Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “RADIATION FLUX”

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 667 records · Page 37

Laboratory-Based Thermal Shock Investigation of Heat Flux Sensors for the Mars 2020 Backshell

In 2012 during the entry, descent, and landing of the Mars Science Laboratory (MSL), the MSL Entry, Descent, and Landing Instrumentation (MEDLI) sensor suite was collecting in-flight heatshield pressure and temperature data. The data collected by the MEDLI instruments has since been used for reconstruction of vehicle aerodynamics, atmospheric conditions, aerothermal heating, and Thermal Protection System (TPS) performance as well as material response model validation and refinement. The Mars Entry, Descent, and Landing Instrumentation 2 (MEDLI2) sensor suite for the Mars 2020 heatshield and backshell is being designed to expand on the measurements and knowledge gained from MEDLI. Similar to MEDLI, MEDLI2 will measure the pressure and temperature of the heatshield. MEDLI2 will additionally measure the temperature, pressure, total heat flux, and radiative heat flux on the backshell.Since the backshell instrumentation is new to MEDLI2, Do No Harm (DNH) testing was conducted on instrumented backshell TPS (SLA-561V) panels. The panels consisted of four pressure port holes, one Mars Entry Atmospheric Data System (MEADS) pressure port plug, one MEDLI2 Integrated Sensor Plug (MISP) thermal plug, and one heat flux sensor. DNH testing was conducted to ensure the performance of the TPS was not degraded due to sensor integration and to characterize any TPS performance changes. The testing consisted of environmental testing— vibration, shock, thermal vacuum (TVAC) cycling— and bounding aerothermal (arc jet) testing. During arc jet testing, the heat flux sensors embedded in the SLA-561V panels exhibited an unexpected temporary reduction in the heat flux sensor temperature and response. After review of the test results, it was determined that this unexpected response was confined to the two heat flux sensors that experienced the greatest thermal shock condition. This condition consisted of a liquid nitrogen (LN2) bath that induced temperatures of approximately -190°C, and then a transition (thermal shock) to an arc jet test at a heat rate of approximately 21 W/cm2. Both heat flux sensors that were exposed to this thermal shock experienced a blister in the thermal coating during the arc jet test.Two heat flux sensor thermal shock test series were performed to investigate the cause of the blistering and subsequent energy release. In these tests, the heat flux sensor was first cold soaked in either a dry ice or LN2 bath to induce temperatures of approximately -78°C or -190°C, respectively. Then the sensors were thermally shocked using two propane torches with a heat rate of either approximately 8 W/cm2 or 21 W/cm2. The key findings indicated that there is a correlation between thermal shock and the blistering observed in the DNH test series, and that the cause appeared to be rooted in the heat flux sensor epoxy that encapsulates the sensor thermopile.Since the heat flux sensors are required to measure heat fluxes up to 15 W/cm2 during the Mars 2020 entry, a third test series was designed to determine if blistering is an issue at this maximum expected flight heat flux. Results from all three thermal shock test series and a discussion about whether or not blistering of the heat flux sensor thermal coating could be an issue for the Mars 2020 mission will be presented.

Miller, R. A.↗

TPSAS-NF1676L-32099-DND

This talk provides a short overview of the new POWER web site that provides data parameters to energy sector societal benefit areas from NASA research projects. The NASA research projects include the GEWEX Surface Radiation Budget project, the CERES Fast Shortwave and Longwave radiative flux project (FLASHFlux) and NASA Goddard's Global Modeling and Assimilation Office (GMAO) MERRA-2 atmospheric reanalysis. Data products are customized to the energy industry and make products available from the daily time scale to long-term climatological averages. The web services allow uses to choose multiple parameters and obtain the data in multiple file formats. This short talk is designed to be delivered at the NASA booth area at the 2018 Fall American Geophysical Union conference.

Paul W Stackhouse, Jr.↗

TPSAS-NF1676L-19238-DND

The 24-hour cycle of solar insolation drives diurnal cycles in Earth system processes critical to climate: radiation, convection, turbulence, and cloud processes. Cloud properties, temperature, radiative fluxes, and precipitation exhibit robust diurnal cycles as a result. The presence of these robust diurnal cycles fundamentally changes the time mean and variability of the TOA energy budget. Therefore, there is a need to understand the diurnal cycle contributions to the TOA energy budget in both observations and climate models. The first objective of this study is to quantify the diurnal cycle impact on the time mean and variability of the TOA energy budget in observations defined as the difference between TOA fluxes computed with diurnally uniform and diurnally varying cloud properties. The required observational input is observed from the combined Terra+Aqua Cloud and Earth's Radiant Energy System (CERES) data products ranging from June 2002 through October 2012. The second objective of this study is to evaluate the impact of known errors in the model diurnal cycle simulation on the time mean and variability of the TOA energy budget. The results indicate that (1) the diurnal cycle impacts on the regional time mean Tropical longwave and shortwave fluxes range from 1-3 W m 2 and 5 25 W m 2, respectively; (2) the diurnal cycle contributions to TOA flux variability exceeds 50% in land convective regions (e.g., central South America and central Africa);(3) the diurnal cycle contributions to the TOA shortwave and longwave flux time mean and variability in the CanAM4 GCM are too small in land convective regions due to errors in the diurnal distribution of convective clouds grid box errors exceed 100%.

Patrick C Taylor↗

CERES Energy Balanced and Filled (EBAF) from Afternoon-Only Satellite Orbits

The Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) data product uses a diurnal correction methodology to produce a shortwave (SW) top-of-atmosphere (TOA) radiative flux time series that accounts for diurnal cycle changes between CERES observation times while ensuring that the stability of the EBAF record is tied as closely as possible to CERES instrument calibration stability. The current EBAF Ed4.1 data product combines observations from Terra and Aqua after July 2002. However, the Terra satellite will start to drift in Mean Local Time (MLT) in early 2021, and Aqua’s MLT will start to drift in 2022. To ensure the EBAF record remains temporally stable, we explore the feasibility of using only CERES instruments from afternoon satellite orbits with a tight 1330 MLT after July 2002. We test this approach by directly comparing SW TOA fluxes generated after applying diurnal corrections to Aqua-only and to Terra + Aqua for 07/2002–06/2019. We find that global climatological mean SW TOA fluxes for these two cases are within 0.01 W/sq.m and the trend of the difference is < is 0.03 W/sq.m per decade.

Norman G Loeb↗

Toward More Realistic Simulation and Prediction of Dust Storms on Mars

Major (regional and global)dust storms dominate weather and climate variability on present-day Mars. Absorption and scattering of visible and IR radiation by dust strongly affect the thermal state of the thin Mars atmosphere, while dust provides condensation nuclei for water and CO2 cloud particles, which also affect radiative fluxes. Global dust storms (GDS) occur ~three times per Mars decade and to date have been observed in only northern fall and winter,when the global circulation is strongest. Tenfold increases in column dust opacity are typical during GDS, with intense vertical motions transporting dust to far higher altitudes than usual. The key processes and feedbacks that produce GDS remain poorly understood, hence current atmospheric models fail to self-consistently simulate observed dust storm activity. This means we have no predictive capability for when GDS may occur, either now or in Mars’s past. And crucially, due to the huge impact of GDS on the atmosphere and surface, our lack of ability to simulate realistic dust storms has major implications for Mars science and exploration: from understanding the present climate (§2.1),to modeling past climates and water cycles (§2.2), to exploring how wind, water, and dust cycles varied over time to interpret geology and assess potential habitability(§2.3), to quantifying and mitigating risks posed to Mars missions (§2.4)

Claire E Newman↗

Relating Changing Aerosols to Changing Clouds: Two Decades of Terra and Aqua Observations

The global aerosol system of today is not the same as it was two decades ago when Terra and Aqua were launched. As a result of a changing climate (natural and anthropogenic) convolved with changes in human activity (deliberate and accidental), some regions have experienced significant changes to their total aerosol burden (increases or decreases of total loading) or their aerosol composition (as defined by relative size or source type). Other regions have had less or no significant changes. At the same time, changes in aerosol amount and composition affect clouds through direct and indirect microphysical and radiative processes. We can theoretically predict what might happen to clouds when you add aerosol to an otherwise pristine environment. Conversely, there is the situation of removing aerosol from a polluted environment. Over the past two decades, sensors on both Earth Observing Satellites (Terra and Aqua) have observed the radiative signatures of aerosols and clouds, as well as their changes. Via massive efforts by their respective characterization teams, the resulting data records appear to have a minimum of artificial drifts. Therefore, we are trying to assess, region by region, our 20-year records of aerosols and clouds, along with meteorological variables. Where have been the most significant changes of aerosols and/or clouds? Where do the changes in clouds conform with expectations based on changes of aerosols and meteorology and where do they not? In addition to separate ‘aerosol’ and ‘cloud’ retrievals from the Moderate Resolution Imaging Spectrometer (MODIS), there is a ‘twilight zone’ that is not accounted for in either product. What are these regions, and have they changed over the past two decades? We will present our early efforts at characterizing the MODIS view of aerosol and cloud changes, while also relating to changes in radiative fluxes at the top-of-atmosphere (TOA) from corresponding observations by the Clouds and the Earth's Radiant Energy System (CERES).

aerosols↗

Global Reference Atmospheric Model (GRAM) Suite Overview and Current Status

• Engineering-oriented atmospheric models that estimate mean values and statistical variations of atmospheric properties for numerous planetary destinations • Currently available for Earth, Mars, Venus, Titan, Neptune, Uranus, and Jupiter • Outputs include atmospheric density, temperature, pressure, chemical composition, radiative fluxes (for Mars-GRAM), and wind components along a user-defined path – Includes seasonal, diurnal, geographic, and altitude variations • Widely used by the engineering community because of their ability to create realistic atmospheric dispersions • Can be integrated into high fidelity flight dynamic simulations of launch, entry, descent and landing (EDL), aerobraking and aerocapture • Optional trajectory input file consisting of time, height, latitude, and longitude can be used to provide the GRAM trajectory path • Optional auxiliary profile consisting of height, latitude, longitude, temperature, pressure, density, eastward wind, and northward wind may be used to replace model data in the GRAMs • Not a forecast model

atmospheric models↗

Advancing NASA SatCORPS Global Data Products with Cloud Computing and Machine Learning

Operational satellite imager radiances are valuable for deriving many different physical parameters that can be used for a variety of weather, aviation, and energy applications. The NASA Satellite ClOud and Radiation Property retrieval System (SatCORPS) applies a suite of algorithms to meteorological satellite data to provide cloud properties, radiative fluxes and other parameters on a global scale. The use of cloud computing has enabled recent enhancements to process a constellation of geostationary satellites at higher spatiotemporal resolutions than previously possible that meet low latency and near real-time needs. Data taken from Meteosat-8 and -11, Himawari, GOES-16, and -17 are processed and combined with operational polar orbiting satellite data and composited on a 3-km grid to provide global coverage. To improve the utility of the data products, machine learning and other innovative methods are applied in various ways to help minimize data product uncertainties under the most challenging conditions and to improve their consistency at all times of day. An update on recent SatCORPS enhancements is presented, highlighting the community benefits achieved with the use of cloud computing and machine learning.

William L Smith↗

The TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI). I. Dry Cases—The Fellowship of the GCMs

With the commissioning of powerful, new-generation telescopes such as the James Webb Space Telescope (JWST) and the ground-based Extremely Large Telescopes, the first characterization of a high molecular weight atmosphere around a temperate rocky exoplanet is imminent. Atmospheric simulations and synthetic observables of target exoplanets are essential to prepare and interpret these observations. Here we report the results of the first part of the TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) project, which compares 3D numerical simulations performed with four state-of-the-art global climate models (ExoCAM, LMD-Generic, ROCKE-3D, Unified Model) for the potentially habitable target TRAPPIST-1e. In this first part, we present the results of dry atmospheric simulations. These simulations serve as a benchmark to test how radiative transfer, subgrid-scale mixing (dry turbulence and convection), and large-scale dynamics impact the climate of TRAPPIST-1e and consequently the transit spectroscopy signature as seen by JWST. To first order, the four models give results in good agreement. The intermodel spread in the global mean surface temperature amounts to 7 K (6 K) for the N2-dominated (CO2-dominated) atmosphere. The radiative fluxes are also remarkably similar (intermodel variations less than 5%), from the surface (1 bar) up to atmospheric pressures ∼5 mbar. Moderate differences between the models appear in the atmospheric circulation pattern (winds) and the (stratospheric) thermal structure. These differences arise between the models from (1) large-scale dynamics, because TRAPPIST-1e lies at the tipping point between two different circulation regimes (fast and Rhines rotators) in which the models can be alternatively trapped, and (2) parameterizations used in the upper atmosphere such as numerical damping.

Martin Turbet↗

Additional characterization of Libya-4 in support of post-launch vicarious calibration of satellite imagers

Libya-4 (28.55° N and 23.39° E) is one of the most characterized and utilized Pseudo Invariant Calibration Site (PICS) for post-launch radiometer drift monitoring and sensor pair radiometric scaling. Libya-4 is one of the driest and most reflective PICS located in an extensive sand dune region void of any vegetation with an elevation of 118 m. It is positioned near the northeast border with Egypt. With minimal cloud cover and the monthly mean precipitation of ~ 1mm, Libya-4 is one of the temporally, spectrally, and spatially stable CEOS recommended PICS and Cosnefroy et al. 1996 identified sites. The Libya-4 PICS has been extensively used for post-launch radiometric calibration and validation of high-, medium, and low-resolution satellite imagers, including Landsat, MODIS, VIIRS, and Meteosats. The CERES Imager and Geostationary Calibration Group (IGCG) at NASA LaRC utilizes Libya-4 to perform an independent assessment of the radiometric stability of the MODIS and VIIRS L1B products. The site is also used for absolute radiometric scaling between MODIS, VIIRS, and geostationary imagers to ensure consistent cloud and radiative flux retrievals. Multi-year Terra-MODIS, Aqua-MODIS , NPP-VIIRS and Metoesat-7 observations over Libya-4 show very similar TOA reflectance temporal variability. Although, the surface reflectance and atmospheric column varies seasonally, the inter-annual variability of the seasonal cycle should be small. Especially during 2013, the Libya-4 TOA reflectance was found to be greater than usual in all 4 satellite records. Preliminary comparisons with mean wind speed and aerosol optical depth (AOD) indicate that the year 2013 is marked by elevated levels of both conditions. The goal of this study is to tie the Libya-4 visible reflectance inter-annual variability with corresponding meteorological measurements to further improve the characterization of the site.

David R. Doelling↗

Illuminating Albedo: Using MOSAiC Data to Assess the CERES Cloud Radiative Swath (CRS) Albedo Quantification Process

Increasing surface and lower tropospheric air temperatures as a result of rising greenhouse gases are expected to be most pronounced over the Arctic. Such rapid changes alter the surface climate of the region, and impacts can be observed atmospherically, oceanographically, and biogeophysically. Accurately quantifying the impact of decreasing surface albedo on the surface energy budget with satellite observations alone is complicated by a lack of shortwave radiation during winter and seasonal/spatial heterogeneity of surface type and associated spectral albedo. NASA’s Clouds and the Earth’s Radiant Energy System (CERES) project features the Cloud Radiative Swath (CRS) product, which builds upon the Single Scanner Footprint (SSF) product by using the NASA Langley Fu-Liou radiative transfer model to calculate a robust and high-quality array of surface and atmospheric radiative fluxes on an instantaneous, footprint-level scale. This study aims to use MOSAiC and CRS data to illuminate potential uncertainties in the CERES albedo production process, with goals of determining 1) spectral albedo under clear sky conditions when stratified by ice concentration, 2) the uncertainty associated with CERES surface albedo “history maps” when compared against observations captured during MOSAiC, and 3) the magnitude of variation between meteorological inputs compared to those from MOSAiC.

Emily Monroe↗

Novel Hourly-Resolved Global Cloud Property Composite from Operational Satellites Imagers

Numerous applications in satellite remote sensing of surface properties, atmospheric state, composition, and radiation require accurate knowledge of the location and characteristics of clouds. Operational satellite imager radiances are valuable for cloud detection and for deriving many different physical parameters that can be used for a variety of weather, aviation, and energy applications. The NASA Satellite ClOud and Radiation Property retrieval System (SatCORPS) applies a suite of algorithms to meteorological satellite data to provide cloud properties, radiative fluxes and other parameters on a global scale. This paper describes a new global high-resolution dataset of cloud properties made available for community use that is constructed from analyses of a constellation of meteorological satellite imagers. Data taken from Meteosat-8/9 and -11, Himawari-8/9, GOES-16, and -17/-18, Aqua, Terra, Suomi-NPP and NOAA-20 are processed and composited on a 3-km grid to provide hourly global coverage. A historical multi-year dataset is available to serve various needs including modeling challenges related to cloud evaluations and parameterizations. Near real-time data products are also currently available between 60N and 60S. Efforts are underway to operationalize polar orbiting satellite cloud detection methods for low-latency applications over polar regions. The cloud detection and retrieval algorithms have been developed over many years to support NASA weather and climate programs such as the Clouds and Earth’s Radiant Energy System (CERES). To improve the utility of the data products, machine learning and other innovative methods are applied in various ways to help minimize data product uncertainties under the most challenging conditions and to improve their consistency at all times of day. A brief description of the methods highlighting the unique aspects of the SatCORPS data products will be presented along with information on their status and availability.

SatCORPS↗

An LES Survey of Cold-Air Outbreaks Spanning ACTIVATE and COMBLE

Two recent field campaigns offer unique new opportunities to survey coupled aerosol and cloud processes operating within cold-air outbreaks (CAOs). NASA's 2019-2023 Aerosol Cloud meTeorology Interactions oVer the western Atlantic Experiment (ACTIVATE) project provided airborne in situ and remote sensing observations in multiple CAOs off the central US Eastern Seaboard. Contemporaneously, DOE's 2019-2020 Cold-air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) provided continuous ground-based in situ and remote sensing measurements during hundreds of hours of CAO conditions at two sites flanking the Norwegian Sea. Here we highlight lessons learned from contrasting sets of aerosol-aware Lagrangian large-eddy simulation case studies derived from each campaign, as well as outstanding uncertainties. Cases simulated include all of the most extensively sampled CAO flights during ACTIVATE, and a wide range of CAO strengths and mesoscale structures during COMBLE. Each case study is also suitable for simulation with large-scale models in single-column model mode or with a limited-domain approach using periodic boundary conditions. We seek to address the central question: what microphysical process pathways control the Lagrangian evolution of surface and top-of-atmosphere radiative fluxes under ACTIVATE and COMBLE conditions? Many science team members, co-investigators, and collaborators will be gratefully acknowledged in association with their contributions to making this work possible.

cold-air outbreaks↗

Role of Small-Scale Impulsive Events in Heating the X-Ray Bright Points of the Quiet Sun

Small-scale impulsive events, known as nanoflares, are thought to be one of the prime candidates that can keep the solar corona hot at its multimillion-Kelvin temperature. Individual nanoflares are difficult to detect with the current generation of instruments; however, their presence can be inferred through indirect techniques such as Differential Emission Measure (DEM) analysis. Here, we employ this technique to investigate the possibility of nanoflare heating of the quiet corona during the minimum of solar cycle 24. We estimate the DEM of disk-integrated quiet Sun and X-ray bright points (XBP) using the observations from XSM on board the Chandrayaan-2 orbiter and AIA on board the Solar Dynamic Observatory. XBPs are found to be the dominant contributor to disk-integrated X-rays, with a radiative flux of ∼2 × 10 5 erg cm −2 s −1 . XBPs consist of small-scale loops associated with bipolar magnetic fields. We simulate such XBP loops using the EBTEL hydrodynamic code. The lengths and magnetic field strengths of these loops are obtained through a potential field extrapolation of the photospheric magnetogram. Each loop is assumed to be heated by random nanoflares having an energy that depends on the loop properties. The composite nanoflare energy distribution for all the loops has a power-law slope close to −2.5. The simulation output is then used to obtain the integrated DEM. It agrees remarkably well with the observed DEM at temperatures above 1 MK, suggesting that the nanoflare distribution, as predicted by our model, can explain the XBP heating.

Solar coronal heating↗

Impacts of Aerosol and Cloud Variability on Satellite-Derived All-skies Direct Aerosol Radiative Effects (DARE) over the North and Southeast Atlantic

The Top-of-Atmosphere (TOA) Shortwave (SW) Direct Aerosol Radiative Effect (DARE) in all-sky conditions (i.e., aerosols in clear skies and aerosols above and below all types of clouds) is the global change in upwelling radiative flux due to aerosols. It is one of the strongest indicators of global climate change due to aerosols. SW DARE at TOA depends on the Earth’s surface albedo, cloud fraction, cloud optical properties, and aerosol optical properties, which are all challenging to accurately characterize from space. The overarching goals of our project are to provide state-of-the-art observational all-sky TOA SW DARE, along with guidance on which aerosol and/or cloud properties are the most important to measure, and at which spatio-temporal scales, for accurate DARE observations. We compute all-sky DARE based on state-of-the-art cloud and aerosol retrieval algorithms from CALIOP (Cloud–Aerosol Lidar with Orthogonal Polarization) and MODIS (Moderate Resolution Imaging spectroradiometer) satellite sensors, as well as aerosol intensive properties from MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications, version 2) simulations over three specific regions of the Atlantic Ocean from 2012 to 2016. In this symposium, we present a characterization of the cloud and aerosol optical and physical properties and the observational TOA SW DARE along three individual satellite tracks in the Southeast Atlantic region -- on September 18 and 20, 2016 and August 13, 2017. We then quantify the impact of assuming homogeneous cloud or aerosol fields in space-based TOA SW DARE calculations. And, finally, the resulting space-based all-skies aerosol vertical distribution and DARE calculations are evaluated using remote sensing observations from coincident suborbital flights from the NASA ORACLES (the ObseRvations of Aerosols above CLouds and their intEractionS, ORACLES field campaign) field campaign. The NASA Atmospheric Observing System (AOS) mission addresses the NASA Aerosol, Cloud, Convection and Precipitation (ACCP) designated observables and proposes, as one of its aerosol objectives, to reduce uncertainties in estimates of global mean all-sky SW DARE at TOA. Well characterizing clouds, aerosol vertical distributions, aerosol types and associated all-skies DARE over the Atlantic Ocean will inform the AOS community on where, when, how, and how often the satellite retrievals should be performed to estimate DARE and reduce all-skies DARE uncertainties most accurately. These comprehensive characterizations will also identify the key regions and times when the AOS (or other ACCP-related) suborbital missions should be conducted to evaluate and improve the AOS space-based observations and retrievals.

aerosol↗

Evaluation of Radiometric Performance of CERES Instruments Aboard Terra

The Terra satellite platform carries the first two flight models of the Clouds and the Earth’s Radiant Energy System, which make radiometric measurements of the Earth to examine the roles of cloud feedback and radiation balance in the Earth System. The Terra-borne instruments use three channels: the shortwave (0.2 - 5 µm), total (0.2 – 100 µm) and window (8 – 12 µm), which are calibrated using an onboard internal calibration module to track the long-term stability of each channel. Observed measurements are converted to top-of-atmosphere radiances by accounting for the instrument optics and detector sensitivity coefficients determined from prelaunch calibrations. Trends in the instrument’s radiometric performance determined through on-orbit calibrations and vicarious studies were applied, and these corrections have shown to produce a stable data record of radiative fluxes over the lifetime of the mission. Changes in instrument observations and new methods to account for them as a result of the discontinuation of station keeping for Terra will be discussed.

Alexander Jarnot↗

Improved Finite-Volume Method for Radiative Hydrodynamics

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy for such simulations on structured and unstructured grids compared to more conventional approaches. Results will be shown for shock radiation during hypersonic reentry. Issues of parallelization within a radiation sweep will also be discussed.

Wray, Alan↗

Comparison of the Radiative Two-Flux and Diffusion Approximations

Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and radiation scattered back by internal scattering sites while the Fresnel reflection only accounts for surface reflections.

Spuckler, Charles M.↗