In the present study, a development of the paper [Can. J. of Phy., 2012, 90(2): 137-149] is introduced. The non-stationary BGK (Bhatnager- Gross- Krook) model of the Boltzmann nonlinear partial differential equations for a rarefied gas mixture affected by nonlinear thermal radiation field, for the first time, are 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, 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 gas mixture such as the temperature and concentration. They are substituted into the corresponding two stream Maxiwallian distribution functions permitting us to investigate the non-equilibrium thermodynamic properties of the system (gas mixture + the heated plate). 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, the second law of thermodynamic and the celebrated Onsager’s reciprocity relation for the system, are investigated. 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 the Argon-Neon binary gas mixture, for various values of both of the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.
| Published in | American Journal of Physics and Applications (Volume 2, Issue 6) |
| DOI | 10.11648/j.ajpa.20140206.13 |
| Page(s) | 121-134 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Binary Gas Mixture, Radiation Field, Exact Solutions, Travelling Wave Method, Unsteady BGK Model, Boltzmann Kinetic Equation, Moments Method, Liu-Lees Model, Boltzmann H-Theorem, Irreversible Thermodynamics
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APA Style
Taha Zakaraia Abdel Wahid. (2014). Travelling Waves Solution of the Unsteady Problem of Binary Gas Mixture Affected by a Nonlinear Thermal Radiation Field. American Journal of Physics and Applications, 2(6), 121-134. https://doi.org/10.11648/j.ajpa.20140206.13
ACS Style
Taha Zakaraia Abdel Wahid. Travelling Waves Solution of the Unsteady Problem of Binary Gas Mixture Affected by a Nonlinear Thermal Radiation Field. Am. J. Phys. Appl. 2014, 2(6), 121-134. doi: 10.11648/j.ajpa.20140206.13
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Download@article{10.11648/j.ajpa.20140206.13,
author = {Taha Zakaraia Abdel Wahid},
title = {Travelling Waves Solution of the Unsteady Problem of Binary Gas Mixture Affected by a Nonlinear Thermal Radiation Field},
journal = {American Journal of Physics and Applications},
volume = {2},
number = {6},
pages = {121-134},
doi = {10.11648/j.ajpa.20140206.13},
url = {https://doi.org/10.11648/j.ajpa.20140206.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20140206.13},
abstract = {In the present study, a development of the paper [Can. J. of Phy., 2012, 90(2): 137-149] is introduced. The non-stationary BGK (Bhatnager- Gross- Krook) model of the Boltzmann nonlinear partial differential equations for a rarefied gas mixture affected by nonlinear thermal radiation field, for the first time, are 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, 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 gas mixture such as the temperature and concentration. They are substituted into the corresponding two stream Maxiwallian distribution functions permitting us to investigate the non-equilibrium thermodynamic properties of the system (gas mixture + the heated plate). 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, the second law of thermodynamic and the celebrated Onsager’s reciprocity relation for the system, are investigated. 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 the Argon-Neon binary gas mixture, for various values of both of the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.},
year = {2014}
}
TY - JOUR T1 - Travelling Waves Solution of the Unsteady Problem of Binary Gas Mixture Affected by a Nonlinear Thermal Radiation Field AU - Taha Zakaraia Abdel Wahid Y1 - 2014/12/05 PY - 2014 N1 - https://doi.org/10.11648/j.ajpa.20140206.13 DO - 10.11648/j.ajpa.20140206.13 T2 - American Journal of Physics and Applications JF - American Journal of Physics and Applications JO - American Journal of Physics and Applications SP - 121 EP - 134 PB - Science Publishing Group SN - 2330-4308 UR - https://doi.org/10.11648/j.ajpa.20140206.13 AB - In the present study, a development of the paper [Can. J. of Phy., 2012, 90(2): 137-149] is introduced. The non-stationary BGK (Bhatnager- Gross- Krook) model of the Boltzmann nonlinear partial differential equations for a rarefied gas mixture affected by nonlinear thermal radiation field, for the first time, are 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, 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 gas mixture such as the temperature and concentration. They are substituted into the corresponding two stream Maxiwallian distribution functions permitting us to investigate the non-equilibrium thermodynamic properties of the system (gas mixture + the heated plate). 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, the second law of thermodynamic and the celebrated Onsager’s reciprocity relation for the system, are investigated. 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 the Argon-Neon binary gas mixture, for various values of both of the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed. VL - 2 IS - 6 ER -
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