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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The effects of laser pulse length and collisional ionization on the acceleration of titanium ions

Abstract The interaction of a relativistic laser pulse ( > 10 18 W cm −2 µ m 2 ) with foil targets can accelerate ions to energies of tens of MeV u −1 with optimized laser and target parameters. We report the results on simulations of the interaction of a 6.0 × 10 20 W cm −2 laser pulse incident on ultrathin (10–500 nm) titanium foils to investigate the roles of laser pulse duration and ionization mechanisms in the acceleration of titanium ions. While holding peak intensity constant, two laser pulse durations were investigated, 140 and 650 fs. The optimum thickness is dependent on pulse duration, as it requires the concurrence of target transparency with the incidence of the peak laser intensity. The collisional processes do not play a significant role in Ti ion beam generation from the 140 fs laser pulse duration at the optimum thickness (30 nm). However, for the 650 fs laser optimum, collisions improve the conversion efficiency of highly energetic ( > 10 MeV u −1 ), high charge titanium (Ti 21 − 22 + ) by a factor of 20, and the titanium ion cutoff energy by ∼15%. This improvement is due to the fact that collisional ionization increases the electron density of the plasma, which delays the time of relativistic transparency, causing collisions to decrease the optimum foil thickness from 150 to 100 nm. Additionally, collisional ionization increases the charge-to-mass ratio of the titanium, and injects more electrons into the accelerating sheath field. At the optimum thickness, target normal sheath acceleration is the dominant mechanism of acceleration, with additional contributions from radiation pressure and shock wave acceleration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

On infall into the Virgo cluster

The history of the study of the Galaxy's motion with respect to the Local Supercluster is reviewed. Direct measurements of the infall pattern suggest an infall component at the Local Group of about 250 km/s. This value is consistent with that expected if the average mass-to-light ratio of galaxies is similar to that dynamically measured in galaxy clusters, a value that gives an Omega of only about 0.3. The infall pattern is also consistent with galaxy density maps produced by IRAS surveys, although it may be only marginally consistent with the 'Great Attractor'. On smaller scales, there is strong evidence that most of the spiral galaxies near the cluster core are still falling in. Using the best distance estimates to the Virgo cluster, the local value of the Hubble constant is about 85 km/s/Mpc.

Huchra, John P.↗
NASA NTRS2012

Gravity, Topography, and Magnetic Field of Mercury from Messenger

On 18 March 2011, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft was inserted into a 12-hour, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapse latitude of 60 deg N, and apoapsis at approximately 15,200 km altitude in the southern hemisphere. This orbit has permitted the mapping of regional gravitational structure in the northern hemisphere, and laser altimetry from the MESSENGER spacecraft has yielded a geodetically controlled elevation model for the same hemisphere. The shape of a planet combined with gravity provides fundamental information regarding its internal structure and geologic and thermal evolution. Elevations in the northern hemisphere exhibit a unimodal distribution with a dynamic range of 9.63 km, less than that of the Moon (19.9 km), but consistent with Mercury's higher surface gravitational acceleration. After one Earth-year in orbit, refined models of gravity and topography have revealed several large positive gravity anomalies that coincide with major impact basins. These candidate mascons have anomalies that exceed 100 mGal and indicate substantial crustal thinning and superisostatic uplift of underlying mantle. An additional uncompensated 1000-km-diameter gravity and topographic high at 68 deg N, 33 deg E lies within Mercury's northern volcanic plains. Mercury's northern hemisphere crust is generally thicker at low latitudes than in the polar region. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 +/- 0.017, where M=3.30 x 10(exp 23) kg and R=2440 km are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of Cm/C = 0.452 +/- 0.035. One proposed model for Mercury's radial density distribution consistent with these results includes silicate crust and mantle layers overlying a dense solid (possibly Fe-S) layer, a liquid Fe-rich outer core of radius 2030 +/- 37 km, and an assumed solid inner core. Magnetic field measurements indicate a northward offset of Mercury's axial magnetic dipole from the geographic equator by 479 +/-3 km and provide evidence for a regional-scale magnetic field approximately collocated with the northern volcanic plains of possible crustal origin. These results from MESSENGER indicate a complex and asymmetric evolution of internal structure and dynamics in this end-member inner planet.

Neumann, Gregory A.↗
DOE OSTI2020

Higher-order phonon scattering: advancing the quantum theory of phonon linewidth, thermal conductivity and thermal radiative properties

Phonon scattering plays a central role in the quantum theory of phonon linewidth, which in turn governs important properties including infrared spectra, Raman spectra, lattice thermal conductivity, thermal radiative properties, and also signifi- cantly affects other important processes such as hot electron relaxation. Since Maradudin and Fein’s classic work in 1962, three-phonon scattering had been considered as the dominant intrinsic phonon scattering mechanism and has seen tremendous advances. However, the role of the higher-order four-phonon scattering had been persistently unclear and so was ignored. The tremendous complexity of the formalism and computational challenges stood in the way, prohibiting the direct and quantitative treatment of four-phonon scattering. In 2016, a rigorous four-phonon scattering formalism was developed, and the prediction was realized using empirical potentials. In 2017, the method was extended using first-principles calculated force constants, and the thermal conductivities of boron arsenides (BAs), Si and diamond were predicted. The predictions for BAs were later confirmed by several independent experiments. Four-phonon scattering has since been investigated in a range of materials and established as an important intrinsic scattering mechanism for thermal transport and radiative properties. Specifically, four-phonon scattering is important when the fourth-order scattering potential or phase space becomes relatively large. The former scenario includes: (i) nearly all materials when the temperature is high; (ii) strongly anharmonic (low thermal conductivity) materials, including most rocksalt compounds, halides, hydrides, chalcogenides and oxides. The latter scenario includes: (iii) materials with large acoustic–optical phonon band gaps, such as XY compounds with a large atomic mass ratio between X and Y; (iv) two- dimensional materials with reflection symmetry, such as single-layer graphene, single-layer boron nitride and carbon nanotubes; and (v) phonons with a large density of states, such as optical phonons, which are important for Raman, infrared and thermal radiative properties. Four-phonon scattering is expected to gain broad interest in various technologically important materials for thermoelectrics, thermal barrier coatings, thermal energy storage, phase change, nuclear power, ultra-high temperature ceramics, infrared spectra, Raman spectra, radiative transport, hot electron relaxation and radiative cooling. Four-phonon scattering has been, and will continue to be, established as an important intrinsic phonon scattering mechanism beyond three-phonon scattering. The prediction of four-phonon scattering will transition from a breakthrough to a new routine in the next decade.

Feng, Tianli↗
DOE OSTI2024

Measurement of the production and elliptic flow of (anti)nuclei in Xe-Xe collisions at √sNN = 5.44 TeV

Measurements of (anti)deuteron and (anti) 3He production in the rapidity range |𝑦|<0.5 as a function of the transverse momentum and event multiplicity in Xe-Xe collisions at a center-of-mass energy per nucleon-nucleon pair of √𝑠𝑁⁢𝑁=5.44 TeV are presented. The coalescence parameters 𝐵2 and 𝐵3 are measured as a function of the transverse momentum per nucleon. The ratios between (anti)deuteron and (anti) 3He yields and those of (anti)protons and pions are reported as a function of the mean charged-particle multiplicity density and compared with two implementations of the statistical hadronization model and with coalescence predictions. The elliptic flow of (anti)deuterons is measured for the first time in Xe-Xe collisions and shows features similar to those already observed in Pb-Pb collisions, i.e., the mass ordering at low transverse momentum and the meson-baryon grouping at intermediate transverse momentum. The production of nuclei is particularly sensitive to the chemical freeze-out temperature of the system created in the collision, which is extracted from a grand-canonical-ensemble-based thermal fit, performed for the first time including light nuclei along with light-flavor hadrons in Xe-Xe collisions. The extracted chemical freeze-out temperature 𝑇chem=(154.2±1.1) MeV in Xe-Xe collisions is similar to that observed in Pb-Pb collisions and close to the crossover temperature predicted by lattice quantum chromodynamics calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1987

Boundary conditions for the paleoenvironment: Chemical and physical processes in the pre-solar nebula

Detailed study of the first interstellar hydrocarbon ring, cyclopropenylidene (C3H2), is continuing. The singly deuterated isotope of this molecule, C3HD, was observed in several cold interstellar clouds. The results of a large survey for C3H2 in galactic sources of various types will soon be completed. It appears that cyclopropenylidene is present in virtually all interstellar clouds of at least moderate density. In order to make the first determinations of the CO2/CO abundance ratio in interstellar sources, observations of protonated CO2 were pursued. The spectrum from 18.5 to 22 GHz for several interstellar clouds is being systematically measured. Particular attention is being given to the cold, dark clouds TMC-1 and L124N, which may be formation sites for solar mass stars. The phenomena of maser emission from molecules of methanol is being studied in certain interstellar clouds. A comparison of 1 millimeter continuum emission from dust with the column density of carbon monoxide as determined from the rare C(18)O isotope for 4 molecular clouds in the Galaxy is nearing completion. Papers published during the period of this report are listed.

Irvine, William M.↗
NASA NTRS2016

ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) - Merging Observations and Laboratory Data

The Diffuse Interstellar Bands (DIBs) are a set of ~500 absorption bands that are detected in the spectra of stars with interstellar clouds in the line of sight. DIBs are found from the NUV to the NIR in the spectra of reddened stars spanning different interstellar environments in our local, and in other galaxies. DIB carriers are a significant part of the interstellar chemical inventory. They are stable and ubiquitous in a broad variety of environments and play a unique role in interstellar physics/chemistry. It has long been realized that the solving of the DIB problem requires a strong synergy between astronomical observations, laboratory astrophysics, and astrophysical modeling of line-of-sights. PAHs are among the molecular species that have been proposed as DIB carriers. We will present an assessment of the PAH-DIB model in view of the progress and the advances that have been achieved over the past years through a series of studies involving astronomical observations of DIBs, laboratory simulation of interstellar analogs for neutrals and ionized PAHs, theoretical calculations of PAH spectra and the modelization of diffuse and translucent interstellar clouds. We will present a summary of what has been learned from these complementary studies, the constraints that can now be derived for the PAHs as DIB carriers in the context of the PAH-DIB model and how these constraints can be applied to the EDIBLES project. The spectra of several neutral and ionized PAHs isolated in the gas phase at low temperature have been measured in the laboratory under experimental conditions that mimic interstellar conditions and are compared with an extensive set of astronomical spectra of reddened, early type stars. The comparisons of astronomical and laboratory data provide upper limits for the abundances of specific neutral PAH molecules and ions along specific lines-of-sight. Something that is not attainable from infrared observations alone. We present the characteristics of the laboratory facilities, MIS and COSmIC, that have been developed for this study and discuss the findings resulting from the comparison of the laboratory data with high resolution, high S/N ratio astronomical observations. MIS stands for Matrix Isolation Spectroscopy, a well-proven technique for isolating cold molecular species in inert solid environments. COSmIC stands for Cosmic Simulation Chamber. It combines a supersonic free jet expansion with discharge plasma and high-sensitivity cavity ringdown spectroscopy and time-of-flight mass spectrometry detection tools for the generation and the detection of cold, isolated gas-phase molecules and ions under experimental conditions that closely mimic interstellar conditions. The column densities of the individual neutral PAH molecules and ions probed in these surveys are derived from the comparison of these unique laboratory data with high resolution, high S/N ratio astronomical observations. The comparisons of astronomical and laboratory data lead to clear and unambiguous conclusions regarding the expected abundances for PAHs of various sizes and charge states in the interstellar environments probed in the surveys. Band profile comparisons between laboratory and astronomical spectra lead to information regarding the molecular structures and characteristics associated with the DIB carriers in the corresponding lines-of-sight. These quantitative surveys of neutral and ionized PAHs in the optical range open the way for unambiguous quantitative searches of PAHs and complex organics in a variety of interstellar and circumstellar environments.

astrophysics↗
NASA NTRS1993

An X-ray method for detecting substructure in galaxy clusters - Application to Perseus, A2256, Centaurus, Coma, and Sersic 40/6

We use the moments of the X-ray surface brightness distribution to constrain the dynamical state of a galaxy cluster. Using X-ray observations from the Einstein Observatory IPC, we measure the first moment FM, the ellipsoidal orientation angle, and the axial ratio at a sequence of radii in the cluster. We argue that a significant variation in the image centroid FM as a function of radius is evidence for a nonequilibrium feature in the intracluster medium (ICM) density distribution. In simple terms, centroid shifts indicate that the center of mass of the ICM varies with radius. This variation is a tracer of continuing dynamical evolution. For each cluster, we evaluate the significance of variations in the centroid of the IPC image by computing the same statistics on an ensemble of simulated cluster images. In producing these simulated images we include X-ray point source emission, telescope vignetting, Poisson noise, and characteristics of the IPC. Application of this new method to five Abell clusters reveals that the core of each one has significant substructure. In addition, we find significant variations in the orientation angle and the axial ratio for several of the clusters.

Mohr, Joseph J.↗
DOE OSTI2026

Quantification of [MTBD][beti] loading and its effects on Pt/HSC electrode performance in hydrogen fuel cells

High surface area carbon-supported platinum catalysts (Pt/HSC) are widely used in polymer electrolyte membrane fuel cells but often suffer from limited proton and oxygen transport within porous domains. To address these challenges, we integrate the ionic liquid [MTBD][beti] into Pt/HSC catalyst layers using two deposition methods-one-pot and sequential deposition-to tune IL distribution within micropores and mesopores. A combination of ex situ and in operando techniques were employed to elucidate electrode structure-performance relationships across a range of IL loadings. Sequential deposition achieved more efficient pore filling and higher IL retention at lower IL:C ratios, enabling enhanced proton conductivity and protection of active sites. Compared to the IL-free Pt/HSC, IL-modified electrodes demonstrated up to 28% improvement in mass activity and enhanced high-current-density performance under low relative humidity, while maintaining comparable performance under humidified conditions. Electrochemical impedance spectroscopy and CO displacement experiments reveal that improvements are linked to reduced ionic resistance and lower sulfonate adsorption on Pt sites, rather than changes in electrochemical surface area. However, excessive IL loading leads to mass transport losses. These results highlight the importance of selective pore filling and efficient IL distribution in achieving kinetic gains without compromising ionic and gas transport.

08 HYDROGEN↗
DOE OSTI2026

Development of Ternary Transition Metal Oxide Catalysts for Oxygen Evolution Reaction

Electrochemical water splitting, a promising method for green hydrogen production, is currently hindered by the high cost of precious-group metal (PGM)-based catalysts for the oxygen evolution reaction (OER). This study addresses this challenge by advancing the development of catalysts for OER, focusing on the development of high-performance PGM-free catalysts using nickel-iron-cobalt (NiFeCo)-based aerogels. The catalysts were synthesized via a sol-gel method and critical point drying to achieve a highly porous structure with an exceptionally high surface area. The designed catalyst structure provides an ideal platform for maximizing catalytic active sites and enhancing mass transport kinetics. Co has been systematically incorporated into the current PGM-free state-of-the-art, NiFeOx catalyst, and the metal ratios have been optimized. In addition to the experimental studies, density functional theory calculations were performed to study the material’s properties of this ternary catalyst and the effect of Co addition on enhancing OER catalysis.

Mizrahi, Michal [Bar-Ilan University, Ramat Gan, I↗
DOE OSTI2023

Silver-decorated palladium on carbon catalyst for enhanced ammonium formate dehydrogenation

Palladium (Pd)-based catalysts efficiently convert ammonium formate solution to hydrogen at low temperatures (<100 °C), but they tend to deactivate quickly during stability testing. This manuscript presents a systematic investigation into the catalytic properties of Pd–Ag bimetallic catalysts, focusing on their surface compositions and exploring the mechanisms behind the deactivation of Pd/Ag-based catalysts. Here this study reports a carbon-supported Pd–Ag bimetallic nanoparticle (NP) catalyst obtained through a galvanic replacement method, which showed enhanced formate dehydrogenation performance. The best catalyst, Pd 3 Ag 10 /ACA-G (Pd–Ag bimetallic NPs with a 3 : 10 mass ratio loaded on acid-washed activated carbon, prepared by the galvanic replacement method), presents the highest activity with a TOF of 5202 h -1 (~2.6-fold of commercial Pd/C). The enhanced electron density of Pd–Ag bimetallic nanoparticles, coupled with the advantages of a smaller nanoparticle size, and the modulation of hydrogen adsorption energy through the Ag/Pd surface alloy on the Ag/Pd(111) facet, collectively resulted in experimentally higher turnover rates of hydrogen production. The changes on the catalyst surface, including surface Ag fraction decrease, NP size growth, and O-containing species (carboxylate, etc.) adsorption, gradually resulted in catalyst deactivation.

08 HYDROGEN↗
DOE OSTI2020

Cosmic Reionization On Computers: The Galaxy-Halo Connection between $5 \leq z \leq10$

We explore the connection between the stellar component of galaxies and their host halos during the epoch of reionization (5 ≤ z ≤ 10) using the CROC (Cosmic Reionization on Computers) simulations. We compare simulated galaxies with observations and find that CROC underpredicts the abundance of luminous galaxies when compared to observed UV luminosity functions, and analogously the most massive galaxies when compared to observed stellar mass functions. We can trace the deficit of star formation to high redshifts, where the slope of the star formation rate to stellar mass relation is consistent with observations, but the normalization is systematically low. This results in a star formation rate density and stellar mass density that are systematically offset from observations. However, the less luminous or lower stellar mass objects have luminosities and stellar masses that agree fairly well with observational data. We explore the stellar-to-halo mass ratio (SHMR), a key quantity that is difficult to measure at high redshifts and that models do not consistently predict. In CROC, the SHMR decreases with redshift, a trend opposite to some abundance-matching studies. These discrepancies uncover where future effort should be focused in order to improve the fidelity of modeling cosmic reionization. We also compare the CROC galaxy bias with observational measurements using Lyman-break galaxy samples, finding reasonable consistency.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1969

High pressure real gas effects for helium and nitrogen

Critical flow factor is calculated that permits the isentropic mass-flow rate of the gases through critical flow nozzles to be calculated from plenum conditions. Results include nozzle throat velocity, compressibility factor, entropy, enthalpy, specific heat, and ratios of throat to plenum pressure, density, and temperature.

Johnson, R. C.↗
NASA NTRS1982

Large beam observations of the galactic center at 150, 200, and 300 microns

Observations with 10 arcmin resolution of a 2 sq deg portion of the galactic plane around the galactic center at 150, 200, and 300 microns are presented, obtained as part of a galactic plane survey. In the galactic center region the mean dust temperature is about 30 K. Both the temperature and the dust-to-gas mass ratio in the galactic center region are typical of a large portion of the galactic plane. Three main emission peaks, Sgr A, B, and C, are detected; these peaks appear as dust column density enhancements rather than temperature enhancements. The dust responsible for the FIR emission may only be a fraction of the dust responsible for the visual extinction toward the galactic center.

Stier, M. T.↗
NASA NTRS1987

Drop size distribution and air velocity measurements in air assist swirl atomizer sprays

Detailed measurements of mean drop size (SMD) and size distribution parameters have been made using a Fraunhofer diffraction particle sizing instrument in a series of sprays generated by an air assist swirl atomizer. Thirty-six different combinations of fuel and air mass flow rates were examined with liquid flow rates up to 14 lbm/hr and atomizing air flow rates up to 10 lbm/hr. Linear relationships were found between SMD and liquid to air mass flow rate ratios. SMD increased with distance downstream along the center line and also with radial distance from the axis. Increase in obscuration with distance downstream was due to an increase in number density of particles as the result of deceleration of drops and an increase in the exposed path length of the laser beam. Velocity components of the atomizing air flow field measured by a laser anemometer show swirling jet air flow fields with solid body rotation in the core and free vortex flow in the outer regions.

Mao, C.-P.↗
NASA NTRS1994

Chondrule formation in the radiative accretional shock

The physical, mineralogical, and isotopic properties of chondrules strongly indicate that they were formed by the rapid melting and resolidification of preexisting solids composed of primitive material. The chondrule precursors were heated to temperatures of about 1800 K in short high-temperature events, followed by cooling with a rate of 10(exp 2)-10(exp 3) K/hr. A heat input of about 1500 J/g is required to heat chondrule precursors to such a temperature and melt them. Lightning discharges and flares in the solar nebula, and heating of the chondrule precursors by friction with gas decelerated in the accretional shock or in a shock (of unspecified origin) within the solar nebula, have been discussed as possible mechanisms for chondrule formation. One advantage of chondrule formation in large-scale shocks is that a lot of dust material can be processed. An accretional shock, which is produced by infalling gas of the presolar cloud when it collides with the solar nebula, belongs to this type of shock. In 1984 Wood considered the possibility of chondrule formation in the accretional shock by heating of chondrule precursors by gas drag. He concluded that the density in the accreting material is much lower than needed to melt silicates at the distance of the asteroid belt if the accreting matter had the cosmic ratio of dust to gas, and the mass of the solar nebula did not exceed 2 solar mass units. Melting of chondrule precursors is difficult because of their effective cooling by thermal radiation. Suppression of the radiative cooling of individual grains in dust swarms, which are opaque to thermal emission, was considered to be the only possible means of chondrule formation in solar nebula shocks. Previous models of solid grain melting in solar nebula shocks have neglected gas cooling behind the shock front, i.e., they considered adiabatic shocks. In this paper we show that large dust grains could be heated much stronger than was supposed by these authors, because of effects associated with the gas cooling.

Ruzmaikina, T. V.↗
NASA NTRS1994

Shuttle Upper Atmosphere Mass Spectrometer Experimental Flight Results

Calibrated pressure measurements for species with mass-to-charge ratios up to 50 amu/e(-) were obtained trom the shuttle upper atmosphere mass spectrometer experiment during re-entry on the STS-35 mission. The principal experimental objective is to obtain measurements of freestream density in the hypersonic rarefied flow flight regime. Data were collected from 180 to about 87 km. However, data above 115 km were contaminated from a source of gas emanating from pressure transdueers connected in parallel to the mass spectrometer. At lower altitudes, the pressure transducer data are compared to the mass spectrometer total pressure with excellent agreement. Near the orifice entrance, a significant amount of CO2 was generated from chemical reactions. The freestream density in the rarefied flow flight regime is calculated using an orifice pressure coefficient model based upon direct simulation Monte Carlo results. This density, when compared with the 1976 U.S. Standard Atmosphere model, exhibits the wavelike nature seen on previous flights using accelerometry. Selected spectra are presented at higher altitudes (320 km) showing the effects of the ingestion of gases from a forward fuselage fuel dump.

Blanchard, R. C.↗
NASA NTRS2002

Optimal Design of Functionally Graded Metallic Foam Insulations

The focus of our work has been on developing an insight into the physics that govern the optimum design of thermal insulation for use in thermal protection systems of launch vehicle. Of particular interest was to obtain optimality criteria for designing foam insulations that have density (or porosity) distributions through the thickness for optimum thermal performance. We investigate the optimum design of functionally graded thermal insulation for steady state heat transfer through the foam. We showed that the heat transfer in the foam has competing modes, of radiation and conduction. The problem assumed a fixed inside temperature of 400 K and varied the aerodynamic surface heating on the outside surface from 0.2 to 1.0 MW/sq m. The thermal insulation develops a high temperature gradient through the thickness. Investigation of the model developed for heat conduction in foams showed that at high temperatures (as on outside wall) intracellular radiation dominates the heat transfer in the foam. Minimizing radiation requires reducing the pore size, which increases the density of the foam. At low temperatures (as on the inside wall), intracellular conduction (of the metal and air) dominates the heat transfer. Minimizing conduction requires increasing the pore size. This indicated that for every temperature there was an optimum value of density that minimized the heat transfer coefficient. Two optimization studies were performed. One was to minimize the heat transmitted though a fixed thickness insulation by varying density profiles. The second was to obtain the minimum mass insulation for specified thickness. Analytical optimality criteria were derived for the cases considered. The optimality condition for minimum heat transfer required that at each temperature we find the density that minimizes the heat transfer coefficient. Once a relationship between the optimum heat transfer coefficient and the temperature was found, the design problem reduced to the solution of a simple nonlinear differential equation. Preliminary results of this work were presented at the American Society of Composites meeting, and the final version was submitted for publication in the AIAA Journal. In addition to minimizing the transmitted heat, we investigated the optimum design for minimum weight given an acceptable level of heat transmission through the insulation. The optimality criterion developed was different from that obtained for minimizing beat transfer coefficient. For minimum mass design, we had to find for a given temperature the optimum density, which minimized the logarithmic derivative of the insulation thermal conductivity with respect to its density. The logarithmic derivative is defined as the ratio of relative change in the dependent response (thermal conductivity) to the relative change in the independent variable (density). The results have been documented as a conference paper that will be presented at the upcoming AIAA.

Haftka, Raphael T.↗