Results for “parameter space exploration” — Page 28

NASA NTRS2016

Application of Interval Predictor Models to Space Radiation Shielding

This paper develops techniques for predicting the uncertainty range of an output variable given input-output data. These models are called Interval Predictor Models (IPM) because they yield an interval valued function of the input. This paper develops IPMs having a radial basis structure. This structure enables the formal description of (i) the uncertainty in the models parameters, (ii) the predicted output interval, and (iii) the probability that a future observation would fall in such an interval. In contrast to other metamodeling techniques, this probabilistic certi cate of correctness does not require making any assumptions on the structure of the mechanism from which data are drawn. Optimization-based strategies for calculating IPMs having minimal spread while containing all the data are developed. Constraints for bounding the minimum interval spread over the continuum of inputs, regulating the IPMs variation/oscillation, and centering its spread about a target point, are used to prevent data over tting. Furthermore, we develop an approach for using expert opinion during extrapolation. This metamodeling technique is illustrated using a radiation shielding application for space exploration. In this application, we use IPMs to describe the error incurred in predicting the ux of particles resulting from the interaction between a high-energy incident beam and a target.

Crespo, Luis G.↗

NASA NTRSDate not supplied

Probing the Sun with Imaging Spectrographs

EUV and X-ray images of the Sun have revolutionized our understanding of our closest star. With them, we can probe the morphology and temperature structure of the solar atmosphere and see how they evolve as a function of space and time. However, image data cannot be used to determine line-of-sight velocities, abundances, or densities. This information is required to calculate the energy budget of eruptive events, provide boundary conditions for global solar models, and explore fundamental processes occurring in the solar atmosphere. For those diagnostics, we require spectroscopy. Because the structures on the Sun are extended sources, most modern-day spectrometers observe the Sun through long narrow slits. Two-dimensional, spectrally pure solar images with velocity, abundance, and density information are built up by stepping the slit over regions of interest. This method implies that two-dimensional information is highly limited by cadence and the temporal evolution and spatial structure of these parameters can never be truly separated. Both spatial and spectral information can be obtained in a single snapshot with slitless spectrometers, which were often used in the 1950-1970s, but were abandoned due to the difficulty of unfolding the overlapping spatial and spectral information. Thanks to advances in computer processing speeds and machine learning algorithms, there have been several techniques developed to complete the spatial/spectral unfolding, unlocking the full capability of slitless spectrometers for solar observations. The goal of this talk is to give an overview of the capability of such instruments, including recent results from a sounding rocket flight, and demonstrate their usefulness in the next decade of solar observatories and beyond.

Amy Winebarger↗

NASA NTRSDate not supplied

Probing the Sun with Imaging Spectrographs

EUV and X-ray images of the Sun have revolutionized our understanding of our closest star. With them, we can probe the morphology and temperature structure of the solar atmosphere and see how they evolve as a function of space and time. However, image data cannot be used to determine line-of-sight velocities, abundances, or densities. This information is required to calculate the energy budget of eruptive events, provide boundary conditions for global solar models, and explore fundamental processes occurring in the solar atmosphere. For those diagnostics, we require spectroscopy. Because the structures on the Sun are extended sources, most modern-day spectrometers observe the Sun through long narrow slits. Two-dimensional, spectrally pure solar images with velocity, abundance, and density information are built up by stepping the slit over regions of interest. This method implies that two-dimensional information is highly limited by cadence and the temporal evolution and spatial structure of these parameters can never be truly separated. Both spatial and spectral information can be obtained in a single snapshot with slitless spectrometers, which were often used in the 1950-1970s, but were abandoned due to the difficulty of unfolding the overlapping spatial and spectral information. Thanks to advances in computer processing speeds and machine learning algorithms, there have been several techniques developed to complete the spatial/spectral unfolding, unlocking the full capability of slitless spectrometers for solar observations. The goal of this talk is to give an overview of the capability of such instruments, including recent results from a sounding rocket flight, and demonstrate their usefulness in the next decade of solar observatories and beyond.

Amy Winebarger↗

NASA NTRSDate not supplied

Probing the Sun with Imaging Spectrographs

EUV and X-ray images of the Sun have revolutionized our understanding of our closest star. With them, we can probe the structure of the solar atmosphere and see how they evolve as a function of space and time. However, image data cannot be used to determine line-of-sight velocities, abundances, or densities. This information is required to calculate the energy budget of eruptive events, provide boundary conditions for global solar models, and explore fundamental processes occurring in the solar atmosphere. For those diagnostics, we require spectroscopy. Because the structures on the Sun are extended sources, most modern-day spectrometers observe the Sun through long narrow slits. Two-dimensional, spectrally pure solar images with velocity, abundance, and density information are built up by stepping the slit over regions of interest. This method implies that two-dimensional information is highly limited by cadence and the temporal evolution and spatial structure of these parameters can never be truly separated. Both spatial and spectral information can be obtained in a single snapshot with slitless spectrometers, which were often used in the 1950-1970s, but were abandoned due to the difficulty of unfolding the overlapping spatial and spectral information. Thanks to advances in computer processing speeds and machine learning algorithms, there have been several techniques developed to complete the spatial/spectral unfolding, unlocking the full capability of slitless spectrometers for solar observations. The goal of this talk is to give an overview of the capability of such instruments and demonstrate their usefulness in the next decade of solar observatories and beyond.

Amy Winebarger↗

NASA NTRSDate not supplied

A Comparative Assessment of Evolvable Martian ISRU Propellant Production for Future Human Missions

In 2022, NASA released its “Moon to Mars Strategy and Objectives Development” document, containing top-level goals and objectives designed to create a blueprint for sustained human presence and exploration throughout the solar system. One objective in this “blueprint” calls for the demonstration of “…Mars ISRU capabilities to support an initial human Mars exploration campaign.” NASA is looking at both the benefits and liens of this concept, as one of several trade space aspects under consideration, for inclusion in the overall architecture of the human exploration of Mars. This paper summarizes results from a series of Martian ISRU-focused trade studies from 2023 and 2024. These studies cover five different approaches to providing propellants for returning crew and equipment from the surface of Mars, using several different combinations of propellants delivered (from Earth) and produced from Martian feedstock material. For comparison purposes, the same ISRU infrastructure elements were used across all options wherever possible. The equipment mass, power, operational complexity, and time needed to produce some or all of these propellants have been quantified and compared when used in a common mission scenario. Analysis results for each option are discussed. Performance parameters for these options are compared side-by-side and observations made, including the positive and negative aspects of each case. The possibility of evolving from a simpler ISRU case to more complex cases that would potentially lead to more sustainable operations are also discussed. While no single case emerged as “better” in all aspects when compared to the others, there are distinct advantages and disadvantages that did emerge when comparing the results generated from a common set of assumptions for all cases. Consequently, specific mission objectives may determine which of these advantages or disadvantages are important for choosing among the cases that could benefit any particular mission or campaign.

Mars↗

NASA NTRSDate not supplied

A Comparative Assessment of Evolvable Martian ISRU Propellant Production for Future Human Missions

In 2022, NASA released its “Moon to Mars Strategy and Objectives Development” document, containing top-level goals and objectives designed to create a blueprint for sustained human presence and exploration throughout the solar system. One objective in this “blueprint” calls for the demonstration of “…Mars ISRU capabilities to support an initial human Mars exploration campaign.” NASA is looking at both the benefits and liens of this concept, as one of several trade space aspects under consideration, for inclusion in the overall architecture of the human exploration of Mars. This paper summarizes results from a series of Martian ISRU-focused trade studies from 2023 and 2024. These studies cover five different approaches to providing propellants for returning crew and equipment from the surface of Mars, using several different combinations of propellants delivered (from Earth) and produced from Martian feedstock material. For comparison purposes, the same ISRU infrastructure elements were used across all options wherever possible. The equipment mass, power, operational complexity, and time needed to produce some or all of these propellants have been quantified and compared when used in a common mission scenario. Analysis results for each option are discussed. Performance parameters for these options are compared side-by-side and observations made, including the positive and negative aspects of each case. The possibility of evolving from a simpler ISRU case to more complex cases that would potentially lead to more sustainable operations are also discussed. While no single case emerged as “better” in all aspects when compared to the others, there are distinct advantages and disadvantages that did emerge when comparing the results generated from a common set of assumptions for all cases. Consequently, specific mission objectives may determine which of these advantages or disadvantages are important for choosing among the cases that could benefit any particular mission or campaign.

Propellant↗

NASA NTRS2003

Results From Cs Activated GaN Photocathode Development for MCP Detector Systems at GSFC

We describe the development of high quantum efficiency W photocathodes for use in large area two dimensional microchannel plate based detector arrays to enable new W space astronomy missions. Future W missions will require improvements in detector sensitivity, which has the most leverage for cost-effective improvements in overall telescope/instrument sensitivity. We use new materials such as p-doped GaN, AIGaN, ZnMgO, Sic and diamond. We have currently obtained QE values > 40 % at 185 nm with Cesiated GaN, and hope to demonstrate higher values in the future. By using controlled internal fields and nano-structuring of the surfaces, we plan to provide field emission assistance for photoelectrons while maintaining their energy distinction from dark noise electrons. We will transfer these methods from GaN to ZnMgO, a new family of wide band-gap materials more compatible with microchannel plates. We also are exploring technical parameters such as doping profiles, internal and external field strengths, angle of incidence, field emission assistance, surface preparation, etc.

Norton, Tim↗

NASA NTRS2014

Orion MPCV Continuum RCS Heating Augmentation Model Development

The reaction control system jets of the Orion Multi Purpose Crew Vehicle can have a significant impact on the magnitude and distribution of the surface heat flux on the leeside of the aft-body, when they are fired. Changes in surface heating are expressed in terms of augmentation factor over the baseline smooth body heating. Wind tunnel tests revealed heating augmentation factors as high as 13.0, 7.6, 2.8, and 5.8 for the roll, pitch down, pitch up, and yaw jets respectively. Heating augmentation factor models, based almost exclusively on data from a series of wind tunnel tests have been developed, for the purposes of thermal protection system design. The wind tunnel tests investigated several potential jet-to-freestream similarity parameters, and heating augmentation factors derived from the data showed correlation with the jet-to-freestream momentum ratio. However, this correlation was not utilized in the developed models. Instead augmentation factors were held constant throughout the potential trajectory space. This simplification was driven by the fact that ground to flight traceability and sting effects are not well understood. Given the sensitivity of the reaction control system jet heating augmentation to configuration, geometry, and orientation the focus in the present paper is on the methodology used to develop the models and the lessons learned from the data. The models that are outlined in the present work are specific to the aerothermal database used to design the thermal protection system for the Exploration Flight Test 1 vehicle.

Heating Augmentation↗

NASA NTRS2015

Utilization of the Deep Space Atomic Clock for Europa Gravitational Tide Recovery

Estimation of Europa's gravitational tide can provide strong evidence of the existence of a subsurface liquid ocean. Due to limited close approach tracking data, a Europa flyby mission suffers strong coupling between the gravity solution quality and tracking data quantity and quality. This work explores utilizing Low Gain Antennas with the Deep Space Atomic Clock (DSAC) to provide abundant high accuracy uplink-only radiometric tracking data. DSAC's performance, expected to exhibit an Allan Deviation of less than 3e-15 at one day, provides long-term stability and accuracy on par with the Deep Space Network ground clocks, enabling one-way radiometric tracking data with accuracy equivalent to that of its two-way counterpart. The feasibility of uplink-only Doppler tracking via the coupling of LGAs and DSAC and the expected Doppler data quality are presented. Violations of the Kalman filter's linearization assumptions when state perturbations are included in the flyby analysis results in poor determination of the Europa gravitational tide parameters. B-plane targeting constraints are statistically determined, and a solution to the linearization issues via pre-flyby approach orbit determination is proposed and demonstrated.

Seubert, Jill↗

NASA NTRSDate not supplied

Enabling Mission Flexibility to Battery Driven Deep Space Endeavors With Generalized Battery-Health-Monitoring Using Physics-Based and Data-Driven Reduced-Order Models

The needs and requirements for an electrochemical energy storage for deep space exploration is well explored. It is often understood that different mission sites and environmental conditions require different battery chemistries or technologies. Additionally, various engineering solutions are deployed to overcome specific chemical challenges. One often overlooked need is the “health” monitoring of an electrochemical storage system. The term generalized health monitoring, as envisioned in this work, refers to the monitoring of various aspects such as electrode health, electrolyte health, reaction pathway health, cooling system health, sensor health, and BMS health [1]. Generalized health monitoring allows mission leads, engineers, and scientists to incorporate flexibility in mission designs, make on-the-fly mission changes, and extend the duration of science missions. Moreover, it enables automation and data-driven decision-making without compromising safety and performance. Recently, our group developed a hierarchy of thermal reduced-order models (TROM) by combining a physics-based modeling approach and data-driven model reduction techniques applied to flight data [2]. The resulting TROMs were found to be not only accurate but also identifiable from the flight data. Consequently, the coefficient of variance of the model parameters is small over the course of hundreds of flights, allowing for monitoring the parameter evolution trajectories as the battery ages and degrades. These parameters constitute the metrics of the generalized health of a battery. Monitoring their evolution allows such models to be used for anomaly detection and prognostics, improving early detection of abnormal behavior and thus enabling timely maintenance, longer battery life, and enhanced battery safety. For this presentation, the practicality of the thermal model will be validated on a pack of 14cells under various topology configurations such as 1S14P, 2P7S, 7S2P, and 1P14S. It is well known that manufacturing and non-uniform aging lead to variability in the performance of a cell, which is exacerbated by cell balancing during active load. Additionally, in extreme scenarios, the paramount objective is to complete the mission, regardless of the stresses on the battery. Topology-induced balancing issues further stress the battery. The goal of this study is to determine if the noise (identifiability) in the reduced-order thermal model parameters is sensitive to topology, cell spacing, cooling strategy, and manufacturing or age variability. The variability in cells is considered by assuming a multimodal distribution for microscopic parameters of a cell (such as porosity, tortuosity, reaction kinetics, volumetric thermal conductivity, and volumetric heat capacity). The compounded effect of manufacturing variability, topological selection, cooling strategies, and cell balancing ages each cell in a battery differently. The study aims to clarify whether the challenge in extracting maximum information depends on the minimum number of sensors or models used for data extraction.

Automation↗

NASA NTRSDate not supplied

Probing the Sun with Imaging Spectrographs

EUV and X-ray images of the Sun have revolutionized our understanding of our closest star. With them, we can probe the morphology and temperature structure of the solar atmosphere and see how they evolve as a function of space and time. However, image data cannot be used to determine line-of-sight velocities, abundances, or densities. This information is required to calculate the energy budget of eruptive events, provide boundary conditions for global solar models, and explore fundamental processes occurring in the solar atmosphere. For those diagnostics, we require spectroscopy. Because the structures on the Sun are extended sources, most modern-day spectrographs observe the Sun through long narrow slits. Two-dimensional, spectrally pure solar images with velocity, abundance, and density information are built up by stepping the slit over regions of interest. This mode of operation implies that two-dimensional information is highly limited by cadence and the temporal evolution and spatial structure of these parameters can never be truly separated. Both spatial and spectral information can be obtained in a single snapshot with slitless spectrographs, which were often used in the 1950-1970s, but were abandoned due to the difficulty of unfolding the overlapping spatial and spectral information. Thanks to advances in computer processing speeds and machine learning algorithms, there have been several techniques developed to complete the spatial/spectral unfolding, unlocking the full capability of slitless spectrographs for solar observations. The goal of this talk is to give a broad overview of the capability of such instruments and demonstrate their usefulness in the next decade of solar observatories and beyond.

Amy Winebarger↗

NASA NTRSDate not supplied

Aviary: An Open-Source Multidisciplinary Design, Analysis, and Optimization Tool for Modeling Aircraft With Analytic Gradients

Demands on aircraft design methods in recent years have begun to require increasingly higher amounts of coupling between disciplines and have also begun to require optimization in order to satisfy competing objectives involving large numbers of parameters that define unconventional configurations. These expanding requirements have amplified a need for new and improved aircraft design, analysis, and optimization codes that are capable of performing coupled design exploiting analytic gradients where possible. Aviary is a multidisciplinary design optimization and analysis framework which allows for tightly coupled simultaneous aircraft and subsystem design using analytic gradients. Aviary has employed the methods of two legacy aircraft analysis tools to provide native analytically differentiated calculations for five different disciplines, and it also has the ability to couple in external discipline analysis tools, whether or not those tools can provide analytic gradients. Preliminary examples and modeling efforts have shown Aviary’s ability to effectively model novel concepts and explore large and non-intuitive design spaces. Finally, a multi-level user interface in Aviary creates an easy entry point for users with any level of multidisciplinary design, analysis, and optimization experience.

multidisciplinary↗

NASA NTRS1995

The redshift-space neighborhoods of 36 loose groups. 2: Analysis

We explore the kinematics of 36 rich RGH89 groups identified from the first two complete slices of the CfA redshift survey. These groups have more than five members identified by a friends-of-friends algorithm at a number density contrast delta rho/rho greater than or equal to 80. To examine the stability of the determination of the velocity dispersion for these systems, we compare results for the original 232 members with results for a larger redshift sample, including 334 fainter members in the redshift neighborhoods. On average, we double the number of group members in each system. The observed distribution of velocity dispersions is stable. In fact, the velocity dispersion based on the original members identified in the CfA redshift survey is a reliable predictor of the value for the enlarged sample in an individual group. The velocity dispersion is thus a stable physical parameter for discrimination among systems galaxies. A larger sample of groups, particularly one selected from a distance limited catalog, should provide an interesting constraint on models for the formation of large-scale structure. We take H(sub 0) = km/s/Mpc.

Ramella, Massimo↗

NASA NTRSDate not supplied

Evaluating Lunar Water Processing System Model Configurations for Small Scale Oxygen and Hydrogen Production Within JAXA'S ISRU Technology

Introduction: In-Situ Resource Utilization (ISRU) refers to novel methods of extracting and processing local resources for use in life support and propulsion systems, reducing or eliminating the required consumables to be transferred from Earth. Current estimates of water-ice availability embedded in regolith within the Moon’s permanently shadowed regions (PSR’s) range between 1-5% by weight. However, the composition and characteristics of the “wet” regolith is unknown. Alternate ISRU excavation techniques and Concept of Operations (ConOps) must be explored to optimize surface system operations based on these factors. To assess the feasibility of different ISRU subsystem technologies and compare system architecture configurations, an interchangeable system model was generated to incorporate technologies spanning excavation of raw materials to storage of products and determine optimal arrangement of total system processing needs. Total Mass, Volume, and Power (M/V/P) requirements were computed for 168 design iterations of this water processing plant. System Model: In FY24, the System Engineering and Integration (SE&I) ISRU Modeling and Analysis (SIMA) team developed a lunar water processing system model using the Mission Analysis and Integration Tool (MAIT) to estimate the M/V/P for ISRU subsystems operating under a wide range of Hydrogen (H2) and Oxygen (O2) production targets for the Space Technology Mission Directorate (STMD) [1]. Based on Japan Aerospace Exploration Agency’s (JAXA) surface operational requirements, this system architecture was modified to include the ability to excavate consolidated icy regolith (versus granular ice excavation using Kennedy Space Center’s (KSC) ISRU Pilot Excavator, IPEx) and explore the feasibility of processing the lunar water both inside and outside of the PSR. For the consolidated icy regolith case study, excavation was performed via a mobility transport chassis outfitted with The Regolith Ice Drill for Exploring New Terrain (TRIDENT) for drilling [2] and the Cold Operable Lunar Deployable Arm (COLDArm) [3] for regolith transfer. The system model determines the required rover and payload. M/V/P to handle the required regolith processing rates. The regolith is then sorted and heated to sublimate the ice (via an auger dryer). The exiting high temperature, low pressure vapor is cleaned of volatiles (via cold trap) and electrolyzed to produce H2 and O2. These products are then dried, liquified with 20 K and 90 K cryocoolers (for H2 and O2, respectively), and stored in cylindrical tanks. Study Goals: Due to the different ConOps options of regolith transport to the ridge for processing versus processing it directly inside the PSR, as well as the unknown regolith/water-ice composition, new excavation techniques and their power configurations are being evaluated within a ISRU system architecture for production targets less than NASA’s pilot plant (1 mT). This analysis investigates the feasibility of numerous excavation techniques, power architectures, and logistical operations and determines an optimal system configuration with regards to M/V/P. It aims to investigate which parameters, both locally and globally, have the greatest effect on each subsystem within the plant. This can be used to identify the most critical components of the plant, and guide future decisions on allocating funding for research and development. The results from this study may provide subsystem developers with appropriate interfaces with excavation subsystems and downstream processes, and assessing the overall feasibility of each excavation technique, power architecture, and logistical timeframe. References: [1] Carlson, A. et. al. (2024) ICES. [2] Zacny, K., et. al. (2024) “ASCE Earth and Space”. [3] McCormick, R., et. Al. (2024) IEEE Xplore.

ISRU↗

NASA NTRS2003

ISS Mini AERCam Radio Frequency (RF) Coverage Analysis Using iCAT Development Tool

The long-term goals of the National Aeronautics and Space Administration's (NASA's) Human Exploration and Development of Space (HEDS) enterprise may require the development of autonomous free-flier (FF) robotic devices to operate within the vicinity of low-Earth orbiting spacecraft to supplement human extravehicular activities (EVAs) in space. Future missions could require external visual inspection of the spacecraft that would be difficult, or dangerous, for humans to perform. Under some circumstance, it may be necessary to employ an un-tethered communications link between the FF and the users. The interactive coverage analysis tool (ICAT) is a software tool that has been developed to perform critical analysis of the communications link performance for a FF operating in the vicinity of the International Space Station (ISS) external environment. The tool allows users to interactively change multiple parameters of the communications link parameters to efficiently perform systems engineering trades on network performance. These trades can be directly translated into design and requirements specifications. This tool significantly reduces the development time in determining a communications network topology by allowing multiple parameters to be changed, and the results of link coverage to be statistically characterized and plotted interactively.

Bolen, Steve↗

NASA NTRS2017

Multi-Beam Laser Beacon Propagation Over Lunar Distance: Comparison of Predictions and Measurements

A multi-beam beacon was transmitted from the Optical Communication Telescope Laboratory (OCTL) located at Table Mountain, CA to the Lunar Laser Space Terminal (LLST), on-board the Lunar Atmospheric Dust and Environment Explorer (LADEE) spacecraft, during NASA’s recent Lunar Laser Communication Demonstration (LLCD). The laser beacon (1568?0.1 nm) was square wave modulated and sensed by a LLST quadrant sensor to enable link acquisition and tracking. LLST computed the mean received beacon power and returned 5 kHz sampled power time series over the downlink. Post-processing of the decoded downlink received at OCTL retrieved the uplink power recorded at LLST. The predicted mean irradiance delivered to LLST consistently agreed with the variable beam divergence transmitted from OCTL to within < 1 decibel (dB). Irradiance fluctuations detected at LLST were reconciled with an uplink wave-propagation model derived using independently monitored atmospheric parameters. We report good agreement of the scintillation index and atmospheric coherence time.

Biswas, A↗

NASA NTRS1989

Design of catalytic monoliths for closed-cycle carbon dioxide lasers

Pulsed carbon dioxide (CO2) lasers have many applications in aeronautics, space research, weather monitoring and other areas. Full exploitation of the potential of these lasers in hampered by the dissociation of CO2 that occurs during laser operation. The development of closed-cycle CO2 lasers requires active CO-O2 recombination (CO oxidation) catalyst and design methods for implementation of catalysts in CO2 laser systems. A monolith catalyst section model and associated design computer program, LASCAT, are presented to assist in the design of a monolith catalyst section of a closed cycle CO2 laser system. Using LASCAT,the designer is able to specify a number of system parameters and determine the monolith section performance. Trade-offs between the catalyst activity, catalyst dimensions, monolith dimensions, pressure drop, O2 conversion, and other variables can be explored and adjusted to meet system design specifications. An introduction describes a typical closed-cycle CO2 system, and indicates some advantages of a closed cycle laser system over an open cycle system and some advantages of monolith support over other types of supports. The development and use of a monolith catalyst model is presented. The results of a design study and a discussion of general design rules are given.

Herz, R. K.↗

NASA NTRS1991

Flow boiling with enhancement devices for cold plate coolant channel design

Future space exploration and commercialization will require more efficient heat rejection systems. For the required heat transfer rates, such systems must use advanced heat transfer techniques. Forced two phase flow boiling heat transfer with enhancements falls in this category. However, moderate to high quality two phase systems tend to require higher pressure losses. This report is divided into two major parts: (1) Multidimensional wall temperature measurement and heat transfer enhancement for top heated horizontal channels with flow boiling; and (2) Improved analytical heat transfer data reduction for a single side heated coolant channel. Part 1 summarizes over forty experiments which involve both single phase convection and flow boiling in a horizontal channel heated externally from the top side. Part 2 contains parametric dimensionless curves with parameters such as the coolant channel radius ratio, the Biot number, and the circumferential coordinate.

Boyd, Ronald D.↗