Solution of the Krook kinetic equation model and non-equilibrium thermodynamics of a rarefied gas affected by a non-linear thermal radiation field

2011 ◽  
Vol 36 (1) ◽  
Author(s):  
Aly Maher Abourabia ◽  
Taha Zakaraia Abdel Wahid
Keyword(s):  
Kinetic Equation ◽  
Thermal Radiation ◽  
Radiation Field ◽  
Rarefied Gas ◽  
Equation Model ◽  
Equilibrium Thermodynamics ◽  
Non Linear ◽  
Thermal Radiation Field ◽  
Non 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.

Statistics of the Thermal Radiation Field

1965 ◽  
Vol 139 (1B) ◽  
pp. B202-B211 ◽  
Author(s):  
Evelyn Fox Keller
Keyword(s):  
Thermal Radiation ◽  
Radiation Field ◽  
Thermal Radiation Field

Kinetic and thermodynamic treatments of a neutral binary gas mixture affected by a nonlinear thermal radiation field

2012 ◽  
Vol 90 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Aly Maher Abourabia ◽  
Taha Zakaraia Abdel Wahid
Keyword(s):  
Thermal Radiation ◽  
Radiation Field ◽  
Molar Fraction ◽  
Distribution Functions ◽  
Mixture Component ◽  
Gas Mixture ◽  
Nonlinear Thermal Radiation ◽  
Binary Gas Mixture ◽  
Kinetic Coefficients ◽  
Thermal Radiation Field

In the present study, the kinetic and the irreversible thermodynamic properties of a binary gas mixture, under the influence of a thermal radiation field, are presented from the molecular viewpoint. In a frame comoving with the fluid, the Bhatnagar–Gross–Krook model of the kinetic equation is analytically applied, using the Liu–Lees model. We apply the moment method to follow the behavior of the macroscopic properties of the binary gas mixture, such as the temperature and the concentration. The distinction and comparisons between the perturbed and equilibrium distribution functions are illustrated for each gas mixture component. From the viewpoint of the linear theory of irreversible thermodynamics we obtain the entropy, entropy flux, entropy production, thermodynamic forces, and kinetic coefficients. We verify the second law of thermodynamics and 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 Gibbs’ formula. The results are applied to the argon–neon binary gas mixture, for various values of both the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.

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