Near-frozen quasi-one-dimensional flow II. De-excitation shocks

1967 ◽  
Vol 262 (1125) ◽  
pp. 225-250 ◽  
Keyword(s):  
Power Law ◽  
Infinite Sequence ◽  
Relaxation Frequency ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Nozzle Flows ◽  
Non Equilibrium

The possible existence of compression regions, analogous to condensation shocks, in expanding non-equilibrium nozzle flows is noted. For power-law nozzle shapes the structure and position of these ‘de-excitation shocks’ are derived when the relaxation frequency decays algebraically with temperature. The asymptotic limiting solutions downstream of the de-excitation shocks are also discussed. For certain nozzle shapes it appears that this limiting solution is an infinite sequence of such shocks separated in part by regions of near-frozen flow.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

Statistical Mechanics of Thermotransport of a Heavy Impurity in an Insulating Solid

1971 ◽  
Vol 26 (1) ◽  
pp. 10-17 ◽  
Author(s):  
A. R. Allnatt
Keyword(s):  
Heat Flux ◽  
Time Correlation ◽  
Three Dimensions ◽  
Time Correlation Functions ◽  
Single Vacancy ◽  
One Dimensional ◽  
Enthalpy Of Activation ◽  
Heavy Impurity ◽  
The One ◽  
Non Equilibrium

AbstractA kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice of lighter atoms in a temperature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jump probability and hence the heat of transport, q*. for a single vacancy jump of the impurity, q* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms in­volving time correlation functions. The most important non-equilibrium term concerns the cor­relation between the force on the impurity and a microscopic heat flux. A plausible extension to three dimensions is suggested and the relation to earlier isothermal and non-isothermal theories is indicated

Performance Prediction for Automotive Turbocharger Compressors

1975 ◽  
Vol 189 (1) ◽  
pp. 557-565 ◽  
Author(s):  
A. Whitfield ◽  
F. J. Wallace
Keyword(s):  
Performance Prediction ◽  
Flow Analysis ◽  
Compressor Stage ◽  
Thermodynamic Models ◽  
Flow Rates ◽  
Design Point ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Performance Map ◽  
The Individual

A procedure to predict the complete performance map of turbocharger centrifugal compressors is presented. This is based on a one-dimensional flow analysis using existing published loss correlations that were available and thermodynamic models to describe the incidence loss and slip factor variation at flow rates which differ from the design point. To predict the losses within the complete compressor stage using a one-dimensional flow procedure, it is necessary to introduce a number of empirical parameters. The uncertainty associated with these empirical parameters is assessed by studying the effect of varying them upon the individual losses and upon the overall predicted performance.

scholarly journals Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

2015 ◽  
Vol 114 (12) ◽  
Author(s):  
A. S. Campbell ◽  
D. M. Gangardt ◽  
K. V. Kheruntsyan
Keyword(s):  
Power Law ◽  
Bose Gas ◽  
Sudden Expansion ◽  
One Dimensional
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