scholarly journals Application of Boltzmann’s Kinetic Equation to Research of Approach to Equilibrium Thermal Radiation of Rarefied Gas

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
A. N. Volobuev ◽  
Keyword(s):  
Kinetic Equation ◽  
Thermal Radiation ◽  
Rarefied Gas ◽  
Approach To Equilibrium

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.

Diatomic gas—thermal radiation interaction A model equation for the internal fluid

1972 ◽  
Vol 7 (2) ◽  
pp. 235-246 ◽  
Author(s):  
Warren F. Phillips ◽  
Vedat S. Arpaci
Keyword(s):  
Kinetic Equation ◽  
Thermal Radiation ◽  
Model Equation ◽  
Diatomic Molecules ◽  
Collision Term ◽  
Model Kinetic Equation ◽  
Photon Interaction ◽  
Internal Fluid ◽  
Proposed Model ◽  
Alternative Approach

A model kinetic equation for the internal fluid of diatomic molecules which interacts with thermal radiation is proposed. The cross-collision term developed for the molecule-photon interaction has the property that molecules and the sum of internal and photon energies are conserved. An alternative approach to this term based on the product of two BGKW collision operators yields the same result. It is also shown that the proposed model leads to an H-theorem.

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.

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