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At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

NASA NTRS1996

Fossilization processes in siliceous thermal springs: trends in preservation along thermal gradients

To enhance our ability to extract palaeobiological and palaeoenvironmental information from ancient thermal spring deposits, we have studied the processes responsible for the development and preservation of stromatolites in modern subaerial thermal spring systems in Yellowstone National Park (USA). We investigated specimens collected from silica-depositing thermal springs along the thermal gradient using petrographic techniques and scanning electron microscopy. Although it is known that thermophilic cyanobacteria control the morphogenesis of thermal spring stromatolites below 73 degrees C, we have found that biofilms which contain filamentous thermophiles contribute to the microstructural development of subaerial geyserites that occur along the inner rims of thermal spring pools and geyser effluents. Biofilms intermittently colonize the surfaces of subaerial geyserites and provide a favoured substrate for opaline silica precipitation. We have also found that the preservation of biotically produced microfabrics of thermal spring sinters reflects dynamic balances between rates of population growth, decomposition of organic matter, silica deposition and early diagenesis. Major trends in preservation of thermophilic organisms along the thermal gradient are defined by differences in the mode of fossilization, including replacement, encrustation and permineralization.

NASA Discipline Exobiology↗

NASA NTRS1990

Thermal Conductivity and Temperature Limits of Electron-Beam Physical-Vapor-Deposited ZrO2-7wt%Y2O3 Thermal Barrier Coating

The electron-beam physical-vapor-deposited (EB-PVD) ZrO2-7wt%Y2O3 thermal barrier coating has been widely used to protect engine hot section components in modem aircraft engines. Thermal conductivity and the conductivity increases due to sintering and phase changes are important coating design parameters. There is a need to characterize the coating thermal conductivity behavior and temperature limits, in order to potentially take full advantage of the coating capability. In addition, since the ZrO2-7wt%Y2O3 coating is often used as a baseline coating for the development of advanced lower thermal conductivity and higher temperature capability coatings, a thorough evaluation of the coating conductivity behavior at future higher engine operating temperatures will be useful for more accurately assessing the benefit gained from the new coating systems. In this study, thermal conductivity behavior of EB-PVD ZrO2-7wt%Y2O3 coating has been systematically investigated as a function of temperature (up to 2600 F) and time under steady-state and cyclic test conditions using a laser heat-flux technique. Thermal conductivity change kinetics were determined under realistic engine high temperature thermal gradient conditions, and correlated to the coating microstructural and phase changes. The thermal conductivity prediction models have been established in terms of heat flux, time, and testing temperatures.

Zhu, Dongming↗

NASA NTRS2012

Thermal and Alignment Analysis of the Instrument-Level ATLAS Thermal Vacuum Test

This paper describes the thermal analysis and test design performed in preparation for the ATLAS thermal vacuum test. NASA's Advanced Topographic Laser Altimeter System (ATLAS) will be flown as the sole instrument aboard the Ice, Cloud, and land Elevation Satellite-2 (ICESat-2). It will be used to take measurements of topography and ice thickness for Arctic and Antarctic regions, providing crucial data used to predict future changes in worldwide sea levels. Due to the precise measurements ATLAS is taking, the laser altimeter has very tight pointing requirements. Therefore, the instrument is very sensitive to temperature-induced thermal distortions. For this reason, it is necessary to perform a Structural, Thermal, Optical Performance (STOP) analysis not only for flight, but also to ensure performance requirements can be operationally met during instrument-level thermal vacuum testing. This paper describes the thermal model created for the chamber setup, which was used to generate inputs for the environmental STOP analysis. This paper also presents the results of the STOP analysis, which indicate that the test predictions adequately replicate the thermal distortions predicted for flight. This is a new application of an existing process, as STOP analyses are generally performed to predict flight behavior only. Another novel aspect of this test is that it presents the opportunity to verify pointing results of a STOP model, which is not generally done. It is possible in this case, however, because the actual pointing will be measured using flight hardware during thermal vacuum testing and can be compared to STOP predictions.

Bradshaw, Heather↗

DOE OSTI2020

Higher-order phonon scattering: advancing the quantum theory of phonon linewidth, thermal conductivity and thermal radiative properties

Phonon scattering plays a central role in the quantum theory of phonon linewidth, which in turn governs important properties including infrared spectra, Raman spectra, lattice thermal conductivity, thermal radiative properties, and also signifi- cantly affects other important processes such as hot electron relaxation. Since Maradudin and Fein’s classic work in 1962, three-phonon scattering had been considered as the dominant intrinsic phonon scattering mechanism and has seen tremendous advances. However, the role of the higher-order four-phonon scattering had been persistently unclear and so was ignored. The tremendous complexity of the formalism and computational challenges stood in the way, prohibiting the direct and quantitative treatment of four-phonon scattering. In 2016, a rigorous four-phonon scattering formalism was developed, and the prediction was realized using empirical potentials. In 2017, the method was extended using first-principles calculated force constants, and the thermal conductivities of boron arsenides (BAs), Si and diamond were predicted. The predictions for BAs were later confirmed by several independent experiments. Four-phonon scattering has since been investigated in a range of materials and established as an important intrinsic scattering mechanism for thermal transport and radiative properties. Specifically, four-phonon scattering is important when the fourth-order scattering potential or phase space becomes relatively large. The former scenario includes: (i) nearly all materials when the temperature is high; (ii) strongly anharmonic (low thermal conductivity) materials, including most rocksalt compounds, halides, hydrides, chalcogenides and oxides. The latter scenario includes: (iii) materials with large acoustic–optical phonon band gaps, such as XY compounds with a large atomic mass ratio between X and Y; (iv) two- dimensional materials with reflection symmetry, such as single-layer graphene, single-layer boron nitride and carbon nanotubes; and (v) phonons with a large density of states, such as optical phonons, which are important for Raman, infrared and thermal radiative properties. Four-phonon scattering is expected to gain broad interest in various technologically important materials for thermoelectrics, thermal barrier coatings, thermal energy storage, phase change, nuclear power, ultra-high temperature ceramics, infrared spectra, Raman spectra, radiative transport, hot electron relaxation and radiative cooling. Four-phonon scattering has been, and will continue to be, established as an important intrinsic phonon scattering mechanism beyond three-phonon scattering. The prediction of four-phonon scattering will transition from a breakthrough to a new routine in the next decade.

Feng, Tianli↗

DOE OSTI2025

Field Test and Thermal Performance Comparison of a Novel Underground Thermal Battery with a Single U-tube Borehole Heat Exchanger for Geothermal Heat Pump Application

Geothermal Heat Pumps (GHP) are a proven technology to electrify and decarbonize space heating and cooling by utilizing the thermally consistent underground as a heat sink or source. However, the high drilling costs of conventional borehole heat exchangers (BHEs) associated with GHP systems and subsurface heterogeneity have been two major challenges to their widespread adoption. In this paper, we present results from a field-scale pilot of an Underground Thermal Battery (UTB) as a potential alternative to a conventional BHE. To benchmark the UTB performance, a side-by-side field test was conducted to compare the UTB with a conventional BHE installed at the same site. The UTB was installed in a 7.01-meter-deep borehole having a diameter of 0.9 meter, whereas the conventional BHE (with single U-tube loop) is in a borehole with 36.6-meter depth and 0.15-meter diameter. Both are integrated into a GHP system to meet the thermal energy demands of office space at the Illinois Energy Farm on the University of Illinois Urbana-Champaign campus. The system’s performance is compared in terms of heat transfer rate, outlet temperatures, and contributions to the overall thermal power of the GHP system under varying thermal demands and in different heat pump operation modes: heating only, cooling only, and hybrid (alternative, diurnal heating and cooling). Results to date indicate that the UTB delivers a more consistent response under during a time period of varying thermal demands. Its operational performance is better during short-term with higher thermal demands, while the conventional BHE performs better under continuous, long-term thermal demands.

Pokhrel, Sajjan [ORNL] (ORCID:0000000228523749)↗

DOE OSTI2024

Thermal diode and thermal switch for bi-directional heat transfer in building envelopes

The present disclosure relates to a directional heat transfer using thermal control devices, including a dual phase change thermal diode and an active contact-based thermal switch. The thermal diode includes a positive temperature coefficient switching material and a negative temperature coefficient switching material arranged in series. The thermal switch includes two thermally conducting surfaces which may be moved to contact (i.e., having a distance between them of substantially zero) creating minimal thermal contact resistance. Both thermal control devices may be used to control heat flow into and/or out of a building.

Kishore, Ravi Anant↗

NASA NTRSDate not supplied

Final Thermal Design and Thermal Vacuum Testing of the StarBurst Instrument

The StarBurst Multimessenger Pioneer is a small satellite mission serving as a wide-field gamma-ray observatory designed to capture the initial emissions of short gamma-ray bursts, electromagnetic signatures of neutron star mergers. This paper presents the final thermal design and analysis of the StarBurst Instrument, comprising the bus-to-instrument interface plate, control electronics, and twelve crystal detector units, which form the core of the mission’s science capability. The passive thermal control system design requires consideration of restrictive keep-out zones, unknown orbital parameters, and narrow temperature limits of the detectors. Also summarized is the instrument level thermal vacuum cycle test, correlated model refinements, and updated model results. Following successful completion of the instrument test campaign, the hardware was integrated with the spacecraft bus for spacecraft level testing, including additional thermal vacuum testing. The results from the spacecraft level thermal vacuum test will further inform the instrument thermal model, ensuring accurate flight temperature predictions. StarBurst launches as a secondary payload in 2027 and has a mission duration of at least one year.

StarBurst↗

DOE OSTI2023

Hierarchical thermal-conductive polymer nanocomposites for thermal management

Managing heat in electrical conductors is a major challenge to meet the demands for sustainable energy use and electrical reliability, most notably power electronics and energy-critical electrical machines. Achieving such disparate functionalities, such as high temperature thermal and electrical reliability, require rational design and manufacturing of thermal conductor material and its hierarchical structures. Here we present hierarchical thermal-conductive nanocomposites, consisting of nanostructured ceramic conformal coating and aligned ultrahigh molecular weight polyethylene fiber, to tailor heat dissipation in electric conductors. The hybrid aligned thermal interface exhibits a highly desirable temperature dependent anisotropic high thermal conductivity with 0.98W m –1 K –1 and dielectric strength with 3.4. In addition, electrically insulating thermal interfaces demonstrate high-performing and reliable electrical systems under the dynamic load conditions. The surface temperature of heterogeneous ceramic-polymer encapsulated conductor is 17.8 °C lower than that of polymer-encapsulated conductor at the same electrical load. Consequently, the findings shown here hold great promises for directing heat extraction in electrical machine systems, advancing thermal management for emerging electronic applications.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Adaptive behavior and different thermal experiences of real people: A Bayesian neural network approach to thermal preference prediction and classification

Various observed and unquantifiable factors affect the thermal comfort of occupants in indoor environments and can lead to high uncertainty in the prediction and classification of their thermal preferences. The behavioral adaptation of occupants, by operating window systems for example, changes their thermal experience and expectations and therefore contributes to even higher prediction uncertainty. In this study, we applied a Bayesian neural network (BNN) algorithm to build a predictive model for occupant thermal preference using the ASHRAE Global Thermal Comfort Database II. The Bayesian method allows us to synthesize prior knowledge and available measurements into a unified modeling framework. It also offers a way to express and quantify uncertainty. Here we have performed a systematic study to test the efficiency and robustness of different BNN model configurations. In this study, the results show that the BNN model outperforms conventional thermal comfort models such as Predicted Mean Vote (PMV) and adaptive comfort model. The BNN model tends to produce more confident “prefer cooler” predictions with high possibility and low uncertainty. In contrast, the BNN model produces less certain predictions for “prefer no change” and “prefer warmer” across all occupants. Our findings suggest that linking occupants’ subjective evaluation measures and window opening/closing behavior to thermal comfort modeling effectively improves predictive performance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2016

Coupled thermal-hydrological-mechanical behavior of rock mass surrounding a high-temperature thermal energy storage cavern at shallow depth

The present study is aimed at numerically examining the thermal-hydrological-mechanical (THM) processes within the rock mass surrounding a cavern used for thermal energy storage (TES). We considered a cylindrical rock cavern with a height of 50 m and a radius of 10 m storing thermal energy of 350ºC as a conceptual TES model and simulated its operation for 30 years using THM coupled numerical modeling. At first, the insulator performance was not considered for the purpose of investigating the possible coupled THM behavior of the surrounding rock mass; then, the effects of an insulator were examined for different insulator thicknesses. The key concerns were focused on the hydro-thermal multiphase flow and heat transport in the rock mass around the thermal storage cavern, the effect of evaporation of rock mass, thermal impact on near the ground surface and the mechanical behavior of the surrounding rock mass. It is shown that the rock temperature around the cavern rapidly increased in the early stage and, consequently, evaporation of groundwater occurred, raising the fluid pressure. However, evaporation and multiphase flow did not have a significant effect on the heat transfer and mechanical behavior in spite of the high-temperature (350ºC) heat source. The simulations showed that large-scale heat flow around a cavern was expected to be conductiondominated for a reasonable value of rock mass permeability. Thermal expansion as a result of the heating of the rock mass from the storage cavern led to a ground surface uplift on the order of a few centimeters and to the development of tensile stress above the storage cavern, increasing the potentials for shear and tensile failures after a few years of the operation. Finally, the analysis showed that high tangential stress in proximity of the storage cavern can some shear failure and local damage, although large rock wall failure could likely be controlled with appropriate insulators and reinforcement.

58 GEOSCIENCES↗

DOE OSTI2013

Fiber/Matrix Interfacial Thermal Conductance Effect on the Thermal Conductivity of SiC/SiC Composites

SiC/SiC composites used in fusion reactor applications are subjected to high heat fluxes and require knowledge and tailoring of their in-service thermal conductivity. Accurately predicting the thermal conductivity of SiC/SiC composites as a function of temperature will guide the design of these materials for their intended use, which will eventually include the effects of 14-MeV neutron irradiations. This paper applies an Eshelby-Mori-Tanaka approach (EMTA) to compute the thermal conductivity of unirradiated SiC/SiC composites. The homogenization procedure includes three steps. In the first step EMTA computes the homogenized thermal conductivity of the unidirectional (UD) SiC fiber embraced by its coating layer. The second step computes the thermal conductivity of the UD composite formed by the equivalent SiC fibers embedded in a SiC matrix, and finally the thermal conductivity of the as-formed SiC/SiC composite is obtained by averaging the solution for the UD composite over all possible fiber orientations using the second-order fiber orientation tensor. The EMTA predictions for the transverse thermal conductivity of several types of SiC/SiC composites with different fiber types and interfaces are compared to the predicted and experimental results by Youngblood et al.

SiC/SiC composite, thermal conductance, thermal co↗

DOE OSTI2017

Novel thermal efficiency-based model for determination of thermal conductivity of membrane distillation membranes

Development and selection of membranes for membrane distillation (MD) could be accelerated if all performance-determining characteristics of the membrane could be obtained during MD operation without the need to recur to specialized or cumbersome porosity or thermal conductivity measurement techniques. By redefining the thermal efficiency, the Schofield method could be adapted to describe the flux without prior knowledge of membrane porosity, thickness, or thermal conductivity. A total of 17 commercially available membranes were analyzed in terms of flux and thermal efficiency to assess their suitability for application in MD. The thermal-efficiency based model described the flux with an average %RMSE of 4.5%, which was in the same range as the standard deviation on the measured flux. The redefinition of the thermal efficiency also enabled MD to be used as a novel thermal conductivity measurement device for thin porous hydrophobic films that cannot be measured with the conventional laser flash diffusivity technique.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Thermal-Fluid and Thermal-Structural Response of the T-Tube Modular Divertor to Spatiotemporally Varying Heat Loads

Tungsten (W) is the leading candidate for divertor target plates because of its high melting point (>3000°C), thermal conductivity, and ultimate tensile stress. While W and its alloys are the only solid materials that can survive the high heat fluxes incident on the divertor, W’s low-ductility high ductile-to-brittle transition temperature of ~600°C and relatively low recrystallization temperature (RT) of ~1300°C pose structural (among other) challenges. The objective of this work is to estimate the thermal-fluid and thermal-structural performance of the helium (He)-cooled T-tube divertor, which was originally developed by the Advanced Reactor Innovation and Evaluation Study (ARIES) using numerical simulations. Here, predictions of temperature distributions across the plasma-facing structural component and surface pressures from computational fluid dynamics simulations are used to determine stress distributions using commercial structural finite element modeling software over a range of fusion-relevant conditions. The maximum allowable incident heat fluxes are determined based on the temperature limits imposed by the ITER elastic Structural Design Criteria for In-vessel Components (SDC-IC) and the maximum RT over a range of He mass flow rates and presented in the form of performance design charts. Our recent work found that thermal- structural criteria accounting for the low ductility of W in a finger-type modular divertor constrain the maximum incident heat fluxes to values well below the ITER specifications, and those based on considering only the RT demonstrate that integrated thermal-fluid and elastic structural performance evaluation are required for accurate assessment of divertor performance. This novel analysis of the T-tube considers how nonuniform and transient incident heat fluxes affect its thermal-fluid and thermal-structural performance, as well as the effect of volumetric heating, which can be as great as 27% of the power incident on the divertor surface. The W tile of the T-tube, with its relatively large plasma-facing area of ~15 cm 2 , will likely experience significant spatial variations in incident heat flux. This work therefore assesses whether steady-state incident heat flux profiles with a peak of 10 MW/m 2 and maximum heat flux gradients of 200 MW/m 2 per m exceed the structural limits imposed by the ITER elastic SDC-IC and the maximum RT over a range of fusion-relevant conditions. The effect of transient heat fluxes typical of plasma detachment and reattachment from the target plate due, for example, to gas injection are also evaluated

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Multi-Scale Thermal Analysis for Design of SiC-Based Medium Voltage Motor Drive: Preprint

This paper describes a multi-scale thermal analysis approach for the design of an air-cooled 1.7-kV SiC MOSFET-based medium-voltage variable-speed motor drive. The National Renewable Energy Laboratory supported the project objectives by providing thermal management design support to the project partner The Ohio State University (OSU). The scope of the models and limited resources required efficient and flexible thermal models to be developed. Two modeling techniques are described that significantly reduced model run time and enabled more complex models to be run faster while retaining needed accuracy. The first technique uses the effectiveness-NTU method to extract convection boundary conditions from a computational fluid dynamics (CFD) model that can be applied to a fast-running finite element analysis model. The second is a porous media technique that enables system-level CFD simulations that incorporate effects from heat exchangers (e.g., pin fin heat sinks) that run in a fraction of the time required for fully resolved CFD simulations. The multi-scale approach to the thermal analysis enabled fast and accurate simulation for the converter design ranging from the die level up to the full system with 36 submodules. The modeling results were validated against experimental data from system tests performed by OSU.

DIRECT ENERGY CONVERSION↗

DOE OSTI2024

Numerical Evaluation of Effective Thermal Conductivity of PCM with Metal Foam Incorporating Buoyancy Effects for Thermal Energy Storage

The thermal energy storage (TES) system has the capability to efficiently preserve thermal energy directly derived from the energy source, minimizing any conversion losses. Especially latent heat storage offers distinct advantages, including a substantial increase in energy storage density and minimization of temperature fluctuations within the plants. However, the phase change material (PCM) employed in latent heat storage has low thermal conductivity. Consequently, various studies are being conducted to enhance heat transfer. One approach to enhance heat transfer involves utilizing metal foam to maximize the heat transfer area. However, modeling metal foam with its intricate structure is a challenging task in numerical analysis. For this reason, ongoing research focuses on simplifying the modeling of metal foam. Nevertheless, fully encompassing all the characteristics of actual metal foam proves to be a challenging task for the simplified analytical model. The objective of this paper is to interpret the simple lattice metal foam analysis model from the perspective of behavior induced by buoyancy. When comparing the analysis results of solid PCM and liquid PCM with the same thermal conductivity under changes in porosity and gravity direction, we conducted an analysis to discern the trends in effective thermal conductivity that are overestimated due to convection. In the analysis, a constant heat flux of 10 kW and a constant surface boundary condition of 350 K were applied, and a sensitivity study regarding the mesh was conducted. The results indicate that, from the perspective of gravity in the simple lattice model, the solid analysis yields an effective thermal conductivity 29-47% higher compared to the liquid analysis. Additionally, as porosity increases, there is an observed increase of 24-33% in effective thermal conductivity.

25 ENERGY STORAGE↗

DOE OSTI2024

Retrofittable Thermal Switches for Dynamic Building Envelopes Integrated with Thermal Energy Storage: Preprint

Buildings in the United States consume about 40 quadrillion BTU of primary energy annually, which accounts for the nation's 40% of total energy use, 75% of all electricity use, and 35% of the net carbon emissions. Deploying thermal energy storage in the form of phase change material (PCM) in building envelopes is an effective method to reduce space heating/cooling loads, provide load shedding, and shift demand to periods of lower energy cost. However, the full potential of PCM-integrated envelopes can only be realized if the PCM undergoes complete phase change using free ambient heating/cooling, and the stored energy is effectively transferred between the exterior and the interior environments. Conventional thermal insulation (with a fixed thermal resistance) limits PCM utilization, particularly with the increasing emphasis on higher R-value in building envelopes, which negatively affects the energy-saving potential of a PCM-integrated envelope. In contrast, dynamic building envelopes integrated with PCMs provide the option of varying the thermal resistance based on the indoor and outdoor conditions, thereby enhancing utilization of free ambient cooling and heating to charge/discharge the PCM thermal storage, reducing the buildings' heating and cooling load, and shifting the peak energy demand. In this study, we demonstrate innovative retrofittable thermal switches in the form of the insertable plugs inside an insulation to provide variable thermal resistance depending on the operating temperature and direction of temperature gradient, thus allowing preferential directional heat flow. Notably, they are passive in nature, requiring no external power, and work solely based on the ambient temperature.

buildings↗

NASA NTRSDate not supplied

GOES-T Goddard Magnetometer Sensor Unit Flight Thermal Predictions and On-Orbit Thermal Performance

The GOES-T Goddard Magnetometer (GMAG) sensor unit (SU) thermal design was validated by SU level thermal balance (TB) testing. The correlated SU thermal model was integrated to the observatory thermal model to predict the outboard SU temperatures and operating heater duty cycles in the worst cold case and worst hot case orbits. An orbit with the highest solar beta angle (23.5°) and an orbit with the lowest solar beta angle (0°) were run for each case. A comparison in the SU temperature predictions and heater duty cycles were made. The Autumnal Equinox (AE) cold case orbit is slightly colder than the Winter Solstice (WS) cold case orbit. The WS hot case orbit is slightly warmer than the March Equinox (VE) hot case orbit. Additionally, the lunar eclipse cold case orbit was run. It is the coldest environment. Using a 23°C set point for the SU cover heater controller, there is positive heater control for all the orbits. The heater duty cycle predictions for the AE worst cold case orbit and WS worst hot case orbit were 44.4% and 33% respectively. During the lunar eclipse, the heater cycle increases to 68.8% at the end of the eclipse. The temperature predictions for the bobbins are in the 21.9°C to 22.8°C range in the AE worst cold case orbit and in the 21.8°C to 23.0°C range in the WS worst hot case orbit. The SU temperatures during nominal operation on orbit were expected to be within the design goal, despite seasonal variations in solar beta angle and solar irradiance, and no solar flux in a lunar eclipse. The maximum operating SU cover flight heater duty cycle was expected to comply with GOLD Rule 4.25. The SU thermal design is now flight proven based on its long-term (>1 year) thermal performance on orbit.

GOES-T↗

DOE OSTI2021

Impact of size and thermal gradient on supercooling of phase change materials for thermal energy storage

Phase change material based thermal energy storage has many current and potential applications in the heating and cooling of buildings, battery and electronics thermal management, thermal textiles, and dry cooling of power plants. However, connecting lab scale thermal data obtained with differential scanning calorimetry (DSC) to the performance of large-scale practical systems has been a major challenge primarily due to the dependence of supercooling on the size and temperature gradient of the system. Here we show how a phase change material’s supercooling behavior can be characterized experimentally using common lab scale thermal analysis techniques. We then develop a statistics based theoretical model that uses the lab-scale data on small samples to quantitatively predict the supercooling performance for a general thermal energy storage application of any size, including also allowing for the possibility of temperature gradients. Finally, we validate the modeling methodology by comparing to experimental results for solid-solid phase change in neopentyl glycol, which shows how the model successfully predicts the changes in supercooling temperature across a large range of cooling rates (2 orders of magnitude) and volumes (3 orders of magnitude). By accounting for thermal gradients, the model avoids ~2x error incurred by lumped approximations.

36 MATERIALS SCIENCE↗