Gas flows caused by evaporation and condensation on two parallel condensed phases and the negative temperature gradient: Numerical analysis by using a nonlinear kinetic equation

1994 ◽  
Vol 6 (3) ◽  
pp. 1379-1395 ◽  
Author(s):  
Kazuo Aoki ◽  
Noboru Masukawa
Keyword(s):  
Kinetic Equation ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Negative Temperature ◽  
Gas Flows ◽  
Condensed Phases ◽  
Evaporation And Condensation ◽  
Nonlinear Kinetic

Weighted statistical modelling algorithms with branching and extension of a model ensemble of interacting particles

2016 ◽  
Vol 31 (4) ◽  
Author(s):  
Sergey V. Rogasinsky
Keyword(s):  
Approximate Solution ◽  
Kinetic Equation ◽  
Numerical Analysis ◽  
Model Problem ◽  
Statistical Modelling ◽  
Model Ensemble ◽  
Interacting Particles ◽  
Nonlinear Kinetic

AbstractA modification of the weighted statistical modelling of the evolution of an ensemble of interacting particles is constructed for approximate solution of a nonlinear kinetic equation. If the auxiliary weight exceeds one, we propose to use randomized branching of trajectory of the model ensemble of particles or its corresponding extension. Numerical analysis of constructed algorithms is performed for specifically formulated model problem on relaxation of a mixture of two gases with very different concentrations.

A Numerical Method for Heat Conduction Problems

1974 ◽  
Vol 96 (3) ◽  
pp. 307-312 ◽  
Author(s):  
M. J. Reiser ◽  
F. J. Appl
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Steady State ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Singular Integral ◽  
Integral Method ◽  
Two Dimensional ◽  
Convection Boundary ◽  
Steady State Heat

A singular integral method of numerical analysis for two-dimensional steady-state heat conduction problems with any combination of temperature, gradient, or convection boundary conditions is presented. Excellent agreement with the exact solution is illustrated for an example problem. The method is used to determine the solution for a fin bank with convection.

Solidification of AlSi Alloys in the ARTEMIS and ARTEX Facilities Including Rotating Magnetic Fields – A Combined Experimental and Numerical Analysis

2006 ◽  
Vol 508 ◽  
pp. 199-204 ◽  
Author(s):  
Marc Hainke ◽  
Sonja Steinbach ◽  
Johannes Dagner ◽  
Lorenz Ratke ◽  
Georg Müller
Keyword(s):  
Magnetic Field ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Temperature Gradient ◽  
Magnetic Fields ◽  
Time Dependent ◽  
Flow Conditions ◽  
Rotating Magnetic Fields ◽  
Microstructural Parameters ◽  
Wide Range

The solidification microstructure is the consequence of a wide range of process parameters, like the growth velocity, the temperature gradient and the composition. Although the influence of these parameters is nowadays considerably well understood, an overall theory of the influence of convection on microstructural features is still lacking. The application of time dependent magnetic fields during directional solidification offers the possibility to create defined solidification and flow conditions. In this work, we report about solidification experiments in the ARTEMIS and ARTEX facilities including rotating magnetic fields (RMF). The effect of the forced melt flow on microstructural parameters like the primary and secondary dendrite arm spacing is analyzed for a wide range of magnetic field parameters. The experimental analysis is supported by a rigorous application of numerical modeling. An important issue is hereby the prediction of the resulting macrosegregation, i.e., differences in the composition on the scale of the sample (macroscale) due to the RMF. For the considered configuration and parameters an axial enrichment of Si is found beyond a certain magnetic field strength. The results are compared to available theories and their applicability is discussed.

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