scholarly journals Thermal ignition in a reactive slab with unsymmetric boundary temperatures

1983 ◽  
Vol 24 (3) ◽  
pp. 279-288 ◽  
Author(s):  
K. K. Tam ◽  
P. B. Chapman
Keyword(s):  
Steady State ◽  
Critical Role ◽  
Upper And Lower Solutions ◽  
Lower Solution ◽  
Time Dependent ◽  
Thermal Ignition ◽  
Time Dependent Problem ◽  
Steady State Solutions

AbstractThe problem of thermal ignition in a reactive slab with unsymmetric temperatures equal to 0 and T is considered. Steady state upper and lower solutions are constructed. It is found that T plays a critical role. Results similar to the case with symmetric boundary temperatures are expected when T is small. When T is sufficiently large, there is only one steady state upper or lower solution. The time dependent problem is then considered. Phenomena suggested by studying the upper and lower steady state solutions are confirmed.

Laser Beam-Hygroscopic Aerosol Interactions

1977 ◽  
Vol 99 (2) ◽  
pp. 281-286 ◽  
Author(s):  
G. E. Caledonia ◽  
J. D. Teare
Keyword(s):  
Steady State ◽  
Laser Beam ◽  
Water Droplet ◽  
Atmospheric Aerosol ◽  
Phase Shifts ◽  
Time Dependent ◽  
Small Water ◽  
Steady State Solutions

A model for the prediction of the temperature and vapor fields created about a small water droplet undergoing irradiation by a laser beam has been developed. Time-dependent and steady-state solutions of the model are discussed. Estimates of characteristic phase shifts to be expected in propagating through standard atmospheric aerosol distributions are also presented. While the model is quite general, the calculations are limited to DF laser wavelengths.

scholarly journals STUDY OF THE EIGENVALUE SPECTRA OF THE NEUTRON TRANSPORT PROBLEM IN PN APPROXIMATION

2021 ◽  
Vol 247 ◽  
pp. 03018
Author(s):  
P. Saracco ◽  
N. Abrate ◽  
M. Burrone ◽  
S. Dulla ◽  
P. Ravetto
Keyword(s):  
Transport Equation ◽  
Cross Sections ◽  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Time Dependent ◽  
Neutron Transport Equation ◽  
Generalized Eigenvalue Problems ◽  
Time Dependent Problem ◽  
Steady State Solutions ◽  
Insight Into

The study of the steady-state solutions of neutron transport equation requires the introduction of appropriate eigenvalues: this can be done in various different ways by changing each of the operators in the transport equation; such modifications can be physically viewed as a variation of the corresponding macroscopic cross sections only, so making the different (generalized) eigenvalue problems non-equivalent. In this paper the eigenvalue problem associated to the time-dependent problem (α eigenvalue), also in the presence of delayed emissions is evaluated. The properties of associated spectra can give different insight into the physics of the problem.

Time-Dependent Simulations of Shear-Thinning Elastic Flows Through Contractions

2001 ◽  
Author(s):  
Paulo J. Oliveira
Keyword(s):  
Steady State ◽  
Unsteady Flow ◽  
Experimental Work ◽  
Shear Thinning ◽  
Time Dependent ◽  
Numerical Work ◽  
Viscoelastic Models ◽  
Vortex Merging ◽  
Constant Viscosity ◽  
Steady State Solutions

Abstract Past numerical work with constant-viscosity viscoelastic fluids through planar contractions has enabled steady-state solutions to be obtained at relatively high Weissenberg numbers (We up to 10). Those solutions for the upper-convected Maxwell and Oldroyd-B models showed steady flow patterns for increasing We with the appearance of lip-vortices, vortex growth, and comer-lip vortex merging, in agreement with recent simulations and some experimental work. When similar simulations were performed with two shear-thinning viscoelastic models, namely the Phan-Thien – Tanner and the Giesekus models, steady state solutions could not be obtained beyond a certain value of We, but the solution was seen to follow a periodic unsteady flow pattern. The present paper reports preliminary numerical results which highlight the formation of the lip vortices through a sequence of time dependent events.

scholarly journals On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere

2001 ◽  
Vol 43 (1) ◽  
pp. 77-85 ◽  
Author(s):  
R. O. Weber ◽  
G. C. Wake ◽  
H. S. Sidhu ◽  
G. N. Mercer ◽  
B. F. Gray ◽  
...  
Keyword(s):  
Steady State ◽  
Unit Sphere ◽  
Steady States ◽  
Temperature Profiles ◽  
Thermal Ignition ◽  
Unstable Steady State ◽  
Steady State Temperature ◽  
Parameter Values ◽  
Steady State Solutions ◽  
Unstable Intermediate

AbstractSteady state solutions for spontaneous thermal ignition in a unit sphere are considered. The multiplicity of unstable, intermediate, steady state, temperature profiles is calculated and shown for selected parameter values. The crossing of the temperature profiles corresponding to the unstable, intermediate, steady states is exhibited in a particular case and is proven in general using elementary ideas from analysis. Estimates of the location of crossing points are given.

Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks

1965 ◽  
Vol 21 (4) ◽  
pp. 623-633 ◽  
Author(s):  
Carl E. Pearson
Keyword(s):  
Steady State ◽  
Viscous Flow ◽  
Numerical Solutions ◽  
Preceding Paper ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Main Body ◽  
Rotating Disks ◽  
High Reynolds ◽  
Steady State Solutions

The nature of the steady-state viscous flow between two large rotating disks has often been discussed, usually qualitatively, in the literature. Using a version of the numerical method described in the preceding paper (Pearson 1965), digital computer solutions for the time-dependent case are obtained (steady-state solutions are then obtainable as limiting cases for large times). Solutions are given for impulsively started disks, and for counter-rotating disks. Of interest is the fact that, at high Reynolds numbers, the solution for the latter problem is unsymmetrical; moreover, the main body of the fluid rotates at a higher angular velocity than that of either disk.

scholarly journals Stability features of steady-state solutions for a diode with electron and ion counter-streams

2021 ◽  
Vol 2103 (1) ◽  
pp. 012204
Author(s):  
L A Bakaleinikov ◽  
V I Kuznetsov ◽  
E Yu Flegontova
Keyword(s):  
Steady State ◽  
Potential Distribution ◽  
Complex Frequency ◽  
Exponential Potential ◽  
Perturbation Amplitude ◽  
The Poisson Equation ◽  
Potential Perturbation ◽  
Time Dependent Problem ◽  
Steady State Solutions ◽  
Limiting Value

Abstract Stability features of steady-state solutions for a diode with counter-streaming electron and ion flows are studied. For this purpose, the time-dependent problem for an exponential potential perturbation with complex frequency is considered. By linearization of the Poisson equation and electron and ion densities integrodifferential equation for the potential perturbation amplitude is derived. In the case of uniform unperturbed potential distribution an explicit solution of this equation is obtained. Eigen modes of the perturbation are studied. The limiting value of the diode length above which steady state solutions in question are unstable is found. The obtained analytical Eigen modes coincide with the result of numerical simulation of the potential perturbation evolution.

scholarly journals The solution of Problems Involving the Melting and Freezing of Finite Slabs by a Method due to Portnov

1964 ◽  
Vol 14 (2) ◽  
pp. 109-128 ◽  
Author(s):  
F. Jackson
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Temperature Distribution ◽  
Heat Fluxes ◽  
Poisson Integral ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Infinite Slab ◽  
The Face ◽  
Steady State Solutions

In a recent paper (1) Portnov used a form of Poisson integral to find the exact solution for the temperature distribution in a freezing semi-infinite slab occupying the region x > 0, and having an arbitrary time dependent temperature applied at the face x = 0. Previously, Boley (2) had used a method based on Duhamel's theorem to find solutions for problems involving melting, in both finite and semi-finite regions, caused by time dependent heat fluxes. Steady-state solutions have been investigated by Landau (3), Masters (4) and others (5).

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current

1968 ◽  
Vol 2 (1) ◽  
pp. 51-57 ◽  
Author(s):  
R. C. Hewson-Browne ◽  
D. N. Burghes
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Time History ◽  
Time Dependent ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Line Current ◽  
History Of ◽  
Steady State Solutions ◽  
The Magnetic Field

This paper concerns the time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current. The two-dimensional problem is formulated and solved with two particular classes of solutions being given; namely, the steady-state solutions and the time-history of the interaction with a cloud of flux.

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