Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

Tenney, D. R.↗
NASA NTRS1975

Rigid format alter packets for the analysis of electromagnetic field problems

The computer program NASTRAN is used to solve electromagnetic field problems. The diffusion equation and the boundary conditions valid for problems of these kinds together with a replacing potential energy function are given. The extent to which an analogy with finite element displacement and temperature approaches holds is indicated. The outputting of complex quantities is made possible after adjustment of standard rigid format 1 input data blocks to module SDR2. The applications made involve the study of the proximity effect in a system of three parallel conductors and the analysis of the magnetic field in the vicinity of the points of contact in circuit breakers.

Spreeuw, E.↗
NASA NTRS1977

Monte Carlo analysis of uncertainty propagation in a stratospheric model. 1: Development of a concise stratospheric model

A concise model has been developed to analyze uncertainties in stratospheric perturbations, yet uses a minimum of computer time and is complete enough to represent the results of more complex models. The steady state model applies iteration to achieve coupling between interacting species. The species are determined from diffusion equations with appropriate sources and sinks. Diurnal effects due to chlorine nitrate formation are accounted for by analytic approximation. The model has been used to evaluate steady state perturbations due to injections of chlorine and NO(X).

Rundel, R. D.↗
NASA NTRS1977

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite difference solution of the diffusion equation. It is shown that hygroscopic induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

Farley, G. L.↗
NASA NTRS1977

Microscopic Lagrangian description of warm plasmas. III - Nonlinear wave-particle interaction

The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.

Galloway, J. J.↗
NASA NTRS1978

Optically thick X-ray transfer - The shell game

This paper investigates the radiative transfer of X-rays through a shell that is optically thick to Compton scattering, surrounding a point source of continuum X-rays. The emission and absorption of X-rays due to K-shell transitions of iron are included. The calculations are done in two entirely independent ways: by Monte Carlo simulation and by solving a Fokker-Planck diffusion equation. The emergent spectra agree very well for Thomson depths of at least about 2. The validity is confirmed of the modification to the Fokker-Planck equation of Kompaneets (1957) that is required when the photon energy is large compared with the average thermal energy of the electrons. A procedure is also developed for treating models of compact X-ray sources consisting of incomplete shells.

Langer, S. H.↗
NASA NTRS1978

Uncertainty propagation in a stratospheric model. I - Development of a concise stratospheric model. II - Monte Carlo analysis of imprecisions due to reaction rates

The paper discusses the development of a concise stratospheric model which uses iteration to obtain coupling between interacting species. The one-dimensional, steady-state, diurnally-averaged model generates diffusion equations with appropriate sources and sinks for species odd oxygen, H2O, H2, CO, N2O, odd nitrogen, CH4, CH3Cl, CCl4, CF2Cl2, CFCl3, and odd chlorine. The model evaluates steady-state perturbations caused by injections of chlorine and NO(x) and may be used to predict ozone depletion. The model is used in a Monte Carlo study of the propagation of reaction-rate imprecisions by calculating an ozone perturbation caused by the addition of chlorine. Since the model is sensitive to only 10 of the more than 50 reaction rates considered, only about 1000 Monte Carlo cases are required to span the space of possible results.

Rundel, R. D.↗
NASA NTRS1979

Silicon solar cell fabrication technology

The laser cell scanner was used to characterize a number of solar cells made in various materials. An electron beam-induced current (EBIC) study was performed using a stereoscan scanning electron microscope. Planar p-n junctions were analyzed. A theory for the EBIC based on the analytical solution of the ambipolar diffusion equation under the influence of electron beam excitation parameter z (which is related to beam penetration), the junction depth Z sub j, the beam current and the surface recombination, was formulated and tested. The effect of a grain boundary was studied.

Stafsudd, O. M.↗
NASA NTRS1979

Variational description of the positive column with two-stem ionization

The ionization balance in diffusion dominated discharges which depends on both one and two step ionization processes is considered. The Spenke diffusion equation (D sq delta n + neutrino n + sq kn =0) describing such conditions is solved by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between neutrino,k,D and the discharge dimensions, are derived for planar and cylindrical geometry, and compared with exact computations for certain limiting cases.

Crawford, F. W.↗
NASA NTRS1978

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite-element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite-difference solution of the diffusion equation. It is shown that hygroscopic-induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

Farley, G. L.↗
NASA NTRS1980

Variational description of the positive column with two-step ionization

The ionization balance in diffusion-dominated discharges may depend on both one- and two-step ionization processes. The Spenke diffusion equation describing such conditions is solved in this paper by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between the equation parameter, and the discharge dimensions, are derived for planar and cylindrical geometry and compared with exact computations for certain limiting cases.

Crawford, F. W.↗
NASA NTRS1981

Pseudospectral method for problems with nonperiodic boundary conditions

The capability of the pseudospectral technique and the time integration scheme for the time dependent nonperiodic problem is demonstrated. Significant improvements are shown in the accuracy for calculation of the two dimensional time dependent advection diffusion equation. The pseudospectral method is a viable alternative to the finite difference methods for the equation of the spatial deriviations.

Lee, H. N.↗
NASA NTRS1981

Magnetic field diffusion and dissipation in reversed-field plasmas

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

Drake, J. F.↗
NASA NTRS1980

Theory of positronium formation and positron emission at metal surfaces

The range of metallic surface processes available to the implanted positron is examined with a view to bare positron escape, positron surface state trapping, surface state detrapping, and positronium atom conversion. The stopping distance and its rms deviation are calculated. The effect of the elastic positron-ion core scattering, and the finite temperature corrections in the positron-phonon scattering are included. Overall conversion and emission efficiencies are calculated by solving an appropriate diffusion equation with boundary conditions set by the branching ratios for the surface processes. The temperature and incident energy dependence of the results for positronium atom conversion and positron emission efficiency are compared to experimental data.

Nieminen, R. M.↗
NASA NTRS1981

Hot oxygen atoms in the upper atmosphere of Venus

Using data obtained by an ultraviolet spectrometer on the Pioneer-Venus Orbiter, energy and altitude distribution of nonthermal oxygen atoms in the Venus atmosphere for typical daytime and nighttime conditions are calculated using two different numerical methods. Agreement is found between results obtained by the two-stream transport method and the diffusion equation technique. Dissociative recombination of molecular oxygen ions and charge exchange of atomic oxygen ions with the neutral hydrogen and oxygen gas are the source terms, and calculations show that the dissociative recombination term is the dominant one. It is shown that measured hot atom concentrations exceed estimates of the thermal hydrogen atom concentrations derived from Brinton et al. (1980) over most of the daytime exosphere, and the calculated concentrations do so to an even greater extent. It is concluded that hot oxygen atoms are an important component of the dayside exosphere of Venus, their most important effect being the absorption of solar wind.

Nagy, A. F.↗
NASA NTRS1981

Statistical acceleration of electrons by lower-hybrid turbulence

The statistical acceleration of electrons along an ambient magnetic field by large-amplitude lower-hybrid turbulence is discussed. Perturbations driven by a crossfield current and propagating nearly perpendicular to the applied magnetic field are considered. It is assumed that the instability saturates rapidly and that the fluctuating electric field is predominantly electrostatic. If the turbulence is characterized by a spectrum of small parallel wavenumbers, such that the parallel phase velocity of the waves is greater than the electron thermal velocity, then the turbulence can only accelerate electrons moving with large velocities along the magnetic field. The quasi-linear diffusion equation is solved using a Green's function technique, assuming a power law spectral energy density. The time evolution of an initial Maxwellian distribution is given and the time rate of change of the mean electron energy is calculated for various cases.

Wu, C. S.↗
NASA NTRS1981

Effect of shear stress on cell cultures and other reactor problems

Anchorage dependent cell cultures in fluidized beds are tested. Feasibility calculations indicate the allowed parameters and estimate the shear stresses therein. In addition, the diffusion equation with first order reaction is solved for the spherical shell (double bubble) reactor with various constraints.

Schleier, H.↗
NASA NTRS1982

Coupled hydromagnetic wave excitation and ion acceleration upstream of the earth's bow shock

A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.

Lee, M. A.↗