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Plane-stress analysis of an edge-stiffened rectangular plate subjected to loads and temperature gradients
Mechanical and thermal stress in elastic edge- stiffened plate under edge loading
Convection and magnetic fields in an atmosphere with constant temperature gradient. I - Hydrodynamic flows
In order to deduce the fluid and field conditions deep in the supergranules from the fluid motions and magnetic fields observed in the solar photosphere, it is necessary to have some idea of the depth to which the supergranules extend and the form of their internal fluid velocities. Toward this end a number of analytic solutions of the Navier-Stokes equations are given for circumstances possessing various facets of the supergranule environment in the sun. These solutions, together with the earlier work by others, shows that the granules extend to depths in excess of their mean diameters, that the convective velocities probably do not diminish much, if any, with depth, and that across the tops of the supergranules at the photosphere the horizontal velocity is more or less independent of depth.
Convection and magnetic fields in an atmosphere with constant temperature gradient. II - The supergranules and magnetic fields
The hydrodynamic properties of convective motions in a stratified atmosphere suggest that the supergranules in the solar photosphere extend to depths in excess of their horizontal diameters. The calculations presented here show that the weak fields which appear at the photosphere are as strong as, or stronger than, the horizontal fields anywhere in the supergranules below the surface. Hence the general 10 to 100 gauss azimuthal field of the sun, whose presence is indicated by the emerging bipolar magnetic regions, must lie below the base of the supergranules, i.e., below a depth probably of the order of 20,000 to 50,000 km. Presumably then the azimuthal field is generated by nonuniform rotation below the supergranule convection and does not appear in the supergranule layer because of the high rate of turbulent diffusion loss from that layer.
Empirical relations between seasonal changes in meridional temperature gradients and meridional fluxes of heat
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Non-Maxwellian velocity distribution functions associated with steep temperature gradients in the solar transition region. I - Estimate of the electron velocity distribution functions. II - The effect of non-Maxwellian electron distribution functions on ionization equilibrium calculations for carbon, nitrogen and oxygen
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Temperature gradient and electric field driven electrostatic instabilities
The stability of electrostatic waves to thermodynamic and electric potential gradients was investigated. It is shown that thermodynamic gradients drive instabilities even when the internal electric field vanishes. Skewing of the distribution function is not included in the dielectric.
Effect of design variables, temperature gradients and speed of life and reliability of a rotating disk
A generalized methodology to predict the fatigue life and reliability of a rotating disk such as used for aircraft engine turbines and compressors is advanced. The approach incorporates the computed life of elemental stress volumes to predict system life and reliability. Disk speed and thermal gradients as well as design variables such as disk diameter and thickness and bolt hole size, number and location are considered.
Vertical temperature gradients on Uranus - Implications for layered convection
Analyses of Voyager IR spectroscopy and radio occultation measurements confirm ground-based observations that the deep lapse rate of Uranus exceeds that for an adiabat of H2 in thermodynamic equilibrium. However, in approximately the same region of the atmosphere, Voyager IR and ground-based observations also indicate that the ratio of ortho to para hydrogen is near the equilibrium value. These two sets of observations can be reconciled by postulating the existence of rapid convective overturning within layers which are thin in comparison to a pressure scale height. Two forms of layered convection are examined. In one case, deposition of kinetic energy results in thin, rapidly overturning layers. Possible kinetic energy sources include braking waves and local instabilities. In the second case considered, molecular-weight discontinuities due to CH4 stratification stabilize the interfaces of thin layers. It is argued that both forms may be important in the convective portion of the Uranus atmosphere.
Effect of design variables, temperature gradients, and speed on life and reliability of a rotating disk
A generalized methodology to predict the fatigue life and reliability of a rotating disk such as used for aircraft engine turbines and compressors is advanced. The approach incorporates the computed life of elemental stress volumes to predict system life and reliability. Disk speed and thermal gradients as well as design varibles such as disk diameter and thickness and bolt hole size, number and location are considered.
Lower solar chromosphere-corona transition region. I - Theoretical models with small temperature gradients
A study of transition region models including the effects of classical thermal conduction, heating, and radiative cooling is carried out with attention directed toward the problem of understanding the observed emission in the lower transition region. It is found that the observationally inferred emission measure curve implies a near-balance between heating and radiative cooling in the lower transition region, and that the presence of strong hydrogen Ly-alpha cooling leads to the existence of singularities in the solutions of the force balance and energy balance equations when such a near-balance between heating and cooling is assumed. These singularities place strong constraints on the nature of viable models of the lower transition region and must be considered when Ly-alpha cooling is important. Previously suggested explanations of the observed emission from the lower transition region are considered in the context of the results of the present study, and conditions for the applicability of these suggested explanations are discussed.
Collective effects of temperature gradients and gravity on droplet coalescence
The interaction and coalescence of small spherical drops in dilute, homogeneous dispersions are considered theoretically under conditions, where drop motion results from gravity settling and thermocapillary migration acting simultaneously. A trajectory analysis is used to predict pairwise collision rates, and population dynamics equations are solved to predict the time evolution of the droplet size distribution. The rate of droplet collisions and growth may be reduced dramatically by antiparallel alignment of the gravitational and thermocapillary velocities. For such antiparallel alignment with the gravitational relative velocity exceeding the thermocapillary relative velocity for two widely separated drops, there is a 'collision-forbidden region' in parameter space. This occurs because the gravitational relative velocity decays more rapidly with decreasing separation distance between the drops than does the thermocapillary relative velocity, and so the resultant relative velocity along the line-of-centers from these two sources combined becomes zero at a finite separation and the drops are unable to collide. As a result, small drops which initially collide and coalesce due to thermocapillary motion will only grow until they reach a critical size for which the oppositely directed gravitational motion balances the thermocapillary motion.
Experimental Investigation of Rim Cracking in Disks Subjected to High Temperature Gradients
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Direct method of design and stress analysis of rotating disks with temperature gradient
A method is presented for the determination of the contour of disks, typified by those of aircraft gas turbines, to incorporate arbitrary elastic-stress distributions resulting from either centrifugal or combined centrifugal and thermal effects. The specified stress may be radial, tangential, or any combination of the two. Use is made of the finite-difference approach in solving the stress equations, the amount of computation necessary in the evolution of a design being greatly reduced by the judicious selection of point stations by the aid of a design chart. Use of the charts and of a preselected schedule of point stations is also applied to the direct problem of finding the elastic and plastic stress distribution in disks of a given design, thereby effecting a great reduction in the amount of calculation. Illustrative examples are presented to show computational procedures in the determination of a new design and in analyzing an existing design for elastic stress and for stresses resulting from plastic flow.
Near-surface temperature gradients and their effects on thermal-infrared emission spectra of particulate planetary surfaces
The infrared energy emitted from a planetary surface is generated within a finite depth determined by the material's absorption skin depth. This parameter varies significantly with wavelength in the infrared but has an average value of around 50 microns for most geologic materials. In solid rock, heat transfer is efficient enough so that this 50 micron zone of the near surface from which the radiation emanates will be more or less isothermal. In particulate materials, however, heat transfer is more complicated and occurs via a combination of mechanisms, including solid conduction within grains and across grain contacts, conduction through the interstitial gas, and thermal radiation within individual particles and across the void spaces in between grains. On planets with substantial atmospheres, the gas component dominates the heat transfer and tends to mitigate near-surface thermal gradients. However, on airless bodies, the gas component is absent and heat transfer occurs via solid conductions and radiation. If the particles are small relative to the average absorption skin depth, then the top 50-100 microns or so of the surface will be cooled by radiation to space allowing the creation of significant near-surface thermal gradients. In those regions of the spectrum where the absorption coefficient is low, the emission will come from the deeper, warmer parts of the medium, whereas in regions of high absorption, the emission will emanate from shallower, cooler parts of the medium. The resulting emission spectrum will show non-compositional features as a result of the thermal structure in the material. We have modeled the heat transfer in a particulate medium in order to determine the magnitude of near-surface thermal gradients for surfaces on airless bodies and on Mars. We use the calculated thermal structure to determine the effects it has on the infrared emission spectrum of the surface.
Numerical Analysis of Temperature Gradients and Interface Shape During Directional Solidification of Al and Al-Cu Alloy Under Microgravity Conditions
Numerical modeling was undertaken to analyze the influence of radial thermal gradient on solid/liquid (s/1) interface shape and convection patterns during solidification of pure Al and Al-4 wt% Cu alloy. The objective of the numerical task was to predict the influence of convective velocity on an insoluble particle near a s/l interface. These predictions would then be used to define the minimum gravity level (g) required to investigate the fundamental physics of interaction between a particle and a s/I interface. To satisfy this objective, steady state calculations were performed for different gravity levels and orientations with the gravity vector. ne furnace configuration used in this analysis is the proposed International Space Station Furnace, Quench Module Insert (QMI) 1. Results from a thermal model of the furnace core were used as initial boundary conditions for solidification modeling. General model of binary alloy solidification was based on the finite element code FIDAP. It was found that for the worst case orientation of 90 degrees with the gravity vector and a g level of 10(exp -4)g(sub o) (g(sub o) = 9.8 m/s(exp 2)) the dominant forces acting on the particle would be the fundamental drag and interfacial forces.
Solar Wind Ion Temperature Gradients as Observed by Ulysses at High Latitudes
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Application and Comparison of Satellite-Derived Sea Surface Temperature Gradients to Identify Seasonal and Interannual Variability off the California Coast: Preliminary Results and Future Perspectives
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