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Travelling Wave Solution of the Unsteady BGK Model for a Rarefied Gas Affected by a Thermal Radiation Field. |
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PP: 75-87 |
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Author(s) |
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Taha Zakaraia Abdel Wahid,
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Abstract |
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| In the present study, a development of the paper [JNET, 2011, 36 (1), 75-98] is introduced. The non-stationary BGK (Bhatnager- Gross- Krook) model of the kinetic equations for a rarefied gas affected by nonlinear thermal radiation field is solved instead of the stationary equations. 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, a system of nonlinear partial differential equations should be solved 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 rarefied gas such as the temperature and concentration. The non-equilibrium thermodynamic properties of the system (gas + the heated plate) are investigated. The entropy, entropy flux, entropy production, thermodynamic forces, kinetic coefficients are obtained for the mixture. The verification of the Boltzmann H-theorem, Le Chatelier principle and the second law of thermodynamic for the system, are presented. 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. 3D-graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed. |
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