Kinetic equation for an extremely rarefied gas of fast particles interacting with a crystal

1977 ◽  
Vol 20 (4) ◽  
pp. 487-490
Author(s):  
I. I. Ol'khovskii ◽  
M. B. Ependiev ◽  
N. M. Sadykov
Keyword(s):  
Kinetic Equation ◽  
Rarefied Gas

scholarly journals On the simulation of gas ionization by fast electrons

2021 ◽  
pp. 1-12
Author(s):  
Andrei Vsevolodovich Berezin ◽  
Aleksandr Duhanin Aleksandr Duhanin ◽  
Oleg Sergeevich Kosarev ◽  
Mikhail Borisovich Markov ◽  
Sergey Vladimirovich Parot'kin ◽  
...  
Keyword(s):  
Kinetic Equation ◽  
Cross Sections ◽  
Impact Ionization ◽  
Rarefied Gas ◽  
Initial Distribution ◽  
Secondary Electrons ◽  
Spatial Homogeneity ◽  
Fast Electrons ◽  
Gas Dynamic ◽  
Gas Ionization

The gas-dynamic parameters of an ionized medium formed during impact ionization of a rarefied gas by fast electrons are considered. The concentration, drift velocity, and specific energy of low-energy secondary electrons are constructed by an approximate solution of the kinetic equation. Approximations of the spatial homogeneity of the kinetic equation and the isotropy of the initial distribution of secondary electrons during impact ionization are used. Additional approximations are related to the structure of the distribution function of secondary electrons and averaging of the cross sections.

scholarly journals Rarefied Poiseuille Flow in a Circular Tube

2019 ◽  
Vol 224 ◽  
pp. 02001
Author(s):  
Oksana Germider ◽  
Vasily Popov
Keyword(s):  
Kinetic Equation ◽  
Chebyshev Polynomials ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Circular Tube ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Model Kinetic Equation ◽  
Algebraic Equations ◽  
Rarefied Gas Flows

An isothermal rarefied gas flow through a long circular tube due to longitudinal pressure gradient (a three-dimensional Poiseuille problem) was studied using the linearized Bhatnagar-Gross-Krook model kinetic equation over the whole range of the Knudsen numbers covering both free molecular and hydrodynamic regimes. The solution of the model kinetic equation with the diffuse boundary condition is obtained by the collocation method. This approach is based on the Chebyshev polynomials and rational Chebyshev functions. Choosing the zeros of Chebyshev polynomials in the multivariate range of integration for the collocation points, we reduce this problem to a set of algebraic equations. Based on the proposed approach, we have calculated the mass and the heat fluxes through the tube. The obtained results have also been compared with other studies. The developed approach may also be applied to a more general class of problems of rarefied gas flows in microand nanotubes.

Exact solution of the unsteady Krook kinetic model and nonequilibrium thermodynamic study for a rarefied gas affected by a nonlinear thermal radiation field

2013 ◽  
Vol 91 (3) ◽  
pp. 201-210 ◽  
Author(s):  
Taha Zakaraia Abdel Wahid
Keyword(s):  
Exact Solution ◽  
Kinetic Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Radiation Field ◽  
Rarefied Gas ◽  
Nonlinear Partial Differential Equations ◽  
Nonequilibrium Thermodynamic ◽  
Nonlinear Thermal Radiation

A development of the previous paper (J. Non-Equilib. Thermodyn. 36, 75 (2011)) is introduced. The nonstationary Krook kinetic equation model for a rarefied gas affected by nonlinear thermal radiation field is solved, instead of the stationary equation. In a frame comoving with the fluid, analytically the Bhatnager–Gross–Krook model kinetic equation is applied. The travelling wave solution method is used to get the exact solution of the nonlinear partial differential equations. These equations were produced from applying the moment method to the unsteady Boltzmann equation. Now we should solve nonlinear partial differential equations in place of nonlinear ordinary differential equations, which represent an arduous task. The unsteady solution gives the problem a great generality and more applications. The new problem is investigated to follow the behavior of the macroscopic properties of the gas, such as the temperature and concentration. They are substituted into the corresponding two-stream maxiwallian distribution functions permitting us to investigate the nonequilibrium thermodynamic properties of the system (gas particles + the heated plate). The entropy, entropy flux, entropy production, thermodynamic forces, and kinetic coefficients are obtained. We investigate the verification of the Boltzmann H-theorem, Le Chatelier principle, the second law of thermodynamic and the celebrated Onsager's reciprocity relation for the system. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive parameters are estimated via the Gibbs formula. The results are applied to helium gas for various radiation field intensities due to different plate temperatures. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.

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.

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