Publications

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Novel designs to increase light trapping and thermal efficiency of concentrating solar receivers at multiple length scales have been conceived and tested. The fractal-like geometries and features are introduced at both macro (meters) and meso (millimeters to centimeters) scales. Advantages include increased solar absorptance, reduced thermal emittance, and increased thermal efficiency. Radial and linear structures at the meso (tube shape and geometry) and macro (total receiver geometry and configuration) scales redirect reflected solar radiation toward the interior of the receiver for increased absorptance. Hotter regions within the interior of the receiver can reduce thermal emittance due to reduced local view factors to the environment, and higher concentration ratios can be employed with similar surface irradiances to reduce the effective optical aperture, footprint, and thermal losses. Coupled optical/fluid/thermal models have been developed to evaluate the performance of these designs relative to conventional designs, and meso-scale tests have been performed. Results show that fractal-like structures and geometries can increase the thermal efficiency by several percentage points at both the meso and macro scales, depending on factors such as intrinsic absorptance. The impact was more pronounced for materials with lower intrinsic solar absorptances (<0.9). The goal of this work is to increase the effective solar absorptance of oxidized substrate materials from ∼0.9 to 0.95 or greater using these fractal-like geometries without the need for coatings.

Falling particle receivers (FPR) utilize small particles as a heat collecting medium within a cavity receiver structure. Previous analysis for FPR systems include computational fluid dynamics (CFD), analytical evaluations, and experiments to determine the feasibility and achievability of this CSP technology. Sandia National Laboratories has fabricated and tested a 1 MWth FPR that consists of a cavity receiver, top hopper, bottom hopper, support structure, particle elevator, flux target, and instrumentation. Design requirements and inherent challenges were addressed to enable continuous operation of flowing particles under high-flux conditions and particle temperatures over 700 °C. Challenges include being able to withstand extremely high temperatures (up to 1200°C on the walls of the cavity), maintaining particle flow and conveyance, measuring temperatures and mass flow rates, filtering out debris, protecting components from direct flux spillage, and measuring irradiance in the cavity. Each of the major components of the system is separated into design requirements, associated challenges and corresponding solutions. The intent is to provide industry and researchers with lessons learned to avoid pitfalls and technical problems encountered during the development of Sandia's prototype particle receiver system at the National Solar Thermal Test Facility (NSTTF).

A 1 MWth high-temperature falling particle receiver was constructed and tested at the National Solar Thermal Test Facility at Sandia National Laboratories. The continuously recirculating system included a particle elevator, top and bottom hoppers, and a cavity receiver that comprised a staggered array of porous chevron-shaped mesh structures that slowed the particle flow through the concentrated solar flux. Initial tests were performed with a peak irradiance of ∼300 kW/m2 and a particle mass flow rate of 3.3 kg/s. Peak particle temperatures reached over 700 °C near the center of the receiver, but the particle temperature increase near the sides was lower due to a non-uniform irradiance distribution. At a particle inlet temperature of ∼440 °C, the particle temperature increase was 27 °C per meter of drop length, and the thermal efficiency was ∼60% for an average irradiance of 110 kW/m2. At an average irradiance of 211 kW/m2, the particle temperature increase was 57.1 °C per meter of drop length, and the thermal efficiency was ∼65%. Tests with higher irradiances are being performed and are expected to yield greater particle temperature increases and efficiencies.

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Direct solar power receivers consist of tubular arrays, or panels, which are typically tubes arranged side by side and connected to an inlet and outlet manifold. The tubes absorb the heat incident on the surface and transfer it to the fluid contained inside them. To increase the solar absorptance, high temperature black paint or a solar selective coating is applied to the surface of the tubes. However, current solar selective coatings degrade over the lifetime of the receiver and must be reapplied, which reduces the receiver thermal efficiency and increases the maintenance costs. This work presents an evaluation of several novel receiver shapes which have been denominated as fractal like geometries (FLGs). The FLGs are geometries that create a light-trapping effect, thus, increasing the effective solar absorptance and potentially increasing the thermal efficiency of the receiver. Five FLG prototypes were fabricated out of Inconel 718 and tested in Sandia's solar furnace at two irradiance levels of ∼15 and 30 W/cm2 and two fluid flow rates. Photographic methods were used to capture the irradiance distribution on the receiver surfaces and compared to results from ray-tracing models. This methods provided the irradiance distribution and the thermal input on the FLGs. Air at nearly atmospheric pressure was used as heat transfer fluid. The air inlet and outlet temperatures were recorded, using a data acquisition system, until steady state was achieved. Computational fluid dynamics (CFD) models, using the Discrete Ordinates (DO) radiation and the k-? Shear Stress Transport (SST) equations, were developed and calibrated, using the test data, to predict the performance of the five FLGs at different air flow rates and irradiance levels. The results showed that relative to a flat plate (base case), the new FLGs exhibited an increase in the effective solar absorptance from 0.86 to 0.92 for an intrinsic material absorptance of 0.86. Peak surface temperatures of ∼1000°C and maximum air temperature increases of ∼200°C were observed. Compared to the base case, the new FLGs showed a clear air outlet temperature increase. Thermal efficiency increases of ∼15%, with respect to the base case, were observed. Several tests, in different days, were performed to assess the repeatability of the results. The results obtained, so far, are very encouraging and display a very strong potential for incorporation in future solar power receivers.

This paper evaluates novel particle release patterns for high-temperature falling particle receivers. Spatial release patterns resembling triangular and square waves are investigated and compared to the conventional straight-line particle release. A design of experiments was developed, and a simulation matrix was developed that investigated three twolevel factors: amplitude, wavelength, and wave type. Results show that the wave-like patterns increased both the particle temperature rise and thermal efficiency of the receiver relative to the straight-line particle release. Larger amplitudes and smaller wavelengths increased the performance by creating a volumetric heating effect that increased light absorption and reduced heat loss. Experiments are also being designed to investigate the hydraulic and thermal performance of these new particle release configurations.

Multiple receiver designs have been evaluated for improved optics and efficiency gains including flat panel, vertical-finned flat panel, horizontal-finned flat panel, and radially finned. Ray tracing using SolTrace was performed to understand the light-trapping effects of the finned receivers. Re-reflections of the fins to other fins on the receiver were captured to give an overall effective solar absorptance. The ray tracing, finite element analysis, and previous computational fluid dynamics showed that the horizontalfinned flat panel produced the most efficient receiver with increased light-trapping and lower overall heat loss. The effective solar absorptance was shown to increase from an intrinsic absorptance of 0.86 to 0.96 with ray trace models. The predicted thermal efficiency was shown in CFD models to be over 95%. The horizontal panels produce a re-circulating hot zone between the panel fins reducing convective loss resulting in a more efficient receiver. The analysis and design of these panels are described with additional engineering details on testing a flat panel receiver and the horizontal-finned receiver at the National Solar Thermal Test Facility. Design considerations include the structure for receiver testing, tube sizing, surrounding heat shielding, and machinery for cooling the receiver tubes.

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Falling solid particle receivers (SPR) utilize small particles as a heat collecting medium within a cavity receiver structure. The components required to operate an SPR include the receiver (to heat the particles), bottom hopper (to catch the falling particles), particle lift elevator (to lift particles back to the top of the receiver), top hopper (to store particles before being dropped through the receiver), and ducting. In addition to the required components, there are additional features needed for an experimental system. These features include: a support structure to house all components, calibration panel to measure incident radiation, cooling loops, and sensors (flux gages, thermocouples, pressure gages). Each of these components had to be designed to withstand temperatures ranging from ambient to 700 °C. Thermal stresses from thermal expansion become a key factor in these types of high temperature systems. The SPR will be housing ∼3000 kg of solid particles. The final system will be tested at the National Solar Thermal Test Facility in Albuquerque, NM.

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Falling particle receivers are being evaluated as an alternative to conventional fluid-based solar receivers to enable higher temperatures and higher efficiency power cycles with direct storage for concentrating solar power applications. This paper presents studies of the particle mass flow rate, velocity, particle-curtain opacity and density, and other characteristics of free-falling ceramic particles as a function of different discharge slot apertures. The methods to characterize the particle flow are described, and results are compared to theoretical and numerical models for unheated conditions.

Closed-loop super-critical carbon dioxide (sCO2) Brayton cycles are being evaluated in combination with concentrating solar power to provide higher thermal-to-electric conversion efficiencies relative to conventional steam Rankine cycles. However, high temperatures (650-700°C) and pressures (20-25 MPa) are required in the solar receiver. In this study an extensive material review was performed along with a tube size optimization following the ASME Boiler and Pressure Vessel Code and B31.1 and B313.3 codes respectively. Subsequently a thermal-structural model was developed using ANSYS Fluent and Structural to design and analyze the tubular receiver that could provide the heat input for a ∼2 MWth plant. The receiver will be required to provide an outlet temperature of 650°C (at 25 MPa) or 700°C (at 20 MPa). The induced thermal stresses were applied using a temperature gradient throughout the tube while a constant pressure load was applied on the inner wall. The resulting stresses have been validated analytically using constant surface temperatures. The cyclic loading analysis was performed using the Larson-Miller creep model in nCode Design Life to define the structural integrity of the receiver over the desired lifetime of ∼10,000 cycles. The results have shown that the stresses induced by the thermal and pressure load can be withstood by the tubes selected. The creep-fatigue analysis displayed the damage accumulation due to the cycling and the permanent deformation of the tubes. Nonetheless, they are able to support the required lifetime. As a result, a complete model to verify the structural integrity and thermal performance of a high temperature and pressure receiver has been developed. This work will serve as reference for future design and evaluation of future direct and indirect tubular receivers.

Cavity receivers used in solar power towers and dish concentrators may lose considerable energy by natural convection, which reduces the overall system efficiency. A validated numerical receiver model is desired to better understand convection processes and aid in heat loss minimization efforts. The purpose ofthis investigation was to evaluate heat loss predictions using the commercial computational fluid dynamics (CFD) software packages fluent 13.0 and solidworks flow simulation 2011 against experimentally measured heat losses for a heated cubical cavity receiver model (Kraabel, 1983, "An Experimental Investigation of the Natural Convection From a Side-Facing Cubical Cavity," Proceedings of the ASME JSME Thermal Engineering Joint Conference, Vol. 1, pp. 299-306) and a cylindrical dish receiver model (Taumoefolau et al., 2004, "Experimental Investigation of Natural Convection Heat Loss From a Model Solar Concentrator Cavity Receiver," ASME J. Sol. Energy Eng., 126(2), pp. 801-807). Simulated convective heat loss was underpredicted by 45% for the cubical cavity when experimental wall temperatures were implemented as isothermal boundary conditions and 32% when the experimental power was applied as a uniform heat flux from the cavity walls. Agreement between software packages was generally within 10%. Convective heat loss from the cylindrical dish receiver model was accurately predicted within experimental uncertainties by both simulation codes using both isothermal and constant heat flux wall boundary conditions except when the cavity was inclined at angles below 15 deg and above 75 deg, where losses were under- and overpredicted by fluent and solidworks, respectively. Comparison with empirical correlations for convective heat loss from heated cavities showed that correlations by Kraabel (1983, "An Experimental Investigation of the Natural Convection From a Side-Facing Cubical Cavity," Proceedings ofthe ASME JSME Thermal Engineering Joint Conference, Vol. 1, pp. 299-306) and for individual heated flat plates oriented to the cavity geometry (Pitts and Sissom, 1998, Schaum's Outline of Heat Transfer, 2nd ed., McGraw Hill, New York, p. 227) predicted heat losses from the cubical cavity to within experimental uncertainties. Correlations by Clausing (1987, "Natural Convection From Isothermal Cubical Cavities With a Variety of Side-Facing Apertures," ASME J. Heat Transfer, 109(2), pp. 407-412) and Paitoonsurikarn et al. (2011, "Numerical Investigation of Natural Convection Loss From Cavity Receivers in Solar Dish Applications," ASME J. Sol. Energy Eng. 133(2), p. 021004) were able to do the same for the cylindrical dish receiver. No single correlation was valid for both experimental receivers. The effect ofdifferent turbulence and air-property models within fluent were also investigated and compared in this study. However, no model parameter was found to produce a change large enough to account for the deficient convective heat loss simulated for the cubical cavity receiver case.

Recent studies have evaluated closed-loop supercritical carbon dioxide (s-CO2) Brayton cycles to be a higher energydensity system in comparison to conventional superheated steam Rankine systems. At turbine inlet conditions of 923K and 25 MPa, high thermal efficiency (∼50%) can be achieved. Achieving these high efficiencies will make concentrating solar power (CSP) technologies a competitive alternative to current power generation methods. To incorporate a s-CO2 Brayton power cycle in a solar power tower system, the development of a solar receiver capable of providing an outlet temperature of 923 K (at 25 MPa) is necessary. The s-CO2 will need to increase in temperature by ∼200 K as it passes through the solar receiver to satisfy the temperature requirements of a s-CO2 Brayton cycle with recuperation and recompression. In this study, an optical-thermal-fluid model was developed to design and evaluate a tubular receiver that will receive a heat input ∼2 MWth from a heliostat field. The ray-tracing tool SolTrace was used to obtain the heat-flux distribution on the surfaces of the receiver. Computational fluid dynamics (CFD) modeling using the Discrete Ordinates (DO) radiation model was used to predict the temperature distribution and the resulting receiver efficiency. The effect of flow parameters, receiver geometry and radiation absorption by s-CO2 were studied. The receiver surface temperatures were found to be within the safe operational limit while exhibiting a receiver efficiency of ∼85%.

Typical Concentrated Solar Power (CSP) central receiver power plants require the use of either an external or cavity receiver. Previous and current external receivers consist of a series of tubes connected to manifolds that form a cylindrical or rectangular shape such as in the cases of Solar One, Solar Two, and most recently the Ivanpah solar plant. These receivers operate at high surface temperatures (>600°C) at which point thermal re-radiation is significant. However, the geometric arrangement of these heat transfer tubes results in heat losses directly to the environment. This work focused on how to fundamentally reduce this heat loss through the manipulation of heat transfer tube configurations. Four receiver configurations are studied: flat receiver (base case study), a radial receiver with finned structures (fins arranged in a circular pattern on a cylinder), a louvered finned structure (horizontal and angled fins on a flat plate), and a vertical finned structure (fins oriented vertically along a flat plate). The thermal efficiency, convective heat loss patterns, and air flow around each receiver design is found using the computational fluid dynamics (CFD) code ANSYS FLUENT. Results presented in this paper show that alternative tubular configurations increase thermal efficiency by increasing the effective solar absorptance of these hightemperature receivers by increasing the light trapping effects of the receiver, reducing thermal emittance to the environment, and reducing the overall size of the receiver. Each receiver configuration has finned structures that take advantage of the directional dependence of the heliostat field resulting in a light trapping effect on the receiver. The finned configurations tend to lead to "hot" regions on the receiver, but the new configurations can take advantage of high local view factors (each surface can "see" another receiver surface) in these regions through the use of heat transfer fluid (HTF) flow patterns. The HTF reduces the temperatures in these regions increasing the efficiency of heat transfer to the fluid. Finally, the new receiver configurations have a lower overall optical intercept region resulting in a higher geometric concentration ratio for the receiver. Compared to the base case analysis (flat plate receiver), the novel tubular geometries results showed an increase in thermal efficiency.

This paper establishes the design requirements for the development and testing of direct supercritical carbon dioxide (sCO2) solar receivers. Current design considerations are based on the ASME Boiler and Pressure Vessel Code (BPVC). Section I (BPVC) considers typical boilers/superheaters (i.e. fired pressure vessels) which work under a constant low heat flux. Section VIII (BPVC) considers pressure vessels with operating pressures above 15 psig [2 bar] (i.e. unfired pressure vessels). Section III, Division I - Subsection NH (BPVC) considers a more detailed stress calculation, compared to Section I and Section VIII, and requires a creep-fatigue analysis. The main drawback from using the BPVC exclusively is the large safety requirements developed for nuclear power applications. As a result, a new set of requirements is needed to perform detailed thermal-structural analyses of solar thermal receivers subjected to a spatially-varying, high-intensity heat flux. The last design requirements document of this kind was an interim Sandia report developed in 1979 (SAND79-8183), but it only addresses some of the technical challenges in early-stage steam and molten-salt solar receivers but not the use of sCO2 receivers. This paper presents a combination of the ASME BPVC and ASME B31.1 Code modified appropriately to achieve the reliability requirements in sCO2 solar power systems. There are five main categories in this requirements document: Operation and Safety, Materials and Manufacturing, Instrumentation, Maintenance and Environmental, and General requirements. This paper also includes the modeling guidelines and input parameters required in computational fluid dynamics and structural analyses utilizing ANSYS Fluent, ANSYS Mechanical, and nCode Design Life. The main purpose of this document is to serve as a reference and guideline for design and testing requirements, as well as to address the technical challenges and provide initial parameters for the computational models that will be employed for the development of sCO2 receivers.

Traditional tubular receivers used in concentrating solar power are formed using tubes connected to manifolds to form panels; which in turn are arranged in cylindrical or rectangular shapes. Previous and current tubular receivers, such as the ones used in Solar One, Solar Two, and most recently the Ivanpah solar plants, have used a black paint coating to increase the solar absorptance of the receiver. However, these coatings degrade over time and must be reapplied, increasing the receiver maintenance cost. This paper presents the thermal efficiency evaluation of novel receiver tubular panels that have a higher effective solar absorptance due to a light-trapping effect created by arranging the tubes in each panel into unique geometric configurations. Similarly, the impact of the incidence angle on the effective solar absorptance and thermal efficiency is evaluated. The overarching goal of this work is to achieve effective solar absorptances of ∼90% and thermal efficiencies above 85% without using an absorptance coating. Several panel geometries were initially proposed and were down-selected based on structural analyses considering the thermal and pressure loading requirements of molten salt and supercritical carbon-dioxide receivers. The effective solar absorptance of the chosen tube geometries and panel configurations were evaluated using the ray-tracing modeling capabilities of SolTrace. The thermal efficiency was then evaluated by coupling computational fluid dynamics with the ray-tracing results using ANSYS Fluent. Compared to the base case analysis (flat tubular panel), the novel tubular panels have shown an increase in effective solar absorptance and thermal efficiency by several percentage points.

Concentrating solar power receivers are comprised of panels of tubes arranged in a cylindrical or cubical shape on top of a tower. The tubes contain heat-transfer fluid that absorbs energy from the concentrated sunlight incident on the tubes. To increase the solar absorptance, black paint or a solar selective coating is applied to the surface of the tubes. However, these coatings degrade over time and must be reapplied, which reduces the system performance and increases costs. This paper presents an evaluation of novel receiver shapes and geometries that create a light-trapping effect, thereby increasing the effective solar absorptance and efficiency of the solar receiver. Several prototype shapes were fabricated from Inconel 718 and tested in Sandiaas solar furnace at an irradiance of ∼30 W/cm2. Photographic methods were used to capture the irradiance distribution on the receiver surfaces. The irradiance profiles were compared to results from raytracing models. The effective solar absorptance was also evaluated using the ray-tracing models. Results showed that relative to a flat plate, the new geometries could increase the effective solar absorptance from 86% to 92% for an intrinsic material absorptance of 86%, and from 60% to 73% for an intrinsic material absorptance of 60%.

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The Ivanpah Solar Electric Generating System (ISEGS), located on I - 15 about 40 miles (60 km) south of Las Vegas, NV, consists of three power towers 459 ft (140 m) tall and over 170,000 reflective heliostats with a rated capacity of 390 MW. Reports of glare from the plant have been submitted by pilots and air traffic controllers and recorded by the Aviation Safety Reporting System and the California Energy Commission since 2013. Aerial and ground - based surveys of the glare were conducted in April, 2014, to identify the cause and to quantify the irradiance and potential ocular impact s of the glare . Results showed that the intense glare viewed from the airspace above ISEGS was caused by he liostats in standby mode that were aimed to the side of the receiver. Evaluation of the glare showed that the retinal irradiance and subtended source angle of the glare from the heliostats in standby were sufficient to cause significant ocular impact (pot ential for after - image) up to a distance of %7E6 miles (10 km), but the values were below the threshold for permanent eye damage . Glare from the receivers had a low potential for after - image at all ground - based monitoring locations outside of the site bound aries. A Letter to Airmen has been issued by the Federal Aviation Administration to notify pilots of the potential glare hazards. Additional measures to mitigate the potential impacts of glare from ISGES are also presented and discussed. This page intentionally left blank

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Solar optical modeling tools are valuable for modeling and predicting the performance of solar technology systems. Four optical modeling tools were evaluated using the National Solar Thermal Test Facility heliostat field combined with flat plate receiver geometry as a benchmark. The four optical modeling tools evaluated were DELSOL, HELIOS, SolTrace, and Tonatiuh. All are available for free from their respective developers. DELSOL and HELIOS both use a convolution of the sunshape and optical errors for rapid calculation of flux profiles on the receiver surfaces. SolTrace and Tonatiuh use ray-tracing methods to determine reflected solar rays on the receiver surfaces and construct flux profiles. We found the raytracing tools, although slower in computation speed, to be more flexible for modeling complex receiver geometries, whereas DELSOL and HELIOS were limited to standard receiver geometries. We provide an example of using SolTrace for modeling non-conventional receiver geometries. We also list the strengths and deficiencies of the tools to show tool preference depending on the modeling and design needs.

Solar thermal receivers absorb concentrated sunlight and can operate at high temperatures exceeding 600°C for production of heat and electricity. New fractal-like designs employing light-trapping structures and geometries at multiple length scales are proposed to increase the effective solar absorptance and efficiency of these receivers. Radial and linear structures at the micro (surface coatings and depositions), meso (tube shape and geometry), and macro (total receiver geometry and configuration) scales redirect reflected solar radiation toward the interior of the receiver for increased absorptance. Hotter regions within the interior of the receiver also reduce thermal emittance due to reduced local view factors in the interior regions, and higher concentration ratios can be employed with similar surface irradiances to reduce the effective optical aperture and thermal losses. Coupled optical/fluid/thermal models have been developed to evaluate the performance of these designs relative to conventional designs. Results show that fractal-like structures and geometries can reduce total radiative losses by up to 50% and increase the thermal efficiency by up to 10%. The impact was more pronounced for materials with lower inherent solar absorptances (< 0.9). Meso-scale tests were conducted and confirmed model results that showed increased light-trapping from corrugated surfaces relative to flat surfaces.

Cavity receivers have been an integral part of Concentrated Solar Power (CSP) plants for many years. However, falling solid particle receivers (SPR) which employ a cavity design are only in the beginning stages of on-sun testing and evaluation. A prototype SPR has been developed which will be fully integrated into a complete system to demonstrate the effectiveness of this technology in the CSP sector. The receiver is a rectangular cavity with an aperture on the north side, open bottom (for particle collection), and a slot in the top (particle curtain injection). The solid particles fall from the top of the cavity through the solar flux and are collected after leaving the receiver. There are inherent design challenges with this type of receiver including particle curtain opacity, high wall fluxes, high wall temperatures, and high heat losses. CFD calculations using ANSYS FLUENT were performed to evaluate the effectiveness of the current receiver design. The particle curtain mass flow rate needed to be carefully regulated such that the curtain opacity is high (to intercept as much solar radiation as possible), but also low enough to increase the average particle temperature by 200°C. Wall temperatures were shown to be less than 1200°C when the particle curtain mass flow rate is 2.7 kg/s/m which is critical for the receiver insulation. The size of the cavity was shown to decrease the incident flux on the cavity walls and also reduced the wall temperatures. A thermal efficiency of 92% was achieved, but was obtained with a higher particle mass flow rate resulting in a lower average particle temperature rise. A final prototype receiver design has been completed utilizing the computational evaluation and past CSP project experiences.

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Solar Two was a demonstration of the viability of molten salt power towers. The power tower was designed to produce enough thermal power to run a 10-MWe conventional Rankine cycle turbine. A critical component of this process was the solar tower receiver. The receiver was designed for an applied average heat flux of 430 kW/m2 with an outlet temperature of 565°C (838.15 K). The mass flow rate could be varied in the system to control the outlet temperature of the heat transfer fluid, which was high temperature molten salt. The heat loss in the actual system was calculated by using the power-on method which compares how much power is absorbed by the molten salt when using half of the heliostat field and then the full heliostat field. However, the total heat loss in the system was lumped into a single value comprised of radiation, convection, and conduction heat transfer losses. In this study, ANSYS FLUENT was used to evaluate and characterize the radiative and convective heat losses from this receiver system assuming two boundary conditions: (1) a uniform heat flux on the receiver and (2) a distributed heat flux generated from the code DELSOL. The results show that the distributed-flux models resulted in radiative heat losses that were ∼14% higher than the uniform-flux models, and convective losses that were ∼5-10% higher due to the resulting non-uniform temperature distributions. Comparing the simulations to known convective heat loss correlations demonstrated that surface roughness should be accounted for in the simulations. This study provides a model which can be used for further receiver design and demonstrates whether current convective correlations are appropriate for analytical evaluation of external solar tower receivers. Copyright © 2012 by ASME.

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