and tangential directions were also measured by the comparison method using the same specimen. The thermal properties obtained by the hot-disk method and the steady-state method were compared, based on the assumption that the thermal diffusivity measured by the hot-disk method was the geometric mean of that in the two main directions in the plane of the sensor, and the thermal conductivity measured by the hot-disk method was a power of that in three main directions. As a result, the thermal conductivity obtained by the hot-disk method was 10–20% higher than that obtained by the steady-state method; the thermal diffusivity measured by the hot-disk method was equal to that obtained by the steady-state method on average, while in the former thermal diffusivity varied widely. These results were found to be explainable in terms of the Dufour effect, which is the heat flow induced by the mass flow caused by the heating of the sensor, and the existing findings on the time dependence of the sensitivity coefficient in the hot-disk method. The present study proposed two methods for calculating the thermal properties of wood from the hot-disk method were proposed, and it was found that the errors between the obtained thermal properties and those obtained by the steady-state method differed depending on the calculation method.

Effect of heat treatment on mechanical properties of carbon-fiber-reinforced themoplastic

In this study, the bending properties and damage accumulation behavior of carbon-fiber-reinforced thermoplastics (CFRTP) were investigated to understand the effect of heat treatment on crystallization. Further, three-point bending tests using the acoustic emission technique were performed. Results indicated that a short period of heat treatment increased the CFRTP bending strength; however, for an excessively long heat treatment (30 h), the CFRTP bending strength decreased. To understand cause for the increase and decrement in the bending strength via heat treatment, surface observations using a laser microscope and thermal property measurement using differential scanning calorimetry were performed. Results showed that the 30-h heat-treated specimens exhibited fiber-matrix debonding before bending tests because of matrix shrinkage caused by crystallization and thermal degradation. Fourier transform infrared spectroscopy analysis revealed that the cause of deterioration was oxidation, and oxidation cleaved the molecular chains and embrittled the matrix. Consequently, we could control the bending properties by crystallization, and the relationship between crystallization and strength agreed with the formulated constitutive equation. However, we must address the thermal degradation when the materials are subjected to heat treatment.

Thermal diffusivity measurement of microscale slabs by rear-surface detection thermoreflectance technique

A new approach to measure the cross-plane thermal diffusivity of a microscale slab sample, which can be fabricated by the focused ion beam and attached to a substrate, is proposed. An intensity-modulated pump laser is applied to heat the front surface of the sample uniformly, and the thermoreflectance signal is observed at the rear surface to evaluate thermal wave transport in the material. The thermal diffusivity can be obtained by fitting the phase lags of the experimental data with a theoretical model. The model was developed for the sample with thin-film coatings and heat transfer to the substrate. Although the absorbed heat can cause a significant DC temperature increase in the microscale sample, a thin-film coating with high thermal conductivity can effectively reduce the DC temperature increase within low thermal conductivity samples. To validate the method, we conducted measurements of a fused silica sample of 2.16 µm thickness, coated with 95 nm Ti film on the front surface and 120 nm Au film on the rear surface. The measured thermal diffusivity is in good agreement with the literature value. The uncertainty analysis shows that the measurement uncertainty is within 6%. This proposed approach, designed for microscale samples, offers a unique option for thermal property measurements of special materials, such as irradiated nuclear fuel or other irradiated materials, to enable microscale property determination while minimizing sample radioactivity.

Rock thermal properties from well-logging data accounting for thermal anisotropy

The limitations of the existing techniques for in situ rock thermal property measurements and numerous cases with non-coring drilling determine the necessity for methods of rock thermal property determination based on well-logging data. Existing approaches for determining rock thermal properties from well-logging data are appropriate only for isotropic rocks. Since many rock types, especially organic-rich shales, exhibit a considerable degree of heterogeneity and anisotropy, advanced approaches for well log-based determination of rock thermal properties are highly desired. The implementation of the new thermal core logging technique, which provides continuous and high-precision measurements of the principal components of the thermal conductivity tensor and volumetric heat capacity from core samples, enabled the development of a new framework for the indirect determination of rock thermal properties. An enhanced technique for determining rock thermal conductivity and volumetric heat capacity from well-logging data accounting for thermal anisotropy and in situ thermobaric conditions is proposed and tested. This technique includes both the application of theoretical models and regression analysis of rock thermal properties, depending on the availability and quality of the input data. Three theoretical models involving a correction factor were compared to provide the best results. The experimental data of rock thermal properties inferred from the thermal core-logging and well-logging data from five wells (1630 samples) drilled through two highly anisotropic unconventional formations – the Bazhenov and the Domanic – were used as the basis of this newly developed approach. It is shown that rock thermal conductivity can be predicted from well-logging data accounting for thermal anisotropy with an uncertainty of less than 12 % and rock volumetric heat capacity with a total uncertainty of less than 5%.

Novel Method of Fast Measurement of Thermal Conductivity in Wide Range of Temperatures

Theoretical aspects and practical realization of a new method of fast measurement of thermal conductivity of coating materials (like deposits on wall and tubes of the boilers using fossil fuel, or high-temperature ceramics and adhesive materials) are presented. The method is based on analytical solution of the problem of unsteady heat transfer from the heated probe with coating to the environmental air. Several models of the phenomenon, taking into account convection and thermal radiation components of heat transfer, are described. The records of the probe temperature are processed numerically and compared with calculated values based on analytical solution. The best fit between the curves of recorded and calculated temperatures yields thermal conductivity value used as a parameter of the best fitting. This approach was applied to measurement of thermal properties of Fouling deposition in a coal-firing boiler. It was also demonstrated how extended version of the method allows one to represent the thermal conductivity of coating as a piecewise constant function of temperature, using a single record of the probe cooling curve. With a specially designed software for efficient calculation according to developed mathematical model, the whole experiment in the range 1500 °K–300 °K takes no more than 35–40 min, including processing on a regular PC. Validation of the suggested method was carried out in a special experiment with the substance of known thermal conductivity (Corn oil). The method was applied to Fouling depositions of two kinds of fuel—Columbian bituminous coal and Russian bituminous coal. It was demonstrated that Fouling in these two cases is characterized by significantly different thermal conductivity which also changes markedly with temperature.

Nano-Fluids as a Coolant for Automotive Engine Radiators: Review Study

Low-efficiency crossflow heat exchangers which are used as radiators in the automotive sector may cause engine damage. Nano-fluids are ideal coolants due to their high heat diffusion coefficient and can be added to almost any process that requires a fast reaction to thermal performance, such as the automobile. The nanofluid's thermal conductivity is greater than that of the base fluid such as water and ethylene glycol and can achieve more than 40% and enhance the heat transfer coefficient by more than 50%. The best results for heat transfer were to use carbon nanoparticles with base fluid. This article reviews previous research investigating the effect of nano-fluid in automotive radiators in which nanoparticles such as Al2O3, CuO, TiO2, and MWCNT are used. The preparation and application of nano-fluid and measurement of thermal properties and the effect of volume fraction on efficiency are discussed. The review also is focused on the numerical and experimental studies of previous work related to nano-fluid performance in automobile radiators

The use of photothermal techniques for thermal conductivity and thermal boundary resistance measurements of phase-change chalcogenides alloys

This article presents three photothermal methods dedicated to the measurement of the thermal properties of chalcogenide alloys, used as a central element in the new generations of non-volatile memory. These materials have two phases, amorphous and crystalline, possessing a sharp contrast in their electrical and thermal properties. In the crystalline phase, the properties also change very significantly with temperature. The control of the temperature of the samples, the choice of transducers, and the time or frequency characteristic values of the photothermal excitation are thoroughly discussed. Each photothermal technique is described from the experimental point of view as well as from the inverse method, performed to identify the parameters of interest. The identified thermal properties mainly concern the thermal conductivity and the thermal resistance at the interfaces between the phase-change materials and the materials in contact as encountered in the production of the microelectronic memory device. Assessing various photothermal techniques, the study suggests that pulsed photothermal radiometry is the most effective method for sensitive high-temperature measurements of thermal properties of the phase-change materials.

Thermal Property Measurements of a Large Prismatic Lithium-ion Battery for Electric Vehicles

Because of the high cost of measuring the specific heat capacity and the difficulty in measuring the thermal conductivity of prismatic lithium-ion batteries, two devices with a sandwiched core of the sample-electric heating film-sample were designed and developed to measure the thermal properties of the batteries based on Fourier’s thermal equation. Similar to electrical circuit modeling, two equivalent thermal circuits were constructed to model the heat loss of the self-made devices, one thermal-resistance steady circuit for the purpose of measuring the thermal conductivity, the other thermal-resistance-capacitance dynamic circuit for the purpose of measuring the specific heat capacity. Using the analytic method and recursive least squares, the lumped model parameters of these two thermal circuits were extracted to estimate the heat loss and correct the measured values of the self-made devices. Compared to the standard values of the reference samples of the glass and steel plates, the measured values were corrected to improve the measurement accuracies beyond 95% through steady thermal-circuit modeling. Compared to the measured value of the specific heat capacity of the battery sample at 50% state of charge using the calorimeter, the measured value using the self-made device was corrected in order to elevate the measurement accuracy by about 90% through dynamic thermal-circuit modeling. As verified through the experiments, it was reliable, convenient, and low cost for the proposed methodology to measure the thermal properties of prismatic lithium-ion batteries.

Thermoelectric effect and devices on IVA and VA Xenes

AbstractEmerging Xenes, mostly group IVA and VA elemental two‐dimensional (2D) materials, have small and tunable band gaps between graphene and transition metal dichalcogenides, giving versatile electrical properties. While their microelectronic or optoelectronic properties are being extensively explored, there remains a lack of study on Xenes' uniquely advantageous thermoelectric performance. This review highlights state‐of‐the‐art experimental and theoretical progress in the thermoelectric effect and devices of IVA and VA Xenes. Vertically displaced, a.k.a. “buckled” or “puckered,” atomic arrays result in exotic and tunable electrical or thermal transport behaviors. Different from chemical doping strategies usually employed in bulk thermoelectric materials, 2D Xenes can be tuned by physical means, such as atomic layer control and quantum confinement effects. A precise and compatible platform for 2D thermoelectric effect and devices study is available via the engagement between micro/nanofabrication of 2D Xene transistors and thermal property measurement techniques. This review also reveals potential thermoelectric applications of Xenes and their compounds (Bi2Te3, Bi2Se3, etc.), such as accurate stretchable temperature sensors, fast terahertz photodetectors, and so on.image

Thermal properties of U-Mo alloys irradiated under high fission power density

A variety of physical and thermal property measurements made on irradiated U-Mo alloy monolithic fuel samples with a Zr diffusion barrier and clad in Al alloy 6061 are reported. These properties form the basis for additional investigations in thermal behavior of U-Mo fuel under high performance research reactor irradiation conditions. Measurements were performed on samples harvested from fuel plates irradiated under high fission power density and surface heat flux and complement previous measurements on samples subjected to moderate fission power density and surface heat flux. Sample measurements reported in this work represented fission density ranging from 2.42 – 4.81 × 1027 fissions•m−3 (20.8 – 36.5 235U depletion) and average plate surface temperatures from 355 – 414 K. Specific heat capacity of irradiated monolithic U-Mo increases with increasing temperature and fission density, but carries large uncertainties associated with thickness measurements used to determine the mass fraction of the layer constituents for extraction of the U-Mo specific heat capacity, specifically the very thin and nonuniform Zr diffusion barrier. Density of irradiated monolithic U-Mo decreases with increasing fission density resulting from fission gas swelling and porosity formation. Thermal diffusivity of irradiated monolithic U-Mo increased with increasing temperature and decreased with increasing fission density. Thermal conductivity of irradiated monolithic U-Mo increased with increasing temperature, and in general, appeared to decrease and become less sensitive to temperature with increasing fission density. Thermal conductivity measurements compared to a semi-empirical model agreed within ±30%. It is suspected that the main driver in deviation between model calculations and measurements is the fission gas swelling determination, which does not account for fission power density or irradiation temperature.

Wireless, soft electronics for rapid, multisensor measurements of hydration levels in healthy and diseased skin

Precise, quantitative measurements of the hydration status of skin can yield important insights into dermatological health and skin structure and function, with additional relevance to essential processes of thermoregulation and other features of basic physiology. Existing tools for determining skin water content exploit surrogate electrical assessments performed with bulky, rigid, and expensive instruments that are difficult to use in a repeatable manner. Recent alternatives exploit thermal measurements using soft wireless devices that adhere gently and noninvasively to the surface of the skin, but with limited operating range (∼1 cm) and high sensitivity to subtle environmental fluctuations. This paper introduces a set of ideas and technologies that overcome these drawbacks to enable high-speed, robust, long-range automated measurements of thermal transport properties via a miniaturized, multisensor module controlled by a long-range (∼10 m) Bluetooth Low Energy system on a chip, with a graphical user interface to standard smartphones. Soft contact to the surface of the skin, with almost zero user burden, yields recordings that can be quantitatively connected to hydration levels of both the epidermis and dermis, using computational modeling techniques, with high levels of repeatability and insensitivity to ambient fluctuations in temperature. Systematic studies of polymers in layered configurations similar to those of human skin, of porcine skin with known levels of hydration, and of human subjects with benchmarks against clinical devices validate the measurement approach and associated sensor hardware. The results support capabilities in characterizing skin barrier function, assessing severity of skin diseases, and evaluating cosmetic and medication efficacy, for use in the clinic or in the home.

Measurement of thermal properties of bulk materials and thin films by modulated thermoreflectance (MTR)

Thermal conductivity and thermal diffusivity of materials must be known at high accuracy for thermal engineering applications, in order to understand energy dissipation in devices and engines. Thermal conductivity libraries can be unreliable since their reported values may not reflect the complexities of the samples under investigation, and new materials may not yet be listed. Over the past three decades, modulated thermoreflectance (MTR) has emerged and evolved as a reliable, non-contact, and noninvasive technique to measure the thermal properties of a wide range of bulk and thin film materials and their interfaces. This Tutorial discusses the basis of, and recent advances in, the MTR technique, and its applications in the thermal characterization of a variety of materials. MTR experiments use two micrometer-wide laser beams. Experimental data (amplitude and phase vs the offset between the pump and the probe) give information about heat diffusion around the heat source along several tens of micrometers. Heat diffusion equations are used to fit the experimental data and extract the required thermal properties. Importantly, best fit procedures are not always needed because some analytical approximations provide evidence of the required thermal properties. We present many examples (bulk materials, layered sample, etc.) which illustrate this.

Tribological and thermal properties of plasma nitrided Ti45Nb alloy

In this study, the effects of plasma nitriding surface treatment on the structural, tribological and thermal properties of Ti45Nb Beta alloy were investigated experimentally. Plasma nitriding process of Ti45Nb alloy was performed in 25% Ar-75% N2 gas mixture, for treatment times of 1–4 hours at the temperatures of 700–750 °C. The tribological tests of the plasma nitrided alloy were performed in dry sliding conditions. Thermal property measurements were applied to the plasma nitrided samples to determine their thermal conductivity and specific heat capacity. The TiNbN2 phase was observed in the compound layer formed after the nitriding process, and the compound layer and diffusion layer thicknesses increased depending on the nitriding temperature and duration. The highest microhardness was obtained for the sample nitrided at 750 °C for 4 hours and the hardness approximately twice increased compared to the untreated alloy. Due to its high surface hardness and nitride layer with sufficient thickness, the lowest wear rate was obtained for the nitrided sample under these conditions. As a result, the most effective parameter on the wear properties of Ti45Nb alloy after nitriding was determined as the process temperature. After the plasma nitriding process, thermal conductivity, thermal diffusion and specific heat capacity values decreased due to the formation of a nitride layer on the surface with a relatively lower thermal conductivity compared to the untreated alloy.

Role of the electron–phonon coupling in tuning the thermal boundary conductance at metal-dielectric interfaces by inserting ultrathin metal interlayers

Varying the thermal boundary conductance at metal-dielectric interfaces is of great importance for highly integrated electronic structures such as electronic, thermoelectric and plasmonic devices where heat dissipation is dominated by interfacial effects. In this paper we study the modification of the thermal boundary conductance at metal-dielectric interfaces by inserting metal interlayers of varying thickness below 10 nm. We show that the insertion of a tantalum interlayer at the Al/Si and Al/sapphire interfaces strongly hinders the phonon transmission across these boundaries, with a sharp transition and plateau within ∼1 nm. We show that the electron–phonon coupling has a major influence on the sharpness of the transition as the interlayer thickness is varied, and if the coupling is strong, the variation in thermal boundary conductance typically saturates within 2 nm. In contrast, the addition of a nickel interlayer at the Al/Si and the Al/sapphire interfaces produces a local minimum as the interlayer thickness increases, due to the similar phonon dispersion in Ni and Al. The weaker electron–phonon coupling in Ni causes the boundary conductance to saturate more slowly. Thermal property measurements were performed using time domain thermo-reflectance and are in good agreement with a formulation of the diffuse mismatch model based on real phonon dispersions that accounts for inelastic phonon scattering and phonon confinement within the interlayer. The analysis of the different assumptions included in the model reveals when inelastic processes should be considered. A hybrid model that introduces inelastic scattering only when the materials are more acoustically matched is found to better predict the thickness dependence of the thermal boundary conductance without any fitting parameters.

Multicriteria Methodology for Open Space Analysis

This paper describes an urban analysis method for the evaluation of the diversity of open spaces. Diversity is understood as the variety of options that a public space offers to the users, giving them the opportunity to choose the area which best suits their needs, activities, and personal preferences. The method facilitates an environmental quality assessment and comparative evaluation between spaces. Decision support tools based on data analysis are developed to facilitate technical urban design decisions. The methodology is based on a multi-criteria analysis of a public square in Madrid, Spain. Field measurements of climatic data and thermal properties of materials, the activities carried out by people and their location, as well as factors related to urban design are collated in the analysis. Data are complimented with bioclimatic and simulation tools. The analysis identifies differentiated thermal profiles, as well as patterns of use of the space. This enables the identification of specific locations currently favored by citizens and the microclimatic and spatial variety of the square.

Thermal transport properties of Ni–Co-based superalloy

We report systematic measurements of thermal transport properties of a Ni–Co-based superalloy at temperatures ranging from room temperature to around 800 K. In this temperature range, the thermal diffusivity and conductivity of the superalloy monotonically increase with an increase in the temperature, while the specific heat capacity is almost temperature-independent. We found that the observed thermal conductivity of the Ni–Co-based superalloy is higher than the electronic thermal conductivity expected from the Wiedemann–Franz law, indicating the substantial contribution of phonon thermal conductivity. The temperature dependence of the phonon thermal conductivity for the Ni–Co-based superalloy was observed to be weaker than that for other Ni-based alloys, which can be qualitatively explained by enhanced phonon scattering due to small γ′-phase precipitates in the superalloy. This result suggests possible tuning of the thermal conductivity of the superalloy based on phonon transport engineering.

Printability, Mechanical and Thermal Properties of Poly(3-Hydroxybutyrate)-Poly(Lactic Acid)-Plasticizer Blends for Three-Dimensional (3D) Printing.

This paper investigates the effect of plasticizer structure on especially the printability and mechanical and thermal properties of poly(3-hydroxybutyrate)-poly(lactic acid)-plasticizer biodegradable blends. Three plasticizers, acetyl tris(2-ethylhexyl) citrate, tris(2-ethylhexyl) citrate, and poly(ethylene glycol)bis(2-ethylhexanoate), were first checked whether they were miscible with poly(3-hydroxybutyrate)-poly(lactic acid) (PHB-PLA) blends using a kneading machine. PHB-PLA-plasticizer blends of 60-25-15 (wt.%) were then prepared using a corotating meshing twin-screw extruder, and a single screw extruder was used for filament preparation for further three-dimensional (3D) fused deposition modeling (FDM) printing. These innovative eco-friendly PHB-PLA-plasticizer blends were created with a majority of PHB, and therefore, poor mechanical properties and thermal properties of neat PHB-PLA blends were improved by adding appropriate plasticizer. The plasticizer also influences the printability of blends, which was investigated, based on our new specific printability tests developed for the optimization of printing conditions (especially printing temperature). Three-dimensional printed test samples were used for heat deflection temperature measurements and Charpy and tensile-impact tests. Plasticizer migration was also investigated. The macrostructure of 3D printed samples was observed using an optical microscope to check the printing quality and printing conditions. Tensile tests of 3D printed samples (dogbones), as well as extruded filaments, showed that measured elongation at break raised, from 21% for non-plasticized PHB-PLA reference blends to 84% for some plasticized blends in the form of filaments and from 10% (reference) to 32% for plasticized blends in the form of printed dogbones. Measurements of thermal properties (using modulated differential scanning calorimetry and oscillation rheometry) also confirmed the plasticizing effect on blends. The thermal and mechanical properties of PHB-PLA blends were improved by the addition of appropriate plasticizer. In contrast, the printability of the PHB-PLA reference seems to be slightly better than the printability of the plasticized blends.

Hydroxyapatite/polyetheretherketone nanocomposites for selective laser sintering: Thermal and mechanical performances

Abstract In this article, the thermal and mechanical properties of hydroxyapatite (HA)/polyetheretherketone (PEEK) nanocomposites were investigated. The surface of the HA particles was modified by stearic acid. Subsequently, the modified HA and PEEK were ultrasonically dispersed in ethanol and then subjected to drying and ball milling treatments. By controlling the concentration of modified HA, HA/PEEK nanocomposite powders containing various amounts of modified HA were successfully prepared. The tensile strength, impact strength, and flexural strength of the nanocomposite reached maximum values at 2.5 wt% HA and were 18.5%, 38.2%, and 5.7% higher than those of the pure PEEK, respectively. Moreover, the flexural modulus of the HA/PEEK nanocomposites increased at 2.5 wt% HA and was approximately 30% higher than that of the pure PEEK. The thermal property measurements (differential scanning calorimetry and thermogravimetric analysis) showed that the nanocomposites with 2.5 wt%-modified HA exhibited enhanced thermal stability as compared to the pure PEEK, showing potential for selective laser sintering.

Performance Evaluation of Current Leads for a 5 Tesla Electromagnetic Properties Measurement System

The development of the Electromagnetic Property Measurement System is underway at the Korea Basic Science Institute. The Electromagnetic Property Measurement System is used for electrical, thermal, and magnetic specimen property measurements in variable magnetic fields and temperatures with a low-temperature superconducting magnet. To activate low-temperature superconducting magnet that operates with liquid helium, we propose the use of vapor-cooled current leads. The low-temperature superconducting magnet is connected to the power supply at room temperature through a pair of current leads. Accordingly, heat inflows through the current leads and represents one of the major contributory factors of the entire heat inflow. Therefore, design optimization and evaluation of the current leads is necessary to minimize heat and liquid helium consumption. Vapor-cooled, and hybrid current leads were designed and fabricated, and testing in liquid helium cryostat was conducted. The low-temperature superconducting magnet was charged with electrical current up to the operating level, and the liquid helium boil-off rate was measured with respect to the supplied electrical current level. The performances of the two current leads were accessed based on the thermal load and boil-off rate of the liquid helium. The experimental and analyzed liquid helium boil-off rates associated with the current leads were in close agreement.