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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

New Developments in Nickel-Hydrogen Dependent Pressure Vessel (DPV) Cell and Battery Design

THe Dependent Pressure Vessel (DPV) Nickel-Hydrogen (NiH2) design is being developed as an advanced battery for military and commercial, aerospace and terrestrial applications. The DPV cell design offers high specific energy and energy density as well as reduced cost, while retaining the established Individual Pressure Vessel (IPV) technology flight heritage and database. This advanced DPV design also offers a more efficient mechanical, electrical and thermal cell and battery configuration and a reduced part count. The DPV battery design promotes compact, minimum volume packaging and weight efficiency, and delivers cost and weight savings with minimal design risk.

Caldwell, Dwight B.↗
NASA NTRS2026

Optimization of X-ray Absorbers for High-Resolution TES Detectors in NewATHENA X-IFU

NewATHENA’s X-ray Integral Field Unit (X-IFU) uses a large-format array of Transition Edge Sensor (TES) microcalorimeters coupled with absorbers made of gold and bismuth providing 4 eV FWHM resolution up to 7 keV in the 0.2- 12 keV band. X-ray absorbers must be thick enough for photon absorption, maintain low heat capacity for energy resolution, and have good thermalization properties. The X-IFU requires total Quantum Efficiency (QE) of 96%, 87%, and 63% at 1, 7, and 9.5 keV, respectively. Optimal thicknesses are 1.05 µm gold and 5.5 µm bismuth to achieve 0.731 pJ/K at 90 mK and 87% QE at 7 keV. While typical TES absorbers are 3-4 µm thick, producing the required 5.5 µm Bi absorbers via standard electroplating creates enlarged grains and surface roughness. The increased roughness and grain size variability produced with our standard recipe have resulted in instances of 1) low energy spectral tails 2) spectral broadening of the energy resolution and 3) thermal shorts between pixels when a large grain bridges the gap between absorbers. In this study, we have introduced a new fabrication process and altered the morphology of the thick Bi through changes in the electroplating process. The process changes are intended to address all three issues as well as reduce particulate contamination observed on the finished detector arrays.

Absorber↗
NASA NTRS2005

Chapter 19B - Antenna Radiation Patterns

Modern civil and military aircraft are equipped with a variety of communication devices, radio navigation equipment, and air traffic control systems. For all of these devices appropriate antennas must be available to transmit and receive the signals. As a result, as many as 30 antennas, and sometimes even more, are mounted around today's aircraft. For this reason, it is necessary to know the capabilities of the receiving/transmitting equipment on board. These capabilities are driven by the antenna characteristics. Therefore, coverage, shading, and beam pointing pattern data are necessary for optimum electronic coverage. The aircraft antenna has to convert the available power density of the electromagnetic field to an electric voltage at its connector. This voltage level must be sufficiently high to operate the connected equipment. The reciprocity principle states that it makes no difference if the antenna is receiving or transmitting. For the certification of the aircraft antennas it must be proven that the antennas are at least generating the minimum receiver input voltage which is required for each radio service. The prime condition is, of course, that the specified field power densities of the different radio navigation and communication services are available. An important property of a radio frequency link is the electro-magnetic field intensity at every point in space for a given output power of the antenna. As the propagation of radio frequency waves in free space is well known, the spatial distribution of the field intensity needs only be measured at one spatial sphere around the antenna. The information is usually given as distributions along the circumference of flat sections through this sphere: each of these is called an ARP. Several ARPs are usually required to describe the complete spatial antenna pattern of an antenna. In addition to mathematical modeling, measurements on sub-scale models, and static measurements on full size models or aircraft on the ground, dynamic measurements on aircraft in flight play the most important role in the aircraft antenna testing and certification. [19B-1] The shape of an ARP, for one given frequency, is determined by the shape of the antenna and the shape and material of the surface it is mounted on. As the directly transmitted waves interfere with waves reflected by the aircraft skin with its complex geometry, and the surface material parameters are only roughly known, it is not possible to predict the ARP with the required accuracy. In ground measurements the earth's surface also acts as a reflector thereby causing the ground ARP to be different from the in-flight ARP. As the in-flight ARP is the ARP we are actually interested in it becomes clear that it is necessary to conduct in-flight ARP measurements. The Flight Test Engineer must be aware of the needs of the specialists who are establishing the test program for measuring antenna patterns and radar cross sections. These tests will require special test equipment and dedicated flights to obtain the data that they require. This Section provides an introduction to the principles of determining antenna patterns and the flight techniques for determining both antenna patterns and radar cross section. Reference 19B-1 provides detailed information.

Helmut Bothe↗
NASA NTRS2026

Benchmarking Bayesian Optimization Frameworks and Acquisition Strategies for Materials Discovery and Autonomous Laboratories

Bayesian optimization (BO) can accelerate materials discovery by guiding expensive experiments toward the most promising processing conditions. We systematically compare five BO surrogate and framework combinations (Gaussian processes in Ax, Gaussian processes and Monte-Carlo neural networks in BayBE, random forests in Lolopy, and tree-structured Parzen (TPE) estimators in Hyperopt) on three benchmarks that mimic common materials design tasks (a discrete solid-electrolyte composition space, a hybrid discrete/continuous laminate-composite design problem solved with micromechanics modeling, and the continuous Ishigami analytic function which is a standard optimization benchmark). Each BO surrogate is paired with posterior mean, probability of improvement, and expected improvement acquisition functions and run for 100 trials from randomized initial samples with uniform random search providing a control. Across five random seeds per setting, BayBE’s Gaussian-process surrogate with expected improvement consistently reached ≥95 % of the known optimum in the fewest evaluations, while Lolopy’s random forest matched or exceeded GP performance on purely categorical or mixed spaces at a higher computational cost. Posterior mean alone often stagnated at local optima, underscoring the need for exploration, whereas probability and expected improvement balanced exploration and exploitation leading to better optimization in fewer trials. Execution times ranged from milliseconds for TPE to minutes for neural-network and random-forest surrogates. These results establish baseline expectations for BO in automated materials laboratories and highlight expected improvement with Gaussian processes as a reliable first choice, with random forests offering a strong alternative when categorical variables dominate. The benchmark suite and code are released to facilitate future surrogate, acquisition, and constraint-handling research in data-driven materials optimization.

Bayesian optimization↗
NASA NTRS2005

Update on Development of 360V, 28kWh Lithium-Ion Battery

Engineering unit submodule batteries (EUSB) the 360V, 28kWh EAPU battery were designed and assembled by COM DEV. These submodules consist of Sony Li-Ion 18650HC cells in a 5P-41S array yielding 180V, 1.4 kWh. Tests of these and of substrings and single cells at COM DEV and at JSC under various performance and abuse conditions demonstrated that performance requirements can be met. The thermal vacuum tests demonstrated that the worst case hot condition is the design driver. Deficiencies in the initial diode protection scheme of the battery were identified as a result of test failures. Potential solutions to the scheme are under development and will be presented.

Davies, Francis↗
NASA NTRSDate not supplied

Motor Configuration Selection for A New Technical Challenge to Develop A 5 MW Cryogenic Motor and Drive

Due to aviation’s appreciable and growing share of humanity’s impact on our environment and estimates that CO2emissions only account for 34% of aviation’s total effective radiative forcing [1], there is a need to reach beyond climate goals that focus only on CO2emissions, such as the US Aviation Climate Action Plan’s [3] goal to reach net-zero carbon emissions by 2050.There is motivation to develop technology that pushes toward future large transport aircraft with net zero climate impact that are highly electrified (i.e., have higher power electrical propulsion system components). This paper describes a new, 6-year technical challenge to address this need by developing a 5 MW superconducting motor and cryogenic drive. Section 1 will detail the motivation for this work. Section 2 will describe the technical challenge and the selected specifications for the motor. Section 3 will present the results of a motor configuration trade study and the down selection of one configuration to develop a detailed design for. The technical challenge focuses on the design of a5 MW superconducting motor and cryogenic drive and demonstration of it at a 2+ MW scale to achieve TRL 3. Both fully superconducting (superconducting stator and rotor) and fully cryogenic (superconducting rotor and cryogenic stator) machine configurations will be explored. An emphasis will be placed on addressing the key tall poles for high power superconducting machines. Further details will be included in the full paper. The requirements and goals of the motor will be detailed. The rated speed (2,000 to 3,000 rpm) is defined to be appropriate for directly driving multi-MW fans or propellers. A range of rated speed is permitted because the motor is not designed for a specific aircraft and to provide design flexibility if AC losses in the stator winding are found to be a significant constraint (i.e., a lower speed can be selected to reduce electrical frequency). Relatively conservative requirements for efficiency (99%) and specific power (20 kW/kg) are defined, because TRL advancement and pushing toward flight readiness is emphasized over performance optimization. However, more aggressive efficiency and specific power goals are specified (99.9% and 40 kW/kg). The 3rd section will present the results of a motor configuration trade study. The study started with a qualitative assessment of sixteen motor configurations based on geometric, mechanical, thermal, and electromagnetic criteria. This assessment has been completed with three evaluators scoring all nine criteria. A configuration down select was made by prioritizing the sixteen configurations into four tiers based on each configuration’s total score and consideration of manufacturability, complexity, and support hardware (e.g., rotary vacuum seals, bearings). Configurations in priority A and B will be further evaluated through quantitative assessments, whereas those in priority C will only be further evaluated if time permits and priority D will not be further evaluated. Eight of the sixteen configurations were down selected for quantitative assessment, which will include analytical calculations and low-to moderate-fidelity finite element analysis to produce a preliminary Pareto front of efficiency versus specific power for each configuration. This assessment emphasizes the calculation of AC losses in the stator winding and an exploration of thermal management approaches to remove that heat and maintain cryogenic temperature. The final paper will include a description of each motor configuration that was considered. The quantitative assessments are underway, and an assessment of one configuration is complete for multiple stator conductor options. The remaining assessments are scheduled to be completed by late March so that the final down select to one configuration can be included in this paper.

Net Zero↗
NASA NTRS1982

Cryopump for Large Pulses of Hydrogen

A test involving a flow of hot hydrazine decomposition products at a rate of 13.6 g/s (0.03 lb/s) established the requirement to maintain pressure in an 11.9-m-(39 ft) diameter space chamber below 200 microns. The flow, 2/3 hydrogen and 1/3 nitrogen by volume, continued for several periods ranging from 3 to 15 min. The pressure requirement was necessary to minimize thermal effects of the gas on the test vehicle but was well beyond the capability of the existing facility pumps. Various methods of obtaining additional temporary jump capacity were considered. From these, the slugged-charcoal approach was selected as the quickest and least expensive method to implement.

B C Moore↗
NASA NTRS2026

Beyond Melting: Amorphous Bonding for Joining and Consolidation

Crystallization may be the hidden constraint in thermoplastic composite manufacturing. It requires tightly controlled cooling, induces residual stresses through shrinkage, and introduces path-dependent behavior that complicates predictive modeling yet remains essential for structural performance. This work asks: can bonding be achieved without relying on melt-driven crystallization? To address this, thin (5–20 μm) polyetherimide (PEI) interlayers are pre-healed to slow-cooled polyaryletherketone (PAEK) in two contexts. The first, Thermabond®, is sub-melt joining of low melt-PAEK laminates. Results show that bond quality is governed primarily by processing (i.e., adequate healing and film handling) rather than modest changes in interlayer thickness. This concept is then extended to laminate-scale manufacturing through an architecture known as OATMEAL (Out-of-autoclave Amorphous/semicrystalline Thermoplastic Material for Energy-efficient Aerospace-grade Laminates). PEI is healed to carbon fiber reinforced polyetheretherketone (PEEK) at the prepreg and excess PEI is then ablated from the surface. Crystallinity is developed off-line during prepreg fabrication, while subsequent consolidation occurs below the melt temperature to preserve it. Cross-ply warpage experiments show that, contrary to intuition, repeated amorphous interfaces reduce global curvature by lowering the effective stress lock-in temperature and eliminating crystallization shrinkage from the lamina response. Correspondingly, laminate behavior is accurately predicted using classical laminate theory (CLT) with a single effective stress-free temperature, whereas conventional CF/PEEK requires accounting for crystallization-driven effects. By decoupling interfacial healing from crystallization, OATMEAL enables sub-melt consolidation, reduces energy consumption by up to 75%, and increases manufacturing throughput by fivefold. These results demonstrate that amorphous bonding is not only a joining strategy, but a pathway to more predictable and scalable thermoplastic composite manufacturing.

solidification↗
NASA NTRS1980

Developments in Fibrous Refractory Composite Insulation

The development of a new insulation material for heat-shielding advanced reusable entry vehicles is reported. The material, called fibrous refractory composite insulation, is a composite of two ceramic fibers with no additional additives to bond the fibers together; it also includes silicon carbide, an emmittance agent, to improve its optical properties at high temperature. One fiber is a drawn 11-micron-diameter aluminoborosilicate fiber, the other fiber is the silica fiber (microquartz) used in producing silica RSI (reusable surface insulation for the Space Shuttle), which is a blown fiber of 1-3 micron diameter and variable length. A composition containing 20%, with a thermal shock resistance of 1.8 that of all silica insulation, has been successfully produced in a pilot plant.

D B Leiser↗
NASA NTRSDate not supplied

Experimental Characterization of Additively Manufactured Nickel-Titanium Shape Memory Alloy Heat Pipes

Shape memory alloys (SMA) have been identified for use in spacecraft components as replacement for conventional deployment mechanisms. They may be used in thermal management components such as radiators to create self-deploying radiators. One SMA, NiTi, has also been developed for additive manufacturing processes. Heat pipes are a common way to create highly effective and lightweight spaceflight radiators, and heat pipes can also be made from NiTi and related alloys. The wick is the critical element of a functioning heat pipe, and recent progress over the past years has led to the development of additively manufactured heat pipe wicks in various materials. The combination of these efforts is the focus of this project: creating an additively manufactured, shape memory alloy self-deploying heat pipe radiator. This paper will focus on the experimental characterization of these additively manufactured NiTi heat pipes. The heat pipe coupons were additively manufactured by direct metal laser sintering (DMLS), with an integral liquid cooled condenser. Heat is input to the heat pipe via a thin film heater. Thermocouples were spot welded to the heat pipes to measure temperature at several axial locations. The heat pipes were tested with two working fluids: water and ethanol. Ethanol is not an ideal working fluid for heat pipes but is useful in characterizing them because it wets well to a wide variety of surfaces. Water is in general a superior working fluid for heat pipes, but its contact angle and therefore wicking performance strongly depends on the surface chemistry of the surface it is in contact with. A particular measurement of interest in this test is the evaporator to condenser thermal conductance, which will be compared in the full paper to recently published correlations for additively manufactured heat pipes. Experimental results for two straight geometry and one bellows geometry heat pipe will be presented. The bellows geometry is of interest for condenser of the self-deploying radiator design.

Additive manufacturing↗
NASA NTRS1998

High Temperature - Thin Film Strain Gages Based on Alloys of Indium Tin Oxide

A stable, high temperature strain gage based on reactively sputtered indium tin oxide (ITO) was demonstrated at temperatures up to 1050 C. These strain sensors exhibited relatively large, negative gage factors at room temperature and their piezoresistive response was both linear and reproducible when strained up to 700 micro-in/in. When cycled between compression and tension, these sensors also showed very little hysteresis, indicating excellent mechanical stability. Thin film strain gages based on selected ITO alloys withstood more than 50,000 strain cycles of +/- 500 micro-in/in during 180 hours of testing in air at 1000 C, with minimal drift at temperature. Drift rates as low as 0.0009%/hr at 1000 C were observed for ITO films that were annealed in nitrogen at 700 C prior to strain testing. These results compare favorably with state of the art 10 micro-m thick PdCr films deposited by NASA, where drift rates of 0.047%/hr at 1050 C were observed. Nitrogen annealing not only produced the lowest drift rates to date, but also produce the largest dynamic gage factors (G = 23.5). These wide bandgap, semiconductor strain sensors also exhibited moderately low temperature coefficients of resistance (TCR) at temperatures up to 1100 C, when tested in a nitrogen ambient. A TCR of +230 ppm/C over the temperature range 200 C < T < 500 C and a TCR of -469 ppm/C over the temperature range 600 C < T < 1100 C was observed for the films tested in nitrogen. However, the resistivity behavior changed considerably when the same films were tested in oxygen ambients. A TCR of -1560 ppm/C was obtained over the temperature range of 200 C < T < 1100 C. When similar films were protected with an overcoat or when ITO films were prepared with higher oxygen contents in the plasma, two distinct TCR's were observed. At T < 800 C, a linear TCR of -210 ppm/C was observed and at T > 800 C, a linear TCR of -2170 DDm/C was observed. The combination of a moderately low TCR and a relatively large gage factor make these semiconducting oxide films promising candidates for the active strain elements in high temperature thin film strain gages, particularly in applications where static strain measurement is desired.

Otto J Gregory↗
NASA NTRSDate not supplied

Battery Cell-to-Pack Scaling Laws for Electric Aircraft

Battery pack gravimetric energy density is one of the most important, yet often miss-estimated design parameters for sizing all-electric aircraft. Proper accounting for thermal, structural, and operational safety margins are frequently lost when extrapolating performance from the cell level to the aircraft level. This paper summarizes the relevant engineering and certification details needed to better account for the penalties associated when assembling battery packs. The relationship between the cell and pack energy density is not linear, as is often assumed. Furthermore, the relationship varies depending on pack requirements, cell chemistry, and architecture. Parametric, high-fidelity models are used to determine optimal battery pack sizes over a range of conditions to better quantify technology scaling effects.

Battery Electric Aircraft↗
NASA NTRSDate not supplied

Hellas, Ken and Me: Adventures in Exhumation and Inundation

Hellas is the largest and deepest basin on Mars. A 1993 study by Moore and Edgett (GRL, 20, 1599-1602) noted that Hellas undergoes net dust erosion. Thus, the exposed surface must represent whatever lag or rock surface and could not be removed by the strong winds blowing at these low elevations. The particle size distributions and particularly the rock or boulder population in this lag was thought to be potentially useful for distinguishing between processes that formed the lithologic units that comprise Hellas Planitia. Earlier studies had suggested the Hellas floor might be paved with basalt or glacial deposits. Ken, who at the time was working with Viking Orbiter IRTM data knew that there were late mission observations of the Hellas floor acquired though clear skies. His derived thermal inertia from these observations strongly suggested that the abundance of particles larger than coarse sand was very low. Hence, our study concluded that the floor deposits were, among other possibilities, ancient loess or lacustrine deposits. In 2001 a subsequent study on the Hellas basin by Moore and Wilhelms (Icarus, 54, 258-276) proposed that the basin was once a site of an ice covered sea, based on a series of circum-basin scarps that follow constant elevations as well as other landforms seen my Mars Global Surveyor’s MOC (an instrument that Ken played a major role in daily operations and data analysis) and topography derived from MOLA. Subsequently the best contiguous observations of the Hellas basin have been acquired from the Mars Reconnaissance Orbiter’s Context Camera, which again Ken has been a central player in its operations. Much of what we know about the grain-scale sedimentology of martian lacustrine deposits comes from the Curiosity Rover’s Mars Hand Lens Imager (which Ken was the PI through development and original operations within Gale crater). Under Ken’s watch several members of the Murray Formation were determined to be deposited in a lacustrine environment. A conclusion strongly demonstrated by MHLI imaging. My personal relationship with Hellas isn’t over. The Europa Clipper flew directly over the Hellas basin including its deepest regions. Ther REASON Ice Penetrating Radar system collected data during this flyby ostensibly for calibration, yet the quality of the observations may yet provide new discoveries from Hellas.

Jeffrey M Moore↗
NASA NTRS1985

Observational Requirements for the Regional Scale

Observational requirements are provided for the 'regional scale' (10 2 to 10 3 km space scale; 3 to 24 h time scale). Given this range, the regional scale represents a spatial and temporal domain in which important scale-interactive processes occur that act to concentrate large vertical wind shears, significant horizontal thermal gradients, and vertical motion patterns into narrow regions. A short review of the mass and momentum adjustments associated with jet streak-induced circulations is discussed. Evidence for the need to specify the wind field in the upper troposphere to accurately simulate forcing for the transverse circulations is also presented. The importance of specifying temperature tendency to resolve the lower tropospheric portion of the transverse circulations is highlighted. The observational requirements are then discussed, along with possible approaches for meeting the requirements on the regional scale.

Louis W Uccellini↗
NASA NTRSDate not supplied

Battery Cell-to-Pack Scaling Trends for Electric Aircraft

Battery pack gravimetric energy density is one of the most important, yet often miss- estimated design parameters for sizing all-electric aircraft. Proper accounting for thermal, structural, and operational safety margins are frequently lost when extrapolating performance from the cell level to the aircraft level. This paper summarizes the relevant engineering and certification details needed to better account for the penalties associated when assembling battery packs. The relationship between the cell and pack energy density is not linear, as is often assumed. Furthermore, the relationship varies depending on pack requirements, cell chemistry, and architecture. Parametric, high-fidelity models are used to determine optimal battery pack sizes over a range of conditions to better quantify technology scaling effects.

Battery Electric Aircraft↗
NASA NTRS2022

Cryogenic Spray Quenching of A Simulated Propellant Storage Tank Wall With Heat Transfer Enhancement By A Thin-Film Coating and Flow Pulsing in Microgravity

Human space exploration to the Moon, Mars, and possibly asteroids is NASA’s biggest challenge for the new millennium. One of the critical elements to this mission is the effective, sufficient, and reliable supply of cryogenic propellant fluids. Future lower-earth-orbiting (LEO) propellant fuel depots and human-carrying orbital transfer spacecraft flying to the moon and Mars will have to utilize the high thrust and high efficiency of liquid cryogenic chemical propulsion or nuclear thermal propulsion. Efficient in-space tank-to-tank propellant transfer (propellant fuel depot to orbital transfer spacecraft) of cryogenic propellants is an enabling technology for the planned Crewed Mars Surface Mission. The transfer of cryogenic propellants in space, however, has yet to be accomplished, solely due to the unavailability of cryogenic quenching heat transfer data during chilldown (quenching) and filling of the propellant receiver tank in reduced gravity and microgravity as liquid propellant cannot be stored in a required liquid state until the tank is quenched down to the liquid temperature. Therefore, highly energy efficient thermal-fluid management breakthrough concepts to conserve and minimize the cryogen consumption during propellant transfer have become the focus of research and engineering development, especially for the deep-space mission to Mars. In this paper, we introduce such concepts and demonstrate their feasibility for cryogenic storage tank chilldown in parabolic flights under a simulated space microgravity condition. In order to maximize the storage tank chilldown efficiency for the least amount of cryogen consumption, the technology adopted included cryogenic spray cooling, Teflon thin-film coating of the simulated tank surface, and spray flow pulsing. The completed flight experiments successfully demonstrated that spray cooling is the most efficient cooling method for the tank chilldown in microgravity. In microgravity, Teflon coating alone can improve the efficiency up to 72% and the efficiency can be improved up to 59% by flow pulsing alone. However, Teflon coating together with flow pulsing was found to substantially enhance the chilldown efficiency in microgravity for up to 113%.

spray↗
NASA NTRS1995

Analysis of Gas Absorption to A Thin Liquid Film in the Presence of A Zero-Order Chemical Reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

S Rajagopalan↗