scholarly journals The heat flux from a relativistic kinetic equation with a simplified collision kernel

2009 ◽  
Author(s):  
A. Sandoval-Villalbazo ◽  
A. L. Garcia-Perciante ◽  
L. S. Garcia-Colin ◽  
Kerstin E. Kunze ◽  
Marc Mars ◽  
...  
Keyword(s):  
Heat Flux ◽  
Kinetic Equation ◽  
Collision Kernel ◽  
Relativistic Kinetic Equation

A KINETIC MODEL FOR DROPLET COALESCENCE IN DENSE SPRAYS

2001 ◽  
Vol 11 (05) ◽  
pp. 867-882 ◽  
Author(s):  
JEAN-MICHEL ROQUEJOFFRE ◽  
PHILIPPE VILLEDIEU
Keyword(s):  
Asymptotic Behavior ◽  
Kinetic Equation ◽  
Kinetic Model ◽  
Continuous Dependence ◽  
Positive Measure ◽  
Mass Conservation ◽  
Collision Kernel ◽  
Droplet Coalescence ◽  
Spatially Homogeneous ◽  
Time Asymptotic Behavior

This paper is devoted to the matematical analysis of a kinetic equation describing the process of droplet coalescence in a spatially homogeneous spray. In the first part, existence of a positive measure valued solution is proved, under very general assumptions on the collision kernel. In the second part, mass conservation and momentum preservation, as well as uniqueness and continuous dependence is established, under some more restrictive — but physically reasonable — assumptions on the model. Lastly, the time-asymptotic behavior of the solution is studied.

scholarly journals Lagrangian Formulation of a Consistent Relativistic Guiding Center Theory

1983 ◽  
Vol 38 (6) ◽  
pp. 601-607 ◽  
Author(s):  
H. K. Wimmel
Keyword(s):  
Kinetic Equation ◽  
Energy Density ◽  
Relativistic Theory ◽  
Lagrangian Formulation ◽  
Moment Equations ◽  
Relativistic Limit ◽  
Relativistic Kinetic Equation ◽  
Center Density ◽  
Liouville’S Theorem

A new relativistic guiding center mechanics is presented that conserves energy (in timeindpendent Fields) and satisfies a Liouville's theorem. The theory reduces to Littlejohn's theory in the non-relativistic limit and agrees to leading orders in ε ≡ rg/L with the relativistic theory by Morozov and Solov'ev (which generally lacks a Liouville's theorem). The new theory is developed from an appropriate Lagrangian and is supplemented by a collisionless relativistic kinetic equation for the guiding centers. Moment equations for guiding center density and energy density are also derived

scholarly journals Relativistic Quantum Kinetic Equation of the Vlasov Type for Systems with Internal Degrees of Freedom

1998 ◽  
Vol 07 (04) ◽  
pp. 515-526 ◽  
Author(s):  
S. A. Smolyansky ◽  
A. V. Prozorkevich ◽  
S. Schmidt ◽  
D. Blaschke ◽  
G. Röpke ◽  
...  
Keyword(s):  
Kinetic Equation ◽  
Conservation Laws ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Quantum Kinetic Equation ◽  
Heisenberg Picture ◽  
Relativistic Kinetic Equation ◽  
Field Systems ◽  
Internal Degrees Of Freedom

We present an approach to derive a relativistic kinetic equation of the Vlasov type. Our approach is especially reliable for the description of quantum field systems with many internal degrees of freedom. The method is based on the Heisenberg picture and leads to a kinetic equation which fulfills the conservation laws. We apply the approach to the standard Walecka Lagrangian and an effective chiral Lagrangian.

scholarly journals Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Mustafa Hadj-Nacer ◽  
Dilesh Maharjan ◽  
Minh-Tuan Ho ◽  
Stefan K. Stefanov ◽  
Irina Graur ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Kinetic Equation ◽  
Temperature Jump ◽  
Rarefied Gas ◽  
Large Temperature ◽  
Model Kinetic Equation ◽  
Temperature Ratio ◽  
Slip Regime ◽  
S Model

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter δ, ratios of hotter to cooler surface temperatures T, and inner to outer radii ratio R. The results of S-model kinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T=1.1 and large radius ratios R≥0.5; however, for large temperature ratio, a pronounced disagreement is observed.

Cross field thermal transport in highly magnetized plasmas

1992 ◽  
Vol 437 (1899) ◽  
pp. 55-65 ◽  
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Kinetic Equation ◽  
Mass Transport ◽  
Heat Transport ◽  
Electrostatic Interactions ◽  
Charged Particles ◽  
Non Local ◽  
Field Lines ◽  
The Magnetic Field

We construct a non-local kinetic equation for a plasma in a very strong magnetic field B where the charged particles coincide with their guiding centres and have zero drifts. It is shown that, although in this system mass transport occurs only along the field lines, heat transport cannot be confined only in the direction of the magnetic field. In particular, we estimate that a finite cross field heat flux scaling as 3/2 n ∂ T /∂ t = ∂( k ∞ ⊥ ∂ T /∂ x )∂ x ; k ∞ ⊥ = 3/2π ½ ( n 2 e 4 / m ½ T 3/2 ) L 2 ⊥ can be driven by collisions between like particles at the limit B → ∞. Hence, the classical B -2 dependence of k ⊥ must be modified to comply with this result. The choice of the cut-off length L ⊥ , representing the distance across B over which electrostatic interactions can be sustained, is discussed briefly at the end of the present work.

Simulation of Heat Transfer Across Rarefied Gas in Annular and Planar Geometries: Comparison of Navier-Stokes, S-Model and DSMC Methods Results

2015 ◽  
Author(s):  
Dilesh Maharjan ◽  
Mustafa Hadj-Nacer ◽  
Minh-Tuan Ho ◽  
Stefan K. Stefanov ◽  
Irina Graur ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Kinetic Equation ◽  
Rarefied Gas ◽  
Model Kinetic Equation ◽  
Parallel Plates ◽  
Coaxial Cylinders ◽  
Aspect Ratios ◽  
S Model ◽  
Analytical Expressions

Steady state heat transfer through a rarefied gas confined between two parallel plates or two coaxial cylinders maintained at different temperatures is investigated using the nonlinear S-model kinetic equation and the DSMC technique for a large range of gas rarefaction. The profiles of heat flux, density and temperature are reported for different values of gas rarefaction parameter and given values of temperature and aspect ratios. In the slip regime the results of the S-model and DSMC technique are compared to the simulations performed using the Lin and Willis temperature jump boundary conditions at the at the solid surface implemented in ANSYS/Fluent CFD simulations. The analytical expressions for density number, temperature and heat flux in the free molecular regimes are obtained for both parallel plates and coaxial cylinders geometries with hot and cold surfaces having different values of the thermal accommodation coefficient. The solutions of these analytical expressions are compared to the S-model kinetic equation and DSMC technique results in the free molecular regime.

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