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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

When should PIC simulations be applied to atmospheric pressure plasmas? Impact of correlation heating

Abstract Molecular dynamics simulations are used to test when the particle-in-cell (PIC) method applies to atmospheric pressure plasmas. It is found that PIC applies only when the plasma density and macroparticle weight are sufficiently small because of two effects associated with correlation heating. The first is the physical effect of disorder-induced heating (DIH). This occurs if the plasma density is large enough that a species (typically ions) is strongly correlated in the sense that the Coulomb coupling parameter exceeds one. In this situation, DIH causes ions to rapidly heat following ionization. PIC is not well suited to capture DIH because doing so requires using a macroparticle weight of one and a grid that well resolves the physical interparticle spacing. These criteria render PIC intractable for macroscale domains. The second effect is a numerical error due to artificial correlation heating (ACH). ACH is like DIH in that it is caused by the Coulomb repulsion between particles, but differs in that it is a numerical effect caused by a macroparticle weight larger than one. Like DIH, it is associated with strong correlations. However, here the macroparticle coupling strength is found to scale as Γ w 2 / 3 , where Γ is the physical coupling strength and w is the macroparticle weight. So even if the physical coupling strength of a species is small, as is expected for electrons in atmospheric pressure plasmas, a sufficiently large macroparticle weight can cause the macroparticles to be strongly coupled and therefore heat due to ACH. Furthermore, it is shown that simulations in reduced dimensions exacerbate these issues.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Heat rectification through single and coupled quantum dots

We study heat rectification through quantum dots in the Coulomb blockade regime using a master equation approach. We consider both cases of two-terminal and four-terminal devices. In the two-terminal configuration, we analyze the case of a single quantum dot with either a doubly-degenerate level or two non-degenerate levels. In the sequential tunneling regime we analyze the behaviour of heat currents and rectification as functions of the position of the energy levels and of the temperature bias. In particular, we derive an upper bound for rectification in the closed-circuit setup with the doubly-degenerate level. We also prove the absence of a bound for the case of two non-degenerate levels and identify the ideal system parameters to achieve nearly perfect rectification. The second part of the paper deals with the effect of second-order cotunneling contributions, including both elastic and inelastic processes. In all cases we find that there exists ranges of values of parameters (such as the levels' position) where rectification is enhanced by cotunneling. In particular, in the doubly-degenerate level case we find that cotunneling corrections can enhance rectification when they reduce the magnitude of the heat currents. For the four-terminal configuration, we analyze the non-local situation of two Coulomb-coupled quantum dots, each connected to two terminals: the temperature bias is applied to the two terminals connected to one quantum dot, while the heat currents of interest are the ones flowing in the other quantum dot. Remarkably, in this situation we find that non-local rectification can be perfect as a consequence of the fact that the heat currents vanish for properly tuned parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Plasma heating by electron cyclotron wave and the temperature effects on lower hybrid current drive on EAST

This paper presents the progress in the long—pulse operation of the electron cyclotron (EC) system and the achievements in high—electron temperature plasmas by the combined EC and lower hybrid (LH) waves heating since the EC system was built in 2015. An electron temperature of up to 12 keV with a duration over 100 s was realized by the simultaneous heating of EC and LH waves at the line-averaged density ${\bar n_{\text{e}}}$ ~1.8 × 10 19 m –3 . The plasma heating effect strongly depends on the location of EC power deposition. H-mode plasmas with solely EC wave auxiliary heating have been obtained on EAST for the first time. These H-mode discharges show an enhanced confinement factor H 98(y,2) around 1.0, which is higher than the previous H-mode using LH power alone (Xu et al 2011 Nucl. Fusion 51 072001). The total heating power is very close to the threshold value for L–H transition according to the international tokamak scaling. In addition to the temperature effects inside the separatrix, higher electron temperature produced by EC wave is found to reduce the LH power loss in the scrape-off layer due to collisional absorption, which is beneficial to further increase the LH current drive efficiency. Ray-tracing/Fokker–Planck modeling results indicate that higher electron temperature can shorten the LH wave propagation on EAST in a multiple-pass regime, thus decreasing the collisional dissipation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Micro-tearing mode dominated electron heat transport in DIII-D H-mode pedestal

Abstract A new, comprehensive set of evidence reveals that Micro-Tearing Modes (MTMs) dominate pedestal electron heat transport in an H-mode experiment in the DIII-D tokamak. The experiment investigates the role of MTMs by scanning pedestal collisionality, a main drive of MTM instability, from 0.43 to 0.84 on the pedestal top. Broadband (150–800 kHz) magnetic and density fluctuations originating from the pedestal gradient region and highly consistent with MTMs are observed, with amplitude increasing during the scan. The higher magnetic fluctuation amplitude correlates with a lower pedestal electron temperature gradient, implying MTMs may regulate the pedestal electron heat transport. The collisionality scan results in profile and transport changes consistent with predicted transport capability of MTMs: (1) experimentally-determined electron heat diffusivity increases ∼40% at the location where the broadband density fluctuations peak; (2) ion heat diffusivity has less increase (<20%); and (3) a locally flattened region in the electron temperature pedestal is observed at high collisionality. A local, linear gyrokinetic simulation finds MTMs as the most unstable mode in the pedestal gradient region. In addition, local, nonlinear simulations suggest MTMs can dominate and drive experimentally-relevant, megawatt-level electron heat flux. This result establishes MTMs as an effective transport mechanism in the H-mode pedestal, in particular at high collisionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Measurements and modeling of type-I and type-II ELMs heat flux to the DIII-D divertor

Type-I and type-II edge-localized-modes (ELMs) heat flux profiles measured at the DIII-D divertor feature a peak in the vicinity of the strike-point and a plateau in the scrape-off-layer (SOL), which extends to the first wall. The plateau is present in attached and detached divertors and it is found to originate with plasma bursts upstream in the SOL. The integrated ELM heat flux is distributed at ~65% in the peak and ~35% in this plateau. The parallel loss model, currently used at ITER to predict power loads to the walls, is benchmarked using these results in the primary and secondary divertors with unprecedented constraints using experimental input data for ELM size, radial velocity, energy, electron temperature and density, heat flux footprints and number of filaments. The model can reproduce the experimental near-SOL peak within ~20%, but cannot match the SOL plateau. Employing a two-component approach for the ELM radial velocity, as guided by intermittent data, the full radial heat flux profile can be well matched. The ELM-averaged radial velocity at the separatrix, which explains profile widening, increases from ~0.2 km s –1 in attached to ~0.8 km s –1 in detached scenarios, as the ELM filaments' path becomes electrically disconnected from the sheath at the target. The results presented here indicate filaments fragmentation as a possible mechanism for ELM transport to the far-SOL and provide evidence on the beneficial role of detachment to mitigate ELM flux in the divertor far-SOL. However, these findings imply that wall regions far from the strike points in future machines should be designed to withstand significant heat flux, even for small-ELM regimes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Operational space for lower hybrid heating scenarios in the full tungsten environment of WEST

In tungsten—W—Environment in Steady-state Tokamak (WEST), the lower hybrid current drive (LHCD) system is key for achieving long pulse operation by providing most of the non-inductive plasma current, as well as a crucial source of electron heating. Therefore, determining the operational space for its application is fundamental. In the present study, the LHCD operational space is deeply analyzed for 0.5 MA pulses. This space is bounded by three limits: (i) the ratio of the LHCD power over density must be above a threshold to compensate tungsten radiation with enough core heating, (ii) the line-averaged density must be high enough to allow good coupling of the hybrid wave with the plasma, and (iii) fast electron ripple losses must be below a limit to avoid reaching a thermal threshold on plasma-facing components. If the tungsten radiation peak or burn-through phase is not safely overcome, a maximum electron temperature of 1.5 keV is obtained, confinement is degraded, and magnetohydrodynamic activity is frequently triggered, potentially causing a disruption. From experimental measurements and interpretative simulations, we highlight the main mechanisms that prevent the plasma from heating up during LHCD power ramp-up. Three parameters play a major role: plasma density, tungsten concentration and LHCD power deposition. A strategy to overcome this limitation is found: a precise density ramp-up performed simultaneously with the increase in LHCD power. Additionally, we show that boronization greatly facilitates the burn-through of tungsten by lowering its content during the heating phase. Finally, taking into account the three constraints given above, the LHCD operational space is determined at power ramp-up and during constant heating phases.

lower hybrid heating and current drive↗
DOE OSTI2024

Excess heat capacity in magnetically ordered Ce heavy-fermion metals

Herein we study the magnetic heat capacity of a series of magnetically ordered Ce-based heavy-fermion materials, which show an anomalous T 3 heat capacity in excess of the phonon contribution in many materials. For compounds for which magnon models have been worked out, we show that the local-moment magnon heat capacity derived from the measured magnon spectra underestimates the experimental specific heat. The excess heat capacity reveals increasing density of states with increasing energy, akin to a pseudogap. We show that this anomalous temperature-dependent term is not associated with proximity to a quantum critical point, but is strongly correlated with T N , indicating the anomalous excitations are governed by the magnetic exchange interaction. This insight may hold key information for understanding magnetically ordered heavy fermions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

A portable on-axis laser-heating system for near-90° X-ray spectroscopy: application to ferropericlase and iron silicide

A portable IR fiber laser-heating system, optimized for X-ray emission spectroscopy (XES) and nuclear inelastic scattering (NIS) spectroscopy with signal collection through the radial opening of diamond anvil cells near 90°with respect to the incident X-ray beam, is presented. The system offers double-sided on-axis heating by a single laser source and zero attenuation of incoming X-rays other than by the high-pressure environment. A description of the system, which has been tested for pressures above 100 GPa and temperatures up to 3000 K, is given. The XES spectra of laser-heated Mg 0.67 Fe 0.33 O demonstrate the potential to map the iron spin state in the pressure–temperature range of the Earth's lower mantle, and the NIS spectra of laser-heated FeSi give access to the sound velocity of this candidate of a phase inside the Earth's core. This portable system represents one of the few bridges across the gap between laser heating and high-resolution X-ray spectroscopies with signal collection near 90°.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Motorette Thermal Performance Testing and Modeling for an Electric Motor with Additively Manufactured Hollow Conductors with Integrated Heat Pipes

This paper discusses the design, build and test of a motorette to characterize the thermal performance of an additively manufactured coil integrated with heat pipes. The motorette is powered using a variable frequency AC power supply and cooled through two independent cooling systems. The first cooling system cools the stator core using forced convection of air flowing over a finned heat sink mounted on the stator outer diameter. The second cooling system cools the heat pipes using forced convection of 50-50 water ethylene glycol (WEG) mixture flowing through condenser chambers. A 3D thermal FEA model of the setup is built and heat transfer coefficients (HTC) of convective boundaries are computed using coolant flow rates from test data and empirical equations. Temperature at locations on the coil and heat sink are recorded and compared to thermal model predicted values. A maximum temperature error of 22.7% occurs at 180ARMS and 800 Hz operating point for the AM dual coil. The thermal model provides higher temperatures compared to test results and hence it is on the conservative side but in general, there is good correlation between test and model results. Lastly, opportunities for improvement to both test data measurement and 3D thermal FEA modeling are discussed.

additive manufacturing↗
DOE OSTI2021

Optimal Energy Scheduling and Sensitivity Analysis for Integrated Power-Water-Heat Systems

The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Species‐Specific Epigenetic Signature Associates With Heat Stress Tolerance in the Perennial Tree Species Populus

Epigenetic regulation in annual plants is recognized as a key component of recurring stress acclimation and adaptation, but reports on perennial tree species are limited. In this study, two contrasting tree species, Populus trichocarpa and Populus deltoides, and an F1 hybrid cross between them showed species-specific epigenetic and physiological responses to heat stress (42°C) following priming (35°C). By analyzing whole-genome methylation, transcriptomics, proteomics, metabolomics, and photosynthesis parameters, we found that P. deltoides expresses specific epigenetic signatures in response to heat, resulting in improved photosynthetic efficiency compared to P. trichocarpa. Conversely, P. trichocarpa displayed stress signaling and defense mechanisms that could not sustain a net assimilation rate despite maintaining higher gas exchange. Heat stress following priming in hybrid plants increased transcript levels of thermotolerance-related transcription factors, such as SPL12. Selected regions in the promoter of SPL12 showed differential methylation between direct heat stress and priming followed by heat stress. As a result, upregulation of downstream genes and associated increases in protein and metabolite abundance for stress adaptation were exhibited. Consequently, hybrid plants showed enhanced photosynthesis and gas exchange rates, a trait lacking in P. trichocarpa. These results imply that priming may not be universally effective in enhancing plant performance under stress, particularly in perennial tree species. However, priming can acclimate the perennial tree species P. deltoides to withstand elevated temperature stress better. Our study has demonstrated that priming-based stress adaptation is species-specific but can be attained through crossbreeding, indicating its potential use in breeding programs.

DNA methylation↗
DOE OSTI2021

Development of in-use engine speed/torque heat maps across multiple heavy-duty commercial vehicle vocations

The U.S. Department of Energy (DOE) established the SuperTruck program with the goal of achieving brake thermal efficiency (BTE) greater than or equal to 55% as demonstrated in an operational heavy-duty (HD) diesel engine at a 65-miles-per-hour (mph) cruise point. Beyond the line-haul application, HD engines operate in a wide range of speed and torque conditions that are unlikely to yield the same efficiency under real-world operation. Thereby, the in-use engine heat maps described in this paper are a valuable tool to illustrate whether the engine-efficiency “sweet spot” matches the most frequent operating conditions. In this study, NREL developed engine heat maps to quantify the important operating points for various vocations using our Fleet DNA database of commercial fleet vehicle operations data. These heat maps clearly show that high-frequency operating points vary significantly according to vehicle vocation, while only a few of them match the sweet spot. Beyond the illustration, engine in-use heat maps can also be leveraged to build up reduced-order engine-efficiency models, needed by many rapid powertrain simulations. As case studies, nine reduced-order models – including line-haul truck, transfer truck, transit bus, transit bus with compressed natural gas (CNG) engine, drayage, refuse pickup, local delivery, utility truck, and school bus with CNG engine – using a trust-region reflective algorithm to fit the on-road data extracted based on the engine in-use heat maps.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2026

Kinetics of Hydrogen Generation from In-Situ Methane Pyrolysis: Enhanced by Electromagnetic Heating and Natural Catalysts of Reservoir Rocks

Catalytic pyrolysis of methane (CH4) is a promising approach to generate hydrogen (H2). The apparent activation energy of this process has a significant influence on the efficiency and required temperature for H2 generation. Preliminary experiments indicate that minerals present in shales have catalytic effects during in-situ H2 generation from shale reservoirs under electromagnetic (EM) heating. However, the quantitative role of such natural catalysts on apparent activation energy is not explored yet. This research evaluated the role of reservoir rock (shale) in EM heating and on the apparent activation energy of methane pyrolysis (MP) for in-situ H2 generation. Experiments are conducted in a customized EM reactor with frequency 2.45 GHz, and reaction temperature and generated gases are measured by a real-time IR pyrometer and gas analyzer, respectively. It is found that shale samples experienced thermal runway (TR) at 420 ºC under 0.15 kW EM power without any artificial heating promoter. In the presence of spent shale, CH4 conversion started approximately at 600 ºC with negligible amount of carbon dioxide (CO2) generated during this process. We further calculated apparent reaction order and apparent activation energy for MP process in the presence of shale under EM heating, which are 0.4357 and 98.12 kJ/mol, respectively. This research paves a way for leveraging the role of minerals as natural catalysts for enhancing H2 generation under EM heating in petroleum reservoirs.

02 PETROLEUM↗
DOE OSTI2021

Test Article and Test Plan for Heat-Pipe Gap-Conductance Testing

The SPHERE Facility at INL is established to test phenomena related to heat pipes in nuclear applications. The current capability of the SPHERE testbed is operation of liquid alkali-metal-cooled heat pipes in a variety of atmospheres. The controlled atmosphere can be used to prevent oxidation of system parts and also to affect the thermal conductivity of gases for any interfacial gaps within the heat-pipe assembly. Currently available modes are vacuum, air, nitrogen, helium, and argon. Controlled mixtures of helium and argon are available to vary the thermal conductivity of the gas. The primary test article will be based on the existing 7-hole block design used for shakedown testing of the SPHERE Facility. The SPHERE test stand will be used with test articles to establish the conductivity between fuel elements as well as between the heat pipe and other layers of the fuel-rod assembly. Existing and new test blocks will be used and modified with additional instrumentation to establish the thermal conductivity between the gap of the block wall and the heat pipes.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

The Use of the High-density UN Fuel in Heat-pipe Microreactors

Heat-pipe microreactors (HPMRs) are very small-scale nuclear reactors that employ heat pipes for heat removal. HPMRs can be easily integrated with other forms of renewable energies, used for emergency responses to disaster relief zones, deployed in remote locations not connected to the grid, and removed from sites and replaced by new ones. HPMRs can also be used for space missions as heat pipes do not rely on gravity for heat transfer. Conventional fuel materials, such as UO 2 and UCO, are currently considered in most existing HPMR designs, but ceramic UN fuel that has high uranium density, high thermal conductivity, and a high melting point may become a better fuel candidate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Identifying Regions Favorable for Geothermal Heating and Cooling Storage

Space heating and cooling represents the single largest category of in building energy use for U.S. residential and commercial buildings, with heating representing 61% of residential and 46% commercial energy consumption. Building heating technologies are dominated by natural gas technologies, and are an important opportunity for building electrification to enable a transition to a low CO 2 energy system. FLXenabler study is a joint analysis effort among multiple analysis teams at NREL and focused on examining the role of geothermal heating and cooling (GHC) system with thermal energy storage (TES) providing flexibility. Utilizing information from ResStock the amount of energy consumption associated with heating and cooling by state was calculated. We applied adjusted load shapes to estimate the a maximum grid savings potential of using TES to address building space conditioning. Normalizing grid, fuel, and emissions impacts locations with higher favorability for further study in FLXenabler were identified.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

UHT-CAMANCHE: Ultra-High Temperature Ceramic Additively Manufactured Compact Heat Exchangers

The conceptual basis for this project is the convergence of advanced ultra-high temperature ceramic materials and additive manufacturing technologies to produce compact ceramic heat exchangers with complex internal flow path geometries. Task areas were broadly divided into materials and manufacturing development, heat exchanger design, component testing, and techno-economic analysis. Technical challenges included the design and commissioning of new test facilities, improving feature resolution and deposition rate of ceramic additive manufacturing techniques, establishing process-structure-property relationships in additively manufactured ultra-high temperature ceramics, and assessing high temperature materials compatibility in CO 2 environments. The primary candidate material evaluated in this work is a composite comprising zirconium diboride (ZrB2) with 30 vol. % silicon carbide (SiC) which was selected based on its desirable combination of high temperature mechanical properties, high thermal and electrical conductivities, and oxidation resistance. High solids loaded ZrB2-SiC pastes suitable for extrusion-based additive manufacturing were developed for the first time as part of this work. Materials compatibility studies indicate this material oxidizes in CO 2 to form a protective borosilicate scale which transforms to pure silica above 1000°C. Parts made by additive manufacturing displayed enlarged grain sizes produced by pressureless sintering as compared to hot-press sintering. Increases in microstructural coarseness have outsized effect on oxidation performance up to 1400°C due to incomplete oxidation of coarse large diameter SiC particles resulting in lower amounts of silica that apparently inhibit protective scale formation. Additive manufacturing as a forming technique did not appear to significantly affect thermal conductivity, hardness, or elastic modulus, though flexural strength was reduced by half or more as compared to traditionally hot-pressed materials. This effect was attributed to the presence of strength-limiting flaws (ca. 40 microns in size) originating from extrudate inhomogeneities that could potentially be eliminated with further process improvements. Attempts to attain economies of scale for production of multi-kilowatt scale heat exchangers by ceramic additive manufacturing proved difficult. Lack of automation and a modest extrusion rate while retaining fine feature resolution made the overall process labor intensive and limited experimental throughput. A number of full-scale components were taken through post-process heat treatments including drying, binder burnout, and sintering; however, none survived without significant flaws or cracks. Therefore, no operational data from a newly installed heat exchanger test loop were able to be obtained during the performance period. Continued research and development is recommended to improve economic feasibility of ceramic additive manufacturing by standardizing the use of advanced sensors, artificial intelligence, and automation tools to reduce associated labor costs and accelerate production rates. The materials and manufacturing techniques demonstrated in this work are likely to find applications in defense and energy applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

First Solar Thermal Energy Planner (STEP 1) and Nationwide Industrial Heat and Power Analysis

The First Solar Thermal Energy Planner (STEP 1) and Nationwide Industrial Heat and Power Analysis (aka the STEP 1 Project or the Project) aimed to (1) developed a brand-new web tool that could provide decision support through free, rapid techno-economic analysis of behind-the-meter solar+storage systems for industrial process heat and (2) conduct high-level analyses of the cost-competitiveness of the same systems across the US in key sectors. The STEP 1 web tool collects key location, land availability, thermal load profile, proccess heat temperature and media, and other key parameters through an easy-to-use user interface (UI). The UI was designed to meet the user at their level of understanding by minimizing the number of required inputs as much as possible while including options for more nuanced inputs if the user desires. STEP 1 advises users on which solar thermal tehcnologies that could fit their needs based on the inputs provided (namely process media and temperature). The tool can model a wide range of solar thermal technologies including flat plate collectors, evacuated tubes, parabolic troughs, linear Fresnel, and molten salt towers all with corresponding thermal energy storage (TES) - solar PV with resistive heating and TES is also included. Once the parameters are collected, a nominal thermal energy production profile for the facility's location is generated using NREL's System Advisory Model (SAM) and then passed to a modified version of NREL's REopt platform to optimize the size (capacity) and dispatch of the solar+storage system to minimize lifecycle costs subject to energy balance, fuel and electricity rates, emission reductions goals, and other constraints. This entire process takes less than 20 minutes, is completely free, requires zero coding skills, and provides the user with a high-level assessment on the techno-economic feasability of deploying solar+storage systems for their energy needs. In addition to the development of the STEP 1 web tool, the project completed two complementary analyses focused on leveraging the backend code of STEP 1, public industrial facility locations and fuel consumption data, and key sector information to assess the economic opportunity of reducing fuel costs at various levels of capacity factor around the US. Both analyses found that there are key markets, locations, industrial sectors (namely food and beverage), and degrees of offset where solar thermal technologies could be cost-effectively deployed, highlighting a key market entry point for these technologies, and assessing deployment potential. In summary, the STEP 1 project improved the opportunities for solar+storage systems to expand into the industrial process heat market through breaking down barriers to assessing these technologies.

14 SOLAR ENERGY↗