Search NASA⌕ Search

SEARCH · Search NASA

Results for “Effective thermal conductivity”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Improved multiphysics model of the High Temperature Engineering Test Reactor for the simulation of loss-of-forced-cooling experiments

We present a multiphysics model of the High Temperature Engineering Test Reactor for comparison with past and predict future loss-of-forced-cooling (LOFC) experiments. The approach selected combines (1) 3-D full-core superhomogenization-corrected neutronics, (2) 3-D full-core homogenized or semi-heterogeneous heat transfer (macroscale), (3) 2-D axisymmetric fuel rod heat transfer (mesoscale), and (4) 1-D thermal-hydraulics channels. Although large sensitivities remain and the available experimental data are insufficient for use in a rigorous validation exercise, the overall transient behavior is successfully reproduced. The novelty of our work includes (1) a new macroscale-mesoscale heat transfer coupling approach relying on gap conductance to drastically speed up numerical convergence by two orders of magnitude, (2) determination of a radial effective thermal conductivity that yields reasonably close results between the homogenized and semi-heterogeneous macroscale thermal models, and (3) a preliminary study of the reactor's early behavior following a LOFC event, thus enabling further assessment of numerical models against fission power measurements.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Composite Structured Surfaces for Durable Dropwise Condensation

Dropwise condensation of steam on hydrophobic substrates has a 10X higher heat transfer coefficient compared to filmwise condensation. To promote dropwise condensation, low surface energy hydrophobic coatings (polymers) are typically utilized. The low intrinsic thermal conductivity (k < 1 W/(m · K)) of polymers, coupled with high heat transfer coefficient of dropwise condensation (100 kW/(m 2 · K)), necessitates that the coating be thin (< 1µm) in order to avoid reducing the overall heat exchanger conductance. However, thin polymeric films easily degrade. The two opposing requirements result in the need for optimization between the durability (thick coating) and the heat transfer (thin coating). To enable high thermal conductivity in thicker coatings, we develop metal-polymer structured surfaces. By using porous structures as inter-connected heat-conducting backbones that are filled with hydrophobic materials, we enable tuning of the coating effective thermal conductivity and surface energy. Three metal structures were studied; micro/nanowires, inverse opals, and sintered spheres. Heat transfer performance was calculated using three-dimensional finite element method simulations with two distinct boundary conditions; convection at the walls and isothermal walls. Interestingly, the overall conductance shows up to 40% difference depending on the boundary condition used in calculating the composite coating effective thermal conductivity. We use our model to predict the heat transfer performance as a function of metal fraction by volume and by surface area for condensation. By coupling our thermal simulations with a previously verified analytical model for predicting wetting behavior on heterogeneous surfaces, we propose a regime map to predict dropwise-to-filmwise transition. Furthermore, our work not only forms a starting point for the development of durable dropwise condensing surfaces, it identifies important considerations needed for computing effective thermal conductivity of composites.

42 ENGINEERING↗
DOE OSTI2022

Thermal conductivity of crack-containing media: A numerical study

The present study aims to evaluate the effective thermal conduction behavior of crack-containing media through micromechanical modeling. Numerical analyses were performed using the finite element method, first using periodic arrays of elliptical pores and then reducing the elliptical minor axis to reach the crack limit. This parametric approach was seen to be able to capture the effect of discontinuity across the crack face in a straightforward manner. The overall thermal conductivity of the model structures, encompassing a range of crack densities and spatial distributions, was investigated. It was found that, for cracks with mixed orientations, the effective thermal conductivity is insensitive to the actual crack alignment and can be uniquely represented by the crack density. The mixed-orientation periodic crack configurations are also representative of random sizes, orientations, and spatial distributions of cracks, thus exhibiting a high degree of generality. The modeling analyses can also be used to determine simple empirical expressions for two- and three-dimensional media containing random cracks.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bimodal particle distributions with increased thermal conductivity for solid particles as heat transfer media and storage materials

Solid particles are being considered in several high temperature thermal energy storage systems and as heat transfer media in a variety of advanced power generation systems, particularly in concentrated solar power plants. The downside of such an approach is the low overall heat transfer coefficients caused by the inherently low thermal conductivity values of the low-cost solid media when coupled to heat exchanger for the power cycle working fluid. Choosing the right particle size distribution, emittance, and material of the solid media can all make a substantial difference in packed bed thermal conductivity. Current research though exclusively focuses on continuous unimodal distributions of particles. Here, in this work, we propose the use of a binary particle system with a bimodal size distribution to significantly increase packed bed thermal conductivity by reducing packed bed porosity. This is the first study related to ceramic solid particle heat transfer that has considered the thermal conductivity of non-unimodal size distributions at room and elevated temperatures. The following study found that for the binary particle system using Carbo particles CP 16/30 – CP 70/140 where the large particle volume fraction was 50% there was an 17–47% increase in packed bed thermal conductivity when compared with a nearly unimodal particle size distribution of CP 16/30 between 50 and 300 °C. Two different porosity and effective thermal conductivity models were studied, with one providing better prediction of porosity but both effective thermal conductivity models providing less predictive capacity. Importantly this approach can have a substantial impact of thermal performance, with little to no impact on the particle cost.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Computational design of isotropic and anisotropic ultralow thermal conductivity polymer foams

Current state-of-the-art commercial polymer thermal insulation foam exhibits a thermal conductivity of 24 mW·m -1 ·K -1 (equivalently thermal resistivity of R-6/in.), similar to that of static air. To further optimize building energy efficiency, achieving even lower thermal conductivity is needed, which is, however, highly challenging. This paper presents computational evidence that demonstrates the feasibility of achieving an ultra-low thermal conductivity of less than 14.4 mW·m -1 ·K -1 (equivalently R-10/in.) using isotropic and anisotropic foam cell designs. For the isotropic design, we have identified analytical effective medium approximation (EMA) models within the accuracy of ±5% as finite element analysis (FEA) in predicting the effective thermal conductivity of foams with various porosities and filler gases. For the anisotropic design, we have developed and validated new EMA models against FEA in predicting the effective thermal conductivity of general anisotropic cuboids and Voronoi foams. For both isotropic and anisotropic designs, the design spaces for 18, 16, and 14.4 mW·m -1 ·K -1 (equivalently R-8, R-9 and R-10/in.) using various filler gases are obtained. It is found that polymer foams can be improved to achieve ultralow thermal conductivity by reducing CO 2 concentration, reducing radiation, increasing porosity, and using anisotropic pore geometry. In conclusion, these findings contribute to the development of highly efficient thermal insulation materials, enhancing building energy efficiency and promoting sustainable construction practices.

42 ENGINEERING↗
DOE OSTI2022

Mesoscale modeling of microstructure-dependent thermal conductivity in U-Zr fuels

In uranium-zirconium (U-Zr) based metallic fuels, different phases can form at different compositions and temperatures. Typically, lamellar δ-UZr 2 and α-U phases are the dominant microstructures in U-rich U-Zr alloys at temperatures below 880 K. In this work, a finite element method based mesoscale modeling technique is used to calculate the effective thermal conductivities of such heterogeneous microstructures, using the thermal conductivities of two individual phases and their interphase thermal resistance (Kapitza resistance) as input parameters. The Kapitza resistance between δ-UZr 2 and α-U is determined at different temperatures, which shows an approximately T 3 dependence in the temperature range between 300 and 800 K. In addition, the Kapitza resistance exhibits a strong dependence on the aspect ratio of the δ-UZr 2 phase. Further, an analytical model is therefore developed to quantify the effects of both temperature and δ-UZr 2 aspect ratio on the Kapitza resistance. Using this newly developed Kapitza resistance model, the effective thermal conductivities of a number of δ-UZr 2 + α-U heterogeneous microstructures in U-Zr alloys, including non-lamellar microstructures, can be estimated accurately.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Thermal conductivity of two-dimensional disordered fibrous materials defined by interfiber thermal contact conductance and intrinsic conductivity of fibers

A general framework for the theoretical analysis and numerical calculations of the effective thermal conductivity of two-dimensional homogeneous and isotropic disordered fibrous materials is developed in this work based on the model of random contacts between soft-core spherocylinders. The analysis accounts for the interfiber contact conductance and intrinsic conductivity of fibers and is performed in a wide space of governing parameters that includes the fiber aspect ratio, Biot number calculated for a single thermal contact between fibers, and material density ranging from values corresponding to the percolation threshold up to those characteristic of dense fiber networks. For dense networks, exact theoretical equations for the thermal conductivity of materials composed of spherocylinders with an arbitrary aspect ratio and Biot number are derived. The effect of the intrinsic conductivity of fibers on the thermal transport in fibrous materials is found to depend on the density of contacts and can be significant in sufficiently dense fiber networks even if the Biot number for a single thermal contact is small. Semiempirical corrections to the theoretical equations are derived for small and moderate fiber densities. The power law exponent describing the approximate dependence of the conductivity on the density parameter is found to vary from values close to 1 up to values exceeding 2 when evaluated within different finite ranges of the density parameter. This finding explains the variability of scaling laws for thermal conductivity of fibrous materials suggested in the literature based on numerical simulations performed in different regions of the space of material parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Comparative neutron-irradiation effects on thermal conductivity degradation and dimensional stability of TiC, TiB 2 , and ZrB 2 at 200–1000 °C

Ultra-high-temperature ceramics (UHTCs), including TiC, Ti 11 B₂, and Zr 11 B₂, show great potential for plasma-facing components due to their excellent high-temperature properties prior to irradiation. However, their response to neutron irradiation remains insufficiently understood, limiting robust assessment of their viability for fusion energy applications. Here, this study examines the thermal conductivity, dimensional stability and microstructure of TiC, TiB₂, and ZrB₂ following neutron irradiation at temperatures of 200–1000 °C and fast neutron fluences of 2.0 × 10 25 to 1.1 × 10 26 n/m 2 (E > 0.1 MeV). Lattice swelling measured by synchrotron X-ray diffraction in all three UHTCs was maximized at 200 °C and decreased with increasing irradiation temperature, with no evidence of amorphization observed at 200 °C. Above 600 °C, significant macroscopic volume swelling was observed in irradiated Ti 11 B₂ and Zr 11 B₂, but not in TiC, likely due to cavity formation in the diborides. The post-irradiation thermal conductivity, measured at the irradiation temperature, ranged from 28 to 45 W/m·K, representing a 34–45% reduction relative to the unirradiated material. Notably, neutron-irradiated UHTCs exhibit recoverable thermal conductivity at elevated temperatures, comparable to ferritic–martensitic steels and potentially superior to W when transmutation effects are considered, highlighting promise for shielding or armor plasma-facing components. At 600 °C, both thermal conductivity degradation and lattice swelling saturated at doses exceeding 2–4 dpa.

fusion materials↗
DOE OSTI2021

Comparing temperature convergence of shocked thin films of tin and iron to a bulk temperature source

An outstanding challenge in developing a complete equation of state for materials at elevated pressure and temperature is a robust method of determining the bulk temperature state under dynamic conditions. In metals, the determination of bulk temperature states by optical pyrometry is complicated by the small optical depth and thermal conduction effects. These effects lead to observed temperatures differing by 20% or more from the bulk temperature state. In this work, we show the presence of thermal conduction effects in temperature measurements of tin and iron coatings during dynamic compression experiments. We demonstrate that tin, in contrast to iron, coatings can fail to converge to a bulk temperature source over the time scale of the experiment, requiring the experimenter to modify assumptions, design, or analysis. This work bounds thermal transport at shocked conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Heat Transfer Characteristics of Particle Flow Through Additively Manufactured (SS 316L) Lattice Frame Material Based on Octet-Shape Topology

Abstract This paper presents experimentally obtained heat transfer characteristics of additively manufactured lattice frame material based on Octet-shaped unit cell. Binder jetting technology was used to print lattices in Stainless Steel 316L material. Lattice porosities ranging from 0.75 to 0.9 were investigated where thermal transport characteristics were obtained for void space occupied by air and particles. Particle diameters were varied from 266–966 microns. Effective thermal conductivity and averaged heat transfer coefficient was calculated through steady-state experiments. It was found that presence of lattice enhances the effective thermal conductivity by 2–4 times when compared to packed bed of particles alone. Furthermore, for gravity-assisted particle flow through lattice panel, significantly high convective heat transfer coefficients ranging from 200–400 W/m2K were obtained for the range of particle diameters tested. The superior thermal transport properties of Octet-shape based lattice frame material for particle flow through them makes it a very promising candidate for particle-to-supercritical carbon dioxide (sCO2) heat exchanger in concentrating solar power (CSP) application.

Aider, Youssef↗
DOE OSTI2021

Signatures of Coherent Phonon Transport in Ultralow Thermal Conductivity Two-Dimensional Ruddlesden–Popper Phase Perovskites

An emerging class of methylammonium lead iodide (MAPbI 3 )-based Ruddlesden-Popper (RP) phase perovskites, BA 2 MA n-1 Pb n I 3n+1 (n = 1-7), exhibit enhanced stability to environmental conditions relative to MAPbI 3 , yet still degrade at elevated temperatures. Here, we experimentally determine the thermal conductivities of these layered RP phases for n = 1-6, where n defines the number of repeated perovskite octahedra per layer. We measure thermal conductivities of 0.37 ± 0.13/0.12, 0.17 ± 0.08/0.07, 0.21 ± 0.05/0.04, and 0.19 ± 0.04/0.03 W/m∙K in thin films of n = 1-4 and 0.08 ± 0.06/0.04, 0.06 ± 0.04/0.03, 0.06 ± 0.03/0.03, and 0.08 ± 0.07/0.04 W/m∙K in single crystals of n = 3-6. With the exception of n = 1, these thermal conductivities are lower than the range of 0.34-0.50 W/m∙K reported for single-crystal MAPbI 3 . Reduced-order lattice dynamics modeling suggests that the initially decreasing trend of thermal conductivity in similarly oriented perovskites with increasing n may result from the transport properties of coherent phonons, emergent from the superstructure, that do not scatter at the interfaces of organic butylammonium chains and perovskite octahedra. Reduced group velocity of coherent phonons in n = 3-6, a consequence of band flattening in the phonon dispersion, is primarily responsible for their ultralow thermal conductivities. Similar effects on thermal conductivity have been experimentally demonstrated in deposited superlattices, but never in naturally defined materials such as RP phases. GIWAXS measurements reveal that higher n RP phase thin films are less orientationally controlled and therefore possess apparently elevated thermal conductivities relative to single crystals of the same n.

2D perovskites↗
DOE OSTI2023

Remarkable enhancement in thermal conductivity of stainless-steel leveraging metal composite via laser powder bed fusion: 316L-Cu composite

This work aimed to significantly enhance the thermal conductivity of the SS matrix by fabricating a metal composite SS-Cu system utilizing a laser powder bed fusion process. The impact of process parameters on the microstructure of SS-Cu samples is investigated. Here, the processing and post-processing factors that influence the effective thermal conductivity of the metal composite SS-Cu system are discussed. Then, the effective thermal conductivity and mechanical properties of the SS-Cu composite are measured at room temperature and operating temperature of 300 °C. The optimized laser powder bed fusion parameters led to low Marangoni convection, high cooling rate, greater macro-segregation, and higher thermal conductivity values albeit at the cost of ductility in SS-Cu metal composite likely due to the presence of the unmelted powder particles. As-printed SS-60 vol % Cu and annealed SS-60 vol % Cu had 2.5X and 6.6X thermal conductivity enhancement, respectively. During annealing, phase separation, partial melting of Cu, and formation of a continuous network of Cu surrounding SS play a key role in enhancing the thermal conductivity of the SS-Cu metal composite structure.

36 MATERIALS SCIENCE↗
DOE OSTI2026

SAM Finite Volume Method Development Status Update: GCR Application, Restart, and MultiApp

The System Analysis Module (SAM) is being developed as a modern system analysis code for advanced non-light-water-reactor safety analysis under the U.S. DOE NEAMS program. Previous feasibility studies have demonstrated that a staggered-grid finite volume method (SG-FVM), implemented under the MOOSE framework, can deliver more than an order of magnitude speedup over the existing continuous Galerkin finite element method (CG-FEM) solver for liquid-cooled, incompressible but thermally expandable flow systems. This work extends the previous effort to compressible, gas-cooled reactor applications, where pressure couples directly into the mass equation adding additional nonlinearity into the equation system. New code capabilities are implemented for pebble bed high-temperature gas-cooled reactor (PB-HTGR) analysis, including a pebble bed CoreChannel component, built-in pebble bed effective thermal conductivity model and channel-to-channel crossflow model. The capabilities are tested, benchmarked, and demonstrated for problems with increased level of model and physical complexities, including the HTTU effective thermal conductivity test, the SANA passive cooling test, and a demonstration case using the GPBR200 reactor design covering steady-state operation, DLOFC and PLOFC transients. Across all cases, the SG-FVM solver demonstrated strong robustness and efficiency, and the solutions agree well with reference results and data. The finding of this work proves that SG-FVM is a viable and efficient solver pathway for compressible, gas-cooled reactor system analysis in SAM. In addition, work has been done to successfully support SAM-FVM recover/restart code feature that is essential to reactor safety analysis applications, and MultiApp code feature that is essential to multi-scale and multi-physics simulations. In summary, this work continued from previous feasibility studies, and further demonstrated that the SG-FVM will serve as a strong foundation for SAM’s advanced solver algorithm for future deployment.

Zou, Ling↗
DOE OSTI2021

Fourier-like Thermal Relaxation of Nanoscale Explosive Hot Spots

Hot spots are local regions of high temperature that are widely considered to govern explosive initiation. Hot spot dynamics rests on a delicate balance between heat generation due to chemical reactions and heat loss through thermal conduction, making accurate determinations of the conductivity under extreme conditions a key component of predictive explosive models. We develop here an approach to directly determine the thermal transport properties of explosive hot spots with realistic initial structures through a combination of molecular dynamics (MD) and diffusive heat equation (HEq) modeling. Effective thermal conductivity values are determined by fitting HEq models to MD predictions of long timescale hot spot relaxation. The approach is applied to model hot spots in the molecular crystalline explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) for a range of shock strengths and two limiting cases for impact orientation. Isotropic and anisotropic HEq models yield similar results, despite TATB exhibiting some of the largest and most anisotropic thermal conductivity values for explosive near normal conditions. The conductivity is found to be a strong function of density, which parametrically captures dependence on temperature, pressure, and material state. The associated root-mean-square errors of the fitted HEq models are approximately 5% of MD predicted final equilibrium temperatures. Here, the conductivity values determined here for TATB hot spots are considerably larger than those used in a prior hot spot criticality study, which may significantly impact predictions for critical hot spot sizes. The approach provides a convenient foundation for determining the effective thermal conductivity for hot spot problems in other explosives and directly yields information on reasonable approximations that might be taken in higher-level models for those materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Giant Isotope Effect of Thermal Conductivity in Silicon Nanowires

Isotopically purified semiconductors potentially dissipate heat better than their natural, isotopically mixed counterparts as they have higher thermal conductivity (κ). But the benefit is low for Si at room temperature, amounting to only ~10% higher κ for bulk 28 Si than for bulk natural Si ( nat Si). Here we show that in stark contrast to this bulk behavior, 28 Si (99.92% enriched) nanowires have up to 150% higher κ than nat Si nanowires with similar diameters and surface morphology. Using a first-principles phonon dispersion model, this giant isotope effect is attributed to a mutual enhancement of isotope scattering and surface scattering of phonons in nat Si nanowires, correlated via transmission of phonons to the native amorphous SiO 2 shell. The Letter discovers the strongest isotope effect of κ at room temperature among all materials reported to date and inspires potential applications of isotopically enriched semiconductors in microelectronics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Conduction Heat Transfer through Solid in Porous Materials: A Comparative Study by Finite-Element Simulations and Effective Medium Approximations

The development of insulation materials with low effective thermal conductivity is essential for energy savings in various applications, including buildings, food services, pipe insulation, and refrigeration. Such materials can be developed by using micro- or nanoporous structures, as well as low-thermal conductivity gases and/or reduced pressure. A variety of effective medium approximation (EMA) models have been developed to study thermal transport through solid in porous structures. However, in many cases, the impacts of porosity on solid conduction are not well predicted by EMA models because of the assumptions made for simplification. Furthermore, the results can vary by a factor of up to 1.5, depending on the morphology of the pores. Hence, proper guidance is needed to choose the appropriate EMA model for a given morphology. This work presents a finite element method study using COMSOL Multiphysics software for various geometries, including hollow cubes, overlapping hollow spheres (normally stacked and tightly packed), and Voronoi structures, and compares the results to those obtained from various EMA models. Simulation results for the hollow cubes and Voronoi structures matched well with the Maxwell-Eucken and Russell model. The results for hollow spheres closely matched the Bauer model and the Glicksman model with fitting parameters. This work provides guidance on analyzing and designing insulation materials for energy savings in the future.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Predicting Thermal Excursions During in situ Oxidative Regeneration of Packed Bed Catalytic Fast Pyrolysis Catalyst

Ex situ catalytic fast pyrolysis (CFP) uses a secondary reactor to upgrade biomass pyrolysis vapors to stabilized CFP oils with reduced oxygen content. In one configuration, the secondary reactor is operated as a packed-bed swing reactor system which allows coke-deactivated beds to be decarbonized in situ while other beds remain online for vapor upgrading. In situ decarbonization must be done carefully to avoid irreversible deactivation and/or physical degradation of catalyst pellets. Given that packed bed reactors are well known to have poor heat transfer characteristics, this is a critical issue impacting scaleability and commercial viability of the technology. To predict thermal excursions during regeneration, finite element computational models have been built to assist in scaling up oxidative decarbonization of a Pt/TiO2 CFP catalyst (0.5 mm spheres) from a bench scale packed bed with 100 g of catalyst to a pilot scale packed bed with 2 kg of catalyst and internal cooling tubes. Based on transient measurements of outlet temperature and effluent CO2 concentration, and using an assumed coke profile and activation energy, this paper demonstrates that specific combinations of effective thermal conductivity and wall heat transfer coefficient can fit bench scale oxidative regeneration data equally well. For the upscaled 2 kg bed, four bench-scale “best fit” parameter pairs give different predictions for location and magnitude of thermal excursions, with the maximum computed bed temperature gradients ranging from 30 °C cm-1 to as high as 3000 °C cm-1. The larger the fraction of heat removal by conduction through the cooling tubes, the greater the differences between the parameter pairs. The modelling results presented in this paper cast doubt on the industrial viability of the proposed combination of catalyst, bed and regeneration process, and point to the need for alternate reactor designs. However, there is considerable uncertainly in some of the key model parameters. The reliability of model predictions can be increased by adding more temperature measurements at key bed locations, testing additional variations in process conditions, performing careful bed dissections to determine the true coke profile, and perhaps most importantly, directly measuring the effective thermal conductivity of the catalyst pellets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Enhancing particle-to-sCO2 heat exchanger effectiveness through novel high-porosity metallic foams

In this project, a novel concept of Octet-shape based lattice frame material was developed for deployment in particle-to-sCO2 heat exchangers for CSP application. A comprehensive experimental and numerical program was performed to investigate and characterize the thermal and flow transport behavior in high porosity lattice frame material. The thermal properties include effective thermal conductivity and interstitial heat transfer coefficient and flow properties including permeability and inertial coefficient. Above quantities were determined for both air flow and heated particle flow through the porous channels which were representative of the hot channel in a typical counter flow heat exchanger. The cold side of the heat exchanger feature minichannels which are known to be very efficient in thermal transport. The goal of this project was to enhance the overall heat transfer coefficient (Up) on the hot side by introducing Octet-shape based lattice frame material through enhancement in effective thermal conductivity of the channel and through enhancement in the interstitial heat transfer coefficient.

14 SOLAR ENERGY↗