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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Estimating Soil Thermal Inertia Profiles From the Passive Equilibration of a Temperature Probe

Knowledge of the distribution of soil thermal properties is important for understanding subsurface hydrological and biogeochemical processes. This study describes and evaluates quick thermal profiling (QTP), a new measurement technique aimed at providing rapid, depth-resolved measurements of soil thermal inertia at numerous locations across the landscape. A cylindrical probe with temperature sensors at multiple depths is quickly inserted into the ground, and soil thermal inertia is estimated from how quickly the probe temperature equilibrates with the soil. To this end, a finite volume heat transfer model is used to generate temperature equilibration time series across combinations of controlling factors, and a gridded search inversion approach is applied to infer soil thermal inertia. Field tests in the Arctic indicate that QTP measurements have a minimum uncertainty of 0.14 J m −2 K −1 s −1/2 and covary with dual-probe heat pulse thermal analyzer measurements (concordance correlation coefficient = 0.56) with a root-mean-square error of 0.40 J m −2 K −1 s −1/2 . Besides demonstrating the value of QTP for estimating thermal inertia, this study identifies various sources of measurement uncertainty, particularly probe-soil contact resistance and frictional heating. Further, analysis of soil samples indicates that thermal inertia can be used to estimate thermal conductivity and dry bulk density in the studied area, although such inferences are highly site-specific. Overall, the QTP method holds promise to generate thermal inertia data products and to complement other characterization approaches for advancing understanding of soil properties across far more locations than is currently possible.

Lamb, J. R. [Lawrence Berkeley National Laboratory↗
DOE OSTI2024

Probing room temperature indirect and minimum direct band gaps of h-BN

Abstract Hexagonal boron nitride (h-BN) has attracted considerable interest as an ultrawide bandgap (UWBG) semiconductor. Experimental studies focused on the detailed near band-edge structure of h-BN at room temperature are still lacking. We report a direct experimental measurement of the near band-edge structure performed on h-BN quasi-bulk wafers via photocurrent excitation spectroscopy (PES). PES resolved the band-to-band transitions near M- and K-points in the Brillion zone (BZ), from which the room temperature indirect band gap of E g M K ∼6.02 eV, minimum direct bandgap at M-point of E g M = 6.36 eV and next lowest direct energy bandgap at K-point of E g K = 6.56 eV , have been simultaneously determined for the first time experimentally. The measured energy differences between K- and M-points in the conduction band minimum (CBM) and valence band maximum (VBM) are Δ E C M K = 0.54 eV and Δ E V M K = 0.34 eV, respectively, in good agreement with the calculation results. Significantly differing from its III-nitride wurtzite counterparts, in which only electrons and holes in the conduction and valence band extremes at the Γ-point are predominantly involved in the optical and transport processes, the results highlighted that charge carriers associated with both M- and K-valleys control to the optical excitation, recombination and charge transport processes in h-BN.

Physics↗
DOE OSTI2025

Synthesis and electronic characterization of Nd2−xSrxNiO4 thin films (0≤x≤1.4)

Layered nickelates have been studied extensively over the last three decades due to their structural similarities to the high-Tc superconducting cuprates. Using reactive oxide molecular beam epitaxy (MBE), we synthesize Nd2−xSrxNiO4 thin films for x=0−1.4 to probe the properties and electronic structure as a function of hole doping. The samples with lower doping show semiconducting behavior across the temperatures probed with an onset of metallic conductivity at x=1.4. We also present polarization-dependent O K and Ni L2,3 x-ray absorption spectra to track the evolution of the oxygen-nickel hybridization, distribution of holes between O 2p and Ni 3d states and the nickel oxidation state across the series. Angle-resolved photoemission spectroscopy (ARPES) measurements reveal a Fermi surface that comprises a cupratelike hole pocket of dx2−y2 character with an additional electron pocket of d3z2−r2 character at Γ. The emergence of a quasiparticle peak at the Fermi vector for x=1.4 corroborates the insulator-to-metal transition at x∼1. Finally, observe a fully two-dimensional Fermi surface with no momentum-dependent pseudogap, in contrast to measurements of the related bulk compound, Eu0.9Sr1.1NiO4.

Taylor, Nicole K↗
DOE OSTI2025

The Role of Snowmelt and Subsurface Heterogeneity in Headwater Hydrology of a Mountainous Catchment in Colorado: A Model‐Data Integration Approach

Mountainous headwater streams are sustained by both snowmelt‐driven streamflow and groundwater discharge in the Upper Colorado River Basin. However, predicting headwater stream discharge magnitude and peak flow timing is challenging in mountainous terrains, where snowmelt rates vary with vegetation type and elevation, and heterogeneous subsurface physical properties influence groundwater storage and its release. We used a model‐data integration approach to investigate the roles of snowmelt and subsurface structure in stream discharge and groundwater level. We ran an ensemble of 100 integrated surface‐subsurface hydrologic models for a mountainous headwater catchment near Crested Butte, Colorado, USA. We also evaluated and calibrated these models against observed data sets, including snow depth measurements using distributed temperature probes, stream discharge, and groundwater levels. Calibration with multiple data sources using neural density estimators has further constrained uncertainty in subsurface properties and snowmelt rates. Results indicated that observed slower snowmelt rates in evergreen forests delayed the peak flow and baseflow onset. In upstream areas with lower subsurface permeability, water was stored within the subsurface but was not released as interflow or shallow groundwater flow, and thereby not contributing to downstream streamflow during recession limb periods. Double peaks in groundwater occurred in areas with spatial subsurface heterogeneity, in our case due to the contrast between granodiorite and Mancos shale. These process‐based insights into groundwater and snowmelt dynamics in mountainous headwaters will help improve predictions of headwater hydrology.

Wang, Lijing [University of Connecticut, Storrs, C↗
DOE OSTI2025

Interplay of 𝑑- and 𝑝-states in RbTi3⁢Bi5 and CsTi3⁢Bi5 flat-band kagome metals

Shifting the Fermi level of the celebrated 𝐴⁢𝑀3⁢𝑋5 (135) compounds into proximity of flat bands strongly enhances electronic correlations and severely affects the formation of density waves and superconductivity. Our broadband infrared spectroscopy measurements of RbTi3⁢Bi5 and CsTi3⁢Bi5 combined with density-functional band-structure calculations reveal that the correlated Ti 𝑑-states are intricately coupled with the Bi 𝑝-states that form a tilted Dirac crossing. Electron-phonon coupling manifests itself in the strong damping of itinerant carriers and in the anomalous shape of the phonon line in RbTi3⁢Bi5. An anomaly in these spectral features around 150 K can be paralleled to the onset of nematicity detected by low-temperature probes. Our findings show that the materials with low band filling open unexplored directions in the physics of kagome metals and involve electronic states of different nature strongly coupled with lattice dynamics.

Wenzel, Matthew [ORNL]↗
DOE OSTI2025

Snow Depth Datasets for Snodgrass Catchment, Colorado, Water Year 2022-2023

This data package presents snow depths data from distributed temperature probes at 18 locations near Snodgrass catchment, Colorado. These data show that snow melt-out dates are approximately one or two weeks later under evergreen forests compared to other vegetation types even at the same elevation. These data were collected to understand how snowmelt heterogeneity impacts headwater hydrology, including streamflow and groundwater levels. They were also used to compare with process-based model simulations of snow depth to evaluate whether the model accurately represents snowmelt dynamics and their effects on headwater hydrology. Snow_DTPs_locations.csv includes all probes locations and their associated elevation and vegetation types. Snow_Depth_Snodgrass_WY2022_2023.csv includes processed snow depths datasets for Water Year (WY) 2022 and 2023. This dataset also includes a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata and a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type. Several probes have recordings for WY 2021.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Acoustic Tomography System (CRADA Final Report)

NREL will install the CU/CIRES acoustic tomography array at the National Wind Technology Center (NWTC). The system consists of 9 freestanding towers of 9.1m height that are currently located at the NWTC. On these towers are installed a series of microphones and speakers. One center tower holds a sonic anemometer and temperature probe. The purpose of the acoustic tomography system is to measure complex flow fields surrounding wind turbine arrays that influence wind farm energy production and reliability. There is currently no funding to test and research the system (just install it), but NREL and CU researchers will write proposals that will fund the actual research with this unique measurement technology.

17 WIND ENERGY↗
DOE OSTI2026

Degradation science: Integrating modeling and experiments to predict localized corrosion processes (Annual Progress Report)

Additively manufactured (AM) eutectic high-entropy alloys (EHEAs), such as nano-lamellar AlCoCrFeNi 2.1 , have excellent strength, ductility, and wear resistance even at elevated temperatures, but their corrosion behavior in aggressive acids at different length scales remain poorly understood. This work investigates the corrosion behavior of laser powder bed–fused (L-PBF) AlCoCrFeNi 2.1 as a function of annealing temperatures, probing degradation mechanisms from nanoscopic to macroscopic length scales. The alloy is dual phase consisting of a ductile FCC L1 2 phase and a high-strength BCC B2 phase. Rapid solidification during L-PBF produces a far-from-equilibrium nano-lamellar structure with nearly homogeneous elemental distribution, which tends to evolve upon annealing toward Cr/Co/Fe-enriched FCC and Al/Ni-enriched B2. Three conditions were studied: as-printed, 600 °C/5 h, and 1000 °C/1 h, over which B2 lamellae coarsen, lamellar spacing increases, and elemental segregation becomes more prominent. Microstructure and chemistry were characterized by scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS), while in-situ electrochemical atomic force microscopy (EC-AFM) was used to link early (<5 h) local dissolution to microstructure after exposure in sulfuric acid. EC-AFM highlights preferential dissolution of the BCC/B2 phase where the surrounding matrix is Cr-depleted and directly quantifies the dissolution rates within individual phases, tracks the transition from early nano-scale attack to partial repassivation, to correlate height differences with current and impedance responses. To monitor longer-term behavior (up to 96 h), ex-situ AFM, SEM, and confocal imaging were combined with conventional bulk electrochemical tests, bridging nanoscale observations to micro/meso-scale damage morphologies. At the meso-scale, the deepest dissolution channels align with the build-direction lamellae and melt-pool boundaries, indicating that printing directionality guides the propagation of these localized corrosion sites. Annealing modifies corrosion by restructuring BCC/FCC phase fractions, lamellar spacing, and Cr/Al segregation, thereby changing the cathode/anode ratio and passive film stability. The results clarify how as-printed and annealed nano-lamellar architectures differ in their susceptibility to selective dissolution; how elemental segregation competes with residual stresses along the build direction. With these insights, future work will use CALPHAD-guided alloy modification to stabilize higher Cr contents in the B2 phase while retaining a dominant FCC+B2/BCC microstructure, with the goal of designing mechanically robust, corrosion-resistant EHEAs for safety-critical applications to leverage the LLNL’s broader national and global security mission.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Crystallization of nanopore-confined imidazolium ionic liquids probed by temperature-resolved in situ grazing-incidence wide angle X-ray scattering (GIWAXS)

The crystallization behavior of ionic liquids (ILs) 1-butyl-3-methylimidazolium [BMIM] hexafluorophosphate [PF 6 ] and chloride [Cl] is investigated upon confinement in 2.3 or 8.2 nm diameter silica nanopore arrays, along with the effects of covalently modifying the pore walls with 1-(3-trimethoxysilylpropyl)3-methylimidazolium [TMS-MIM] + groups. In situ grazing-incidence wide angle x-ray scattering (GIWAXS) is performed during heating from as low as -110 °C to room temperature. Partially ordered “nanodomains” are observed in both ILs in the bulk molten state, but they are disrupted by nanoconfinement. Melting point depression consistent with capillary effects is observed for [BMIM][PF 6 ] in 2.3 nm pores. However, the melting point is elevated for [BMIM][PF 6 ] in 8.2 nm pores, which provide sufficient space to stabilize the crystalline phase. For [BMIM][Cl], crystallization is observed only in 8.2 nm bare silica pores, but the melting point is severely depressed. Tethering with IL-like [TMS-MIM + ] also promotes the crystallization of [BMIM][PF 6 ], resulting in elevated melting points. The combined effects of a larger pore size and pore surface tethering on [BMIM][PF 6 ] result in a single stable crystal phase that persists from -140 °C to 25 °C (vs. the bulk melting point of -11 °C). These results show that when ILs are used in confined systems, complex crystallization behavior can emerge depending on the counterion, pore size, and surface modification that require consideration of ion layering in the confined space in addition to surface free energy effects.

He, Yuxin [University of Kentucky, Lexington, KY (↗
DOE OSTI2024

Active Layer Depth and Permafrost Temperatures at the Teller 47 Field Site, Seward Peninsula, Alaska, 2022

With extreme climate warming in the Arctic, there is increasing focus on mapping permafrost stability and improving understanding of the impacts of thawing permafrost. Summer active layer depths and temperatures at the top of the permafrost were collected at the Teller 47 field site on the Seward Peninsula, Alaska to better understand permafrost thermal state in areas of discontinuous permafrost. Measurements were taken between August 14th and August 20th, 2022. Active layer depths were measured with a 120 cm thaw probe, and temperature measurements were taken with a SpotOn Temperature probe at the top of permafrost and at a maximum depth of XYZ, when no near-surface permafrost (within 120 cm of the surface) was present. Measurements were co-located with ground surface displacement measurements, which can be found in the associated dataset, NGA254. Precise location data were collected at each observation point using a GNSS RTK GPS unit. This dataset contains a *.csv file of permafrost temperature and active layer depths and a *.kml file of measurement locations.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy’s Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy’s Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

PreSens Dissolved Oxygen and Temperature Data, Old Woman Creek National Estuarine Research Reserve, Huron, OH, 2022-07-06 to 2023-12-15

This dataset contains collected dissolved oxygen (DO) and temperature measurements of the air, surface water, and underlying soil of a wetland at Old Woman Creek Estuarine Research Reserve in Huron, OH. Dissolved oxygen and temperature measurements were made in the first few centimeters of wetland sediment to assess how oxygen profiles changed over time with hydrological events. Measurements taken outside of the sediment were taken as comparison. Measurements were taken by hand with a PreSens Fibox 4 transmitter, paired with an oxygen dipping probe and temperature sensor, at each field outing. Measurements were taken approximately every 2 weeks around 10 AM EST. The PreSens_DO_Temp_Datafile.csv contains the recorded measurements, and the PreSens_InstallationMethods.csv describes the deployment of the sensor.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Does H 2 Temperature‐Programmed Reduction Always Probe Solid‐State Redox Chemistry? The Case of Pt/CeO 2

Abstract Redox reactions on the surface of transition metal oxides are of broad interest in thermo, photo, and electrocatalysis. H 2 temperature‐programmed reduction (H 2 ‐TPR) is commonly used to probe oxide reducibility by measuring the rate of H 2 consumption during temperature ramps, assuming that this rate is controlled by oxide reduction. However, oxide reduction involves several elementary steps, such as H 2 dissociation and H‐spillover, before surface reduction and H 2 O formation occur. In this study, we evaluated the kinetics of H 2 consumption over CeO 2 and Pt/CeO 2 with varying Pt loadings and structures to identify the elementary steps probed by H 2 ‐TPR. Literature often attributes changes in H 2 ‐TPR characteristics with Pt addition to increased CeO 2 reducibility. However, our analysis revealed that the H 2 consumption rate is measurement of the rate of H‐spillover at Pt‐CeO 2 interfaces and is determined by the concentration of Pt species on Pt nanoclusters that dissociate H 2 . Therefore, lower temperature H 2 consumption observed with Pt addition does not indicate higher CeO 2 reducibility. Measurements on samples with mixtures of Pt single‐atoms and nanoclusters demonstrated that H 2 ‐TPR can effectively quantify dilute Pt nanocluster concentrations, suggesting caution in directly linking H 2 ‐TPR characteristics to oxide reducibility while highlighting alternative material insights that can be gleaned.

Lee, Jaeha↗
DOE OSTI2024

Does H 2 Temperature–Programmed Reduction Always Probe Solid–State Redox Chemistry? The Case of Pt/CeO 2

Redox reactions on the surface of transition metal oxides are of broad interest in thermo, photo, and electrocatalysis. H 2 temperature-programmed reduction (H 2 -TPR) is commonly used to probe oxide reducibility by measuring the rate of H 2 consumption during temperature ramps, assuming that this rate is controlled by oxide reduction. However, oxide reduction involves several elementary steps, such as H 2 dissociation and H-spillover, before surface reduction and H 2 O formation occur. In this study, we evaluated the kinetics of H 2 consumption over CeO 2 and Pt/CeO 2 with varying Pt loadings and structures to identify the elementary steps probed by H 2 -TPR. Literature often attributes changes in H 2 -TPR characteristics with Pt addition to increased CeO 2 reducibility. However, our analysis revealed that the H 2 consumption rate is measurement of the rate of H-spillover at Pt-CeO 2 interfaces and is determined by the concentration of Pt species on Pt nanoclusters that dissociate H 2 . Furthermore, lower temperature H 2 consumption observed with Pt addition does not indicate higher CeO 2 reducibility. Measurements on samples with mixtures of Pt single-atoms and nanoclusters demonstrated that H 2 -TPR can effectively quantify dilute Pt nanocluster concentrations, suggesting caution in directly linking H 2 -TPR characteristics to oxide reducibility while highlighting alternative material insights that can be gleaned.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Estimating Electron Temperature and Density Using Van Allen Probe Data: Typical Behavior of Energetic Electrons in the Inner Magnetosphere

Abstract The Earth's inner magnetosphere contains multiple electron populations influenced by different factors. The cold electrons of the plasmasphere, warm plasma that contributes to the ring current, and the relativistic plasma of the radiation belts often seem to behave independently. Using omni‐directional flux and energy measurements from the HOPE and Magnetic Electron Ion Spectrometer instruments aboard the Van Allen Probes, we provide a detailed density and temperature description of the inner magnetosphere, offering a comprehensive statistical analysis of the entire Van Allen Probe era. While number density and temperature data at geosynchronous orbit are available, this study focuses on the warm plasma in the inner magnetosphere . Values of density and temperature are extracted by fitting energy and phase space density to obtain the distribution function. The fitted distributions are related to the zeroth and second moments to estimate the number density and temperature. Analysis has indicated that a two Maxwellian fit is sufficient over a wide range of and that there are two independent plasma populations. The more energetic population has a median number density of approximately and a temperature of around 130 keV, with a temperature peak observed between L * = 4 and L * = 4.5. This population is relatively uniform in magnetic local time (MLT). In contrast, the less energetic warm electron population has a median number density of about and a temperature of 7.4 keV. Strong statistical trends in density and temperature across both L * and MLT are presented, along with potential sources driving these variations.

58 GEOSCIENCES↗
DOE OSTI2025

Cleavable quaternary oxychlorides with high magnetic ordering temperatures

Quaternary oxychlorides derived from Ruddlesden–Popper 3d transition metal oxides offer a route to cleavable crystals with bulk antiferromagnetic ordering temperatures reaching at least 550 K. Here, we study the magnetic, optical, and mechanical behavior of Sr 2 FeO 3 Cl, Ca 2 FeO 3 Cl, Ca 3 Fe 2 O 5 Cl 2 , and Sr 3 Fe 2 O 5 Cl 2 . Through optical absorption measurements, we show that these antiferromagnetic semiconductors have optical band gaps of ≈2.1(1) eV. The magnetic ordering symmetries and temperatures were probed by neutron powder diffraction and Mössbauer spectroscopy on polycrystalline samples, demonstrating Néel temperatures (T N ) near room temperature in the single layer Sr 2 FeO 3 Cl (T N ≈ 311 K) and Ca 2 FeO 3 Cl (T N ≈ 360 K), and the double-layer compound Sr 3 Fe 2 O 5 Cl 2 has T N ≈ 545 K. The high-spin moments of Fe 3+ lie within the basal plane and the magnetic structures are compensated within each magnetic layer and characterized by magnetic propagation vectors k = ($\frac{1}{2}$ $\frac{1}{2}$ 0). Magnetization results demonstrate the quasi-2D nature of the magnetism, with a broad maximum in the susceptibility near 2T N for Sr 2 FeO 3 Cl. Scotch tape tests and mechanical exfoliation onto SiO 2 confirm the micaceous nature of these crystals with cleavage down to a single unit cell (two magnetic layers) achieved for Sr 3 Fe 2 O 5 Cl 2 . In conclusion, this paper highlights strong antiferromagnetic interactions, semiconducting band gaps, and cleavability of quaternary Fe-based oxychlorides and motivates future work on crystals and exfoliated flakes of these and related oxyhalide systems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

CFD modeling of natural circulation in LiCl-KCl molten salt closed loop

Characterizing flow within a molten salt closed-loop system is crucial for assessing system requirements, evaluating performance, and identifying potential flaws. Direct flow measurement using instrumentation is challenging due to extreme environmental conditions and the limitations associated with measuring molten salt flow under natural convection. Here, this study aims to provide comprehensive insights into the thermal-hydraulic behavior of a closed loop, with a particular focus on temperature distribution and velocity prediction. The Computational Fluid Dynamics (CFD) model demonstrated the capability to effectively simulate and predict both temperature distributions and flow velocities within the molten salt loop. The CFD model's predictive capability was validated by its ability to replicate temperature measurements under varying boundary conditions. The analysis revealed that the CFD model tends to underpredict temperatures in the cold leg and overpredict them in the hot leg, highlighting the need for continuous model refinement and acknowledging the limitations of using a steady-state approach. Furthermore, the potential of using external temperature measurements to estimate internal molten salt temperatures and predict flow velocity was explored, revealing that this approach could introduce up to a 5.5% error in flow velocity calculations. Line probes mapping temperature distributions across the tube's cross-section and molten salt provided valuable insights into temperature gradients, emphasizing the need for a thermal conductivity equation for molten salt with lower uncertainty to achieve more accurate temperature predictions of the system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Experimental Results on SS 304H and 2.25Cr-1Mo in Support of Developing Inelastic Constitutive Models

To address critical data gaps necessary for updating viscoplastic constitutive material models for Class A materials used in inelastic design analysis under the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 5, High Temperature Reactors, Oak Ridge National Laboratory (ORNL) conducted experimental studies on stainless steel 304H (SS 304H) and 2¼Cr-1Mo steel (F22), to probe their temperature dependent deformation behaviors. These studies covered a range of temperatures up to the maximum limits specified in Division 5 and are intended to support the development of material models by collaborators at Argonne National Laboratory (ANL).

36 MATERIALS SCIENCE↗
DOE OSTI2025

Methods for Measuring and Computing the Reference Temperature in Newton’s Law of Cooling for External Flows

Newton’s law of cooling requires a reference temperature (𝑇 𝑟𝑒𝑓 ) to define the heat-transfer coefficient (ℎ). For external flows with multiple temperatures in the freestream, obtaining 𝑇 𝑟𝑒𝑓 is a challenge. One widely used method, referred to as the adiabatic-wall (AW) method, obtains 𝑇 𝑟𝑒𝑓 by requiring the surface of the solid exposed to convective heat transfer to be adiabatic. Another widely used method, referred to as the linear-extrapolation (LE) method, obtains 𝑇 𝑟𝑒𝑓 by measuring/computing the heat flux ($𝑞^{′′}_𝑠$) on the solid surface at two different surface temperatures (𝑇 𝑠 ) and then linearly extrapolating to $𝑞^{′′}_𝑠$ = 0. A third recently developed method, referred to as the state-space (SS) method, obtains 𝑇 𝑟𝑒𝑓 by probing the temperature space between the highest and lowest in the flow to account for the effects of 𝑇 𝑠 or $𝑞^{′′}_𝑠$ on 𝑇 𝑟𝑒𝑓 . This study examines the foundation and accuracy of these methods via a test problem involving film cooling of a flat plate where $𝑞^{′′}_𝑠$ switches signs on the plate’s surface. Results obtained show that only the SS method could guarantee a unique and physically meaningful 𝑇 𝑟𝑒𝑓 where 𝑇 𝑠 =𝑇 𝑟𝑒𝑓 on a nonadiabatic surface $𝑞^{′′}_𝑠$ = 0. The AW and LE methods both assume 𝑇 𝑟𝑒𝑓 to be independent of 𝑇 𝑠 , which the SS method shows to be incorrect. Though this study also showed the adiabatic-wall temperature, 𝑇 𝐴𝑊 , to be a good approximation of 𝑇 𝑟𝑒𝑓 (<10% relative error), huge errors can occur in ℎ about the solid surface where |𝑇 𝑠 −𝑇 𝐴𝑊 | is near zero because where 𝑇 𝑠 =𝑇 𝐴𝑊 , $𝑞^{′′}_𝑠$ ≠ 0.

Newton's law of cooling↗