Search NASA⌕ Search

SEARCH · Search NASA

Results for “Physics - Physics of elementary particles and fields”

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.

3,397 records · Page 48
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

The Roman Space Telescope Optical System: Status, Test, and Verification Update

The Nancy Grace Roman Space Telescope (“Roman”) is NASA’s next flagship observatory. Launching in 2026, Roman will explore the nature of dark energy as well as expand the census of exoplanets in our galaxy via microlensing. Roman’s large field of view, agile survey capabilities, and excellent stability enable these scientific objectives, yet present unique challenges for the design, test, and verification of its optical system. Roman recently completed a comprehensive thermal vacuum test of the Spacecraft bus + Integrated Payload Assembly (SCIPA), followed by integrating the Outer Barrel Assembly (OBA), Solar Array Sunshield (SASS), and Deployable Aperture Cover (DAC) with SCIPA to complete the Observatory. This paper will present an overview of the thermal vacuum optical testing as well as a status of the optical system performance and verification.

Matthew Bolcar↗
DOE OSTI2025

Chiral edge state control of thermoelectric effects

Thermoelectric responses in two-dimensional electron gases subjected to magnetic fields have the potential to provide unique information about quasiparticle statistics. In this study, we show that chiral edge states play a key role in thermoelectric Hall bar measurements by completely controlling the direction of the internal thermal gradient. To this end, we perform measurements of the magnetothermoelectric responses of cadmium arsenide quantum wells. The magnetothermoelectric responses in the quantum Hall regime agree with theoretical predictions if one considers the role of chiral edge states, which flow in opposite directions on either side of the Hall bar and establish an internal temperature gradient that is perpendicular to the externally applied thermal gradient. We show that the results are self-consistent within this picture under different measurement conditions. We discuss potential applications of the findings, such as in nanoscale control of local temperature gradients and thermoelectric effects along with the characterization of other topological systems with chiral edges states.

Science & Technology - Other Topics↗
DOE OSTI2025

Unique Conductivity Behavior in Water-In-Salt Electrolytes Driven by Ion Clusters

Understanding and predicting ion transport in aqueous electrolytes are crucial for advanced energy storage and biophysics, and many emergent technologies yet remain elusive. Herein, we introduce a unified framework to quantitatively describe and predict electrolyte conductivity that shifts from conventional molar concentration-based metrics to a volume fraction-based approach. Through analyzing a variety of electrolyte solutions via this perspective, we observe a universal conductivity peak at a 37% volume fraction. Small-angle X-ray scattering (SAXS) and molecular dynamics (MD) simulations reveal that nanometer-scale ion clusters drive this general behavior. Moreover, key geometric features of the ion transport pathwayssuch as pore size, tortuosity, and connectivityfollow a consistent dependence with respect to the volume fraction, reinforcing the argument for the universal conductivity trend. This paradigm shift opens new avenues for designing high-performance electrolytes and provides transformative insights for advancing studies in many fields, wherein molecular aggregates dictate transport properties.

Nguyen, Huong T. D.↗
NASA NTRSDate not supplied

Preservation of Previously Unsampled Primordial Isotopic Components in Ryugu and Bennu Samples

Ivuna-type (CI) carbonaceous chondrites are primitive meteorites whose relative elemental abundances closely match the solar photosphere 1 , making them critical benchmarks for the bulk chemical and isotopic composition of the planet-forming disk. Recent sample-return missions to Ryugu 2 and Bennu 3 have enabled direct laboratory analysis of these rubble-pile CI-like asteroids 4 , formed from the reaccumulated fragments of once-larger parent bodies. As such, they may retain a broader spectrum of primordial nucleosynthetic components than is preserved in known meteorites. Here, we report the nucleosynthetic compositions of silicon (μ 30 Si), magnesium (μ 26 Mg*), and iron (μ 54 Fe), three of the four most abundant planet-building elements, in samples from Ryugu and Bennu, along with the newly discovered Oued Chebeika 002 CI chondrite 5 . In contrast to the isotopic homogeneity of CI chondrites, Ryugu and Bennu preserve resolvable μ 26 Mg* and μ 30 Si heterogeneity, revealing μ 26 Mg*- and μ 30 Si-rich nucleosynthetic components not sampled in meteorites. These components may reflect the preservation of previously unsampled primordial isotopic signals, prior to thermal processing 6,7 and late infall of primordial molecular cloud material to the outer disk 8,9 . Additionally, Ryugu particle C0002 exhibits a μ 26 Mg*-poor and μ 54 Cr-rich signature, consistent with incorporation of presolar material from massive supernovae 10,11 . Ryugu and Bennu samples define one end of a μ 54 Fe–μ 30 Si array among carbonaceous asteroid materials 9 , suggesting that the isotopic compositions of these asteroidal materials reflect mixing between early disk isotopic components identified in this study and material derived from the outermost disk 9 . This observation demonstrates that materials with solar chemical abundances can nonetheless exhibit markedly distinct nucleosynthetic signatures. Thus, Ryugu and Bennu samples are critical records of nucleosynthetic diversity among carbonaceous asteroids and underscore the value of sample-return missions in accessing primitive isotopic signatures absent from meteorite collections.

Martin Bizzarro↗
NASA NTRS2002

The Design and Use of Calorimeters For Characterization of High-Enthalpy Flows in Arc-Heated Test Facilities

High-enthalpy, arc-heated flows used for aerothermal testing present a challenging environment for flow characterization. This paper describes the design and use of cooled dwell probes used for heat-transfer and pressure characterization of the NASA and United States Department of Defense (DoD) arc facilities located at Moffett Field, CA, and Arnold Air Force Base, TN. Dwell calorimeters designed, fabricated, and tested by Thermal Technologies, Inc. (TTI) in the NASA IHF and the USAF H1 and H2 arc test facilities provide heat flux and pressure data with excellent repeatability. These calorimeters use standard Gardon calorimeter gages and pressure ports with unique cooling systems enabling them to withstand the severe arc-heated environments for durations sufficient for acquisition of steady-state data. The TTI probes have proven very robust in the extreme aerothermal environments of these facilities. This paper provides an overview of calorimeter instruments typically used in arc facilities, discusses design features of the TTI dwell probes, presents selected data acquired by the TTI calorimeters, and provides comparisons with data acquired from using measurement techniques.

D Mark Smith↗
DOE OSTI2026

Uncovering Hidden Entanglement in Twin Beams

Proper characterization of quantum correlations in multimode optical quantum states is critical for applications in quantum information science. However, standard entanglement measurements can lead to incomplete state reconstruction and characterization. Here, we implement a resonator-based detection system that reveals entanglement between sideband modes of twin beams, achieving full tomography and retrieving often ignored quantum correlations. Unlike standard spectral measurements such as homodyne detection, resonator detection can independently address the sidebands of each beam, thereby accessing these hidden correlations. Additionally, we show how phase shifts between the carrier and the sideband modes of the involved fields redistribute information and modify the observation of entanglement for different witnesses. The ability of the resonant detection to independently address sideband modes of entangled states can contribute to enhancing the capacity for secure communication and quantum networking protocols.

Rincon Celis, Raul [University of Sao Paulo, Brazi↗
NASA NTRSDate not supplied

Experimental and Numerical Investigation of the NASA High Efficiency Centrifugal Compressor Vaned Stage Geometry and Aerodynamic Performance

Since its inception in the early 2010s, the NASA High Efficiency Centrifugal Compressor (HECC) has been enigmatic for the propulsion research community: experimental data and numerical simulations of the stage have generally not aligned in their quantifications of performance metrics. Typically, the fault for these disagreements is assigned to the numerical simulations as the simulations are models, and models are inherently incomplete representations of the experiment. This “incompleteness” may manifest in assumptions regarding roughness or heat transfer, simplifications of the flow path (i.e., neglecting bleed flows), or the oft-scapegoated turbulence model. In the case of HECC, recent work showed unexpected discrepancies between the intended impeller geometry defined in the design report (termed Design-Intent) and the manufactured impeller used in the experimental campaigns (termed As-Manufactured). That work used numerical simulations to establish that the geometric differences between the Design-Intent and As-Manufactured impellers were significant enough to result in drastically different performance predictions for the HECC vaneless diffuser configuration. The Design-Intent impeller simulations over predicted the performance relative to the experiment, whereas the As-Manufactured simulations better represented the experimental data, both in terms of one-dimensional performance metrics and spanwise flow profiles. This effort expands on that work by examining in detail the geometry and aerodynamic performance of the HECC vaned diffuser configuration. Further differences between the Design-Intent and As-Manufactured geometries have been discovered in the vaned diffuser and exit guide vanes, and these differences are documented herein. The summations of the geometric differences for all of the components were used to create two numerical models of HECC vaned diffuser configuration: the Design-Intent simulations which are generated from the original geometry definitions given in the design report and the As-Manufactured simulations which are the best available representation of the manufactured compressor hardware used in the experimental test campaigns. In congruence with the earlier vaneless diffuser work, the numerical predictions of the Design-Intent choked mass flow rate, total pressure ratio, and efficiency were notably greater than that of the As-Manufactured simulations. To increase confidence in the experimental dataset, measurements from a recent test campaign conducted in 2024 are used to validate the original experimental data acquired from 2012 to 2014 with good repeatability overall, especially considering the passage of time and differences in the data acquisition systems between the test campaigns. Both numerical simulations were then extensively evaluated against the experimental data. The As-Manufactured simulations provided better estimates of the stage performance than the Design-Intent cases in terms of most performance metrics. Nonetheless, more detailed results still show opportunities for improvement. Despite a more accurate representation of the physical hardware, characterization of the impeller work input remains a challenge even for rigorously developed numerical models.

vaned diffuser↗
NASA NTRSDate not supplied

Experimental and Numerical Investigation of the NASA High Efficiency Centrifugal Compressor Vaned Stage Geometry and Aerodynamic Performance

Since its inception in the early 2010s, the NASA High Efficiency Centrifugal Compressor (HECC) has been enigmatic for the propulsion research community: experimental data and numerical simulations of the stage have generally not aligned in their quantifications of performance metrics. Typically, the fault for these disagreements is assigned to the numerical simulations as the simulations are models, and models are inherently incomplete representations of the experiment. This “incompleteness” may manifest in assumptions regarding roughness or heat transfer, simplifications of the flow path (i.e., neglecting bleed flows), or the oft-scapegoated turbulence model. In the case of HECC, recent work showed unexpected discrepancies between the intended impeller geometry defined in the design report (termed Design-Intent) and the manufactured impeller used in the experimental campaigns (termed As-Manufactured). That work used numerical simulations to establish that the geometric differences between the Design-Intent and As-Manufactured impellers were significant enough to result in drastically different performance predictions for the HECC vaneless diffuser configuration. The Design-Intent impeller simulations over predicted the performance relative to the experiment, whereas the As-Manufactured simulations better represented the experimental data, both in terms of one-dimensional performance metrics and spanwise flow profiles. This effort expands on that work by examining in detail the geometry and aerodynamic performance of the HECC vaned diffuser configuration. Further differences between the Design-Intent and As-Manufactured geometries have been discovered in the vaned diffuser and exit guide vanes, and these differences are documented herein. The summations of the geometric differences for all of the components were used to create two numerical models of HECC vaned diffuser configuration: the Design-Intent simulations which are generated from the original geometry definitions given in the design report and the As-Manufactured simulations which are the best available representation of the manufactured compressor hardware used in the experimental test campaigns. In congruence with the earlier vaneless diffuser work, the numerical predictions of the Design-Intent choked mass flow rate, total pressure ratio, and efficiency were notably greater than that of the As-Manufactured simulations. To increase confidence in the experimental dataset, measurements from a recent test campaign conducted in 2024 are used to validate the original experimental data acquired from 2012 to 2014 with good repeatability overall, especially considering the passage of time and differences in the data acquisition systems between the test campaigns. Both numerical simulations were then extensively evaluated against the experimental data. The As-Manufactured simulations provided better estimates of the stage performance than the Design-Intent cases in terms of most performance metrics. Nonetheless, more detailed results still show opportunities for improvement. Despite a more accurate representation of the physical hardware, characterization of the impeller work input remains a challenge even for rigorously developed numerical models.

centrifugal compressor↗
DOE OSTI2025

Enhancing cathode composites with conductive alignment synergy for solid-state batteries

Enhancing transport and chemomechanical properties in cathode composites is crucial for the performance of solid-state batteries. Our study introduces the filler-aligned structured thick (FAST) electrode, which notably improves mechanical strength and ionic/electronic conductivity in solid composite cathodes. The FAST electrode incorporates vertically aligned nanoconducting carbon nanotubes within an ion-conducting polymer electrolyte, creating a low-tortuosity electron/ion transport path while strengthening the electrode’s structure. This design not only mitigates recrystallization of the polymer electrolyte but also establishes a densified local electric field distribution and accelerates the migration of lithium ions. The FAST electrode showcases outstanding electrochemical performance with lithium iron phosphate as the active material, achieving a high capacity of 148.2 milliampere hours per gram at 0.2 C over 100 cycles with substantial material loading (49.3 milligrams per square centimeter). This innovative electrode design marks a remarkable stride in addressing the challenges of solid-state lithium metal batteries.

Science & Technology - Other Topics↗
DOE OSTI2024

Remote-Contact Catalysis for Target-Diameter Semiconducting Carbon Nanotube Arrays

Electrostatic catalysis has been an exciting development in chemical synthesis (beyond enzymes catalysis1 ) in recent years, boosting reaction rates and selectively producing certain reaction products2 . Most of the studies to date have been focused on using external electric field (EEF) to rearrange the charge distribution in small molecule reactions such as Diels-Alder addition3 , carbene reaction4 , etc. However, in order for these EEFs to be effective, a field on the order of 1 V/nm (10 MV/cm) is required, and the direction of the EEF has to be aligned with the reaction axis5 . Such a large and oriented EEF will be challenging for large-scale implementation, or materials growth with multiple reaction axis or steps. Here, we demonstrate that the energy band at the tip of an individual single-walled carbon nanotube6 (SWCNT) can be spontaneously shifted in a high-permittivity growth environment, with its other end in contact with a low-work function electrode (e.g., hafnium carbide or titanium carbide7 ). By adjusting the Fermi level at a point where there is a substantial disparity in the density of states (DOS) between semiconducting (s-) and metallic (m-) SWCNTs8 , we achieve effective electrostatic catalysis for s-SWCNT growth assisted by a weak EEF perturbation (200V/cm). This approach enables the production of high-purity (99.92%) s-SWCNT horizontal arrays with narrow diameter distribution (0.95±0.04 nm), targeting the requirement of advanced SWCNT-based electronics for future computing9-11. These findings highlight the potential of electrostatic catalysis in precise materials growth, especially for s-SWCNTs, and pave the way for the development of advanced SWCNT-based electronics12.

Wang, Jiangtao [Department of Electrical Engineeri↗
NASA NTRSDate not supplied

Final Thermal Design and Thermal Vacuum Testing of the StarBurst Instrument

The StarBurst Multimessenger Pioneer is a small satellite mission serving as a wide-field gamma-ray observatory designed to capture the initial emissions of short gamma-ray bursts, electromagnetic signatures of neutron star mergers. This paper presents the final thermal design and analysis of the StarBurst Instrument, comprising the bus-to-instrument interface plate, control electronics, and twelve crystal detector units, which form the core of the mission’s science capability. The passive thermal control system design requires consideration of restrictive keep-out zones, unknown orbital parameters, and narrow temperature limits of the detectors. Also summarized is the instrument level thermal vacuum cycle test, correlated model refinements, and updated model results. Following successful completion of the instrument test campaign, the hardware was integrated with the spacecraft bus for spacecraft level testing, including additional thermal vacuum testing. The results from the spacecraft level thermal vacuum test will further inform the instrument thermal model, ensuring accurate flight temperature predictions. StarBurst launches as a secondary payload in 2027 and has a mission duration of at least one year.

StarBurst↗
NASA NTRS2026

Adaptive Curation at NASA Johnson Space Center: Preparing for Artemis Samples by Leveraging Proven Practices and Innovative Solution

The proper curation of returned astromaterial samples is essential to ensure that high-quality scientific investigations can be conducted for decades, enabling future generations to address evolving research questions. The Astromaterials Acquisition and Curation Office at NASA Johnson Space Center (hereafter JSC Curation) is responsible for curating all of NASA’s extraterrestrial samples. Under the governing document, NASA Procedural Requirement (NPR) 7100.5 “Curation of Extraterrestrial Materials”, JSC Curation is charged with “The curation of all extraterrestrial material under NASA control, including future NASA missions.” The Directive goes on to define Curation as including “...documentation, preservation, preparation, and distribution of samples for research, education, and public outreach.” JSC Curation has a long-standing legacy of curating extraterrestrial materials, including but not limited to Apollo and Luna lunar samples, Genesis solar wind samples, Stardust comet samples, asteroid samples (Hayabusa1, Hayabusa2, and OSIRIS-REx), and Antarctic Meteorite samples from a variety of parent bodies. Building on this foundation, the Artemis program introduces new challenges and opportunities for sample curation, requiring both the application of proven practices and the development of innovative solutions. The Artemis Collection will be curated using established protocols refined through decades of experience with Apollo and subsequent sample collections, including but not limited to the utilization of cleanrooms, custom nitrogen gloveboxes, specialized storage containers and tools; all of which have strict material utilization and prohibition requirements. These practices provide a robust framework for contamination control, documentation, and long-term preservation. However, Artemis samples may present unique scientific and operational requirements, including enhanced contamination control measures (relative to Apollo) driven by evolving science objectives. To meet these needs, JSC Curation is actively developing new technologies and protocols that extend beyond traditional approaches, ensuring that the integrity of samples is maintained under increasingly stringent standards. One critical area of innovation is the development of cold sample curation capabilities. Certain Artemis samples, particularly those from Permanently Shadowed Regions (PSRs) and cold environments, are expected to contain ices and volatile components that require preservation and handling at sub-zero or even cryogenic temperatures. JSC Curation is leveraging best practices from the cold and cryogenic sample industries, as well as other government agencies and academic experts, to design facilities and handling procedures that maintain sample integrity while enabling scientific access. The goal is to develop capabilities to allow researchers to investigate volatiles and other temperature-sensitive materials while minimizing chemical and physical alterations from their returned state. In summary, adaptive curation at JSC combines the reliability of proven methodologies with forward-looking innovations to meet the scientific and operational demands of Artemis. Through enhanced contamination control, advanced cold curation capabilities, and an understanding of known and evolving future science priorities, NASA is preparing to maximize the scientific return from Artemis samples and preserve their value for generations of researchers.

Andrea D Harrington↗
DOE OSTI2026

Are CO2 batteries ready for the grid? A cross-cutting deployment checklist

Metal-CO2 batteries have attracted considerable research interest in the past decade due to the utilization of the greenhouse CO2 gas. The low cost and abundance of CO2 feedstocks, together with high specific capacity metal anodes, make this technology a promising candidate for electricity-demanding data centers and grids. However, nonstandard data reporting, ambiguous hardware designs, and questionable cycling parameters have emerged as the field has grown. A clear checklist and standardized reporting format for research and development are urgently needed. Here, after carefully re-analyzing 15 Na-CO2 and 9 Li-CO2 studies, we propose a general checklist and a flowchart for CO2 batteries and related gas conversion systems. Specific performance values from a deployment-oriented perspective, based on commercial lithium iron phosphate batteries, are integrated into the list. We frame research and development efforts around grid-relevant outputs, including areal rate and capacity, cyclability, gas utilization, and safety. While illustrated for Na- and Li-CO2 cells, this framework is directly transferable to other CO2 batteries and air/oxygen batteries, helping align benchtop demonstrations with systematic metrics that ultimately govern future deployment.

Wu, Wenda [ORNL] (ORCID:000900033307687X)↗
NASA NTRS1990

Interactions Between the Space Station and the Environment: A Preliminary Assessment of EMI

A review of the interactions between proposed Space Station systems/payloads and the environment that contribute to electromagnetic interference was performed. Seven prime sources of interference have been identified. These are: The Space Station power system; active experiments such as beam injection; ASTROMAG; ram and wake density gradients; pick up ions produced by vented or offgassed clouds; waves produced by current loops that include the plasma and structure; arcing from high voltage solar arrays (or possible ESD in polar orbit). This review indicates that: minimizing leakage current from the 20 kHz power system to the structure; keeping the surfaces of the Space Station structure, arrays, and radiators nonconducting; minimizing venting of payloads or systems to non-operational periods; careful placement of payloads sensitive to magnetic field perturbations or wake noise; and designing an operational timeline compatible with experiment requirement are the most effective means of minimizing the effects of this interference. High degrees of uncertainty exist in the estimates of magnitudes of gas emission induced EMI, radiation of 20 kHz and harmonics, ASTROMAG induced interference, and arc threshold/frequency of the solar array. These processes demand further attention so that mitigation efforts are properly calibrated.

G B Murphy↗
NASA NTRS1985

Summary of recent NASA propeller research

Advanced high speed propellers offer large performance improvements for aircraft that cruise in the Mach 0.7 to 0.8 speed regime. At these speeds, studies indicate that there is a 15 to near 40 percent block fuel savings and associated operating cost benefits for advanced turboprops compared to equivalent technology turbofan powered aircraft. Recent wind tunnel results for five eight to ten blade advanced models are compared with analytical predictions. Test results show that blade sweep was important in achieving net efficiencies near 80 percent at Mach 0.8 and reducing nearfield cruise noise about 6 dB. Lifting line and lifting surface aerodynamic analysis codes are under development and some results are compared with propeller force and probe data. Also, analytical predictions are compared with some initial laser velocimeter measurements of the flow field velocities of an eight bladed 45 swept propeller. Experimental aeroelastic results indicate that cascade effects and blade sweep strongly affect propeller aeroelastic characteristics. Comparisons of propeller nearfield noise data with linear acoustic theory indicate that the theory adequately predicts nearfield noise for subsonic tip speeds, but overpredicts the noise for supersonic tip speeds.

Daniel C Mikkelson↗
DOE OSTI2024

Dynamic sparse x-ray nanotomography reveals ionomer hydration mechanism in polymer electrolyte fuel-cell catalyst

Tomographic imaging of time-evolving samples is a challenging yet important task for various research fields. At the nanoscale, current approaches face limitations of measurement speed or resolution due to lengthy acquisitions. We developed a dynamic nanotomography technique based on sparse dynamic imaging and 4D tomography modeling. We demonstrated the technique, using ptychographic x-ray computed tomography as its imaging modality, on resolving the in situ hydration process of polymer electrolyte fuel cell (PEFC) catalyst. The technique provides a 40-time increase in temporal resolution compared to conventional approaches, yielding 28 nm half-period spatial and 12 min temporal resolution. The results allow a quantitative characterization of the water intake process inside PEFC catalysts with nanoscale resolution, which is crucial for understanding their electrochemical mechanisms and optimizing their performance. Our technique enables high-speed operando nanotomography studies and paves the way for wider application of dynamic tomography at the nanoscale.

Science & Technology - Other Topics↗
NASA NTRSDate not supplied

Atmospheric, Non-Combusting Droplet Sizing and Spray Imaging Results From a Non-Proprietary Aero Gas Turbine Engine Pressure Swirl Atomizer using Shadowgraphy and Planar Laser Scatter

Members from industry and federal agencies of the United States have developed a collaborating group focused on improving the understanding of the atomization processes common to gas turbine engines. The group is aimed on providing high quality data using x-ray diagnostics in the internal geometry and the near-field dense spray as well as optical diagnostics in the visible spectrum, downstream of the nozzle. This paper reports results from one of the two non-proprietary injectors designs from the group: the primary-secondary injector. In particular, we characterize the spray from only the primary, pressure-swirl atomizing circuit using water through the nozzle. We observed Sauter mean diameter decreased with increased water pressure drop across the nozzle. SMD was also collected at three axial distances and showed decreased size with distance from the nozzle. Planar laser sheet droplet scattering provided qualitative assessment of the spray. Higher water pressure drops provided better atomization than lower pressure drops. The addition of swirling air flow through the injector alleviates and improves the atomization quality, particularly at the lower water pressure drops.

optical diagnostics↗
NASA NTRS1995

Extensional Flow Convecting a Reactant Undergoing a First Order Homogeneous Reaction and Diffusional Mass Transfer From a Sphere at Low to Intermediate Peclet and Damkohler Numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 ≤ Pe ≤ 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 ≤ Da ≤ 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r,Θ) = Σ c n (r)P n (cosΘ) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions P n (cosΘ), the variable coefficient PDE can be reduced to a system of N+1 second order ODEs for the radial functions C n (r), n=0,1,2, ... ,N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N+ 1) first order differential equations as a two-point boundary value problem on 1 ≤ r ≤ r •• . Convergence of the expansion for a specific value of N can thus be established and provides "spectral" behavior as well as the full concentration field c(r,Θ).

N Y Shah↗