The extension of the previous paper [Can. J. Phys. Vol. 88, (2010), 501–511] has been made. Therefore, the effect of the neutral atoms collisions with electrons and with positive ions is taken into consideration, which was ignored, for the sake of simplicity, in the earlier work. Thus, we will have multi-collision terms (electron–electron, electron–ion, electron– neutral) instead of one term, as was studied before for the sake of facilitation. These collision terms are needed to obtain the real physical situation. The new procedures will increase the ability of the research applications. This study is based on the solution of the BGK (Bhatnager–Gross–Krook) model of the nonlinear partial differential Boltzmann equations coupled with Maxwell’s partial differential equations. The initial-boundary value problem of the Rayleigh flow problem applied to the system of the plasma (positive ions + electrons+ neutral atoms), bounded by a moving plate, is solved. For this purpose, the traveling wave solution method is used to get the exact solution of the nonlinear partial differential equations system. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both dia-magnetic and para-magnetic plasma. The results are applied to a typical model of laboratory argon plasma. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.
| Published in | Fluid Mechanics (Volume 4, Issue 1) |
| DOI | 10.11648/j.fm.20180401.14 |
| Page(s) | 27-37 |
| 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), 2018. Published by Science Publishing Group |
Rayleigh Flow Problem, Charged Gas, Boltzmann Equation, Maxwell Equations, Exact Solution, Boltzmann H-Theorem, Internal Energy, Extended Gibbs Formula
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APA Style
Taha Zakaraia Abdel Wahid. (2018). Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate. Fluid Mechanics, 4(1), 27-37. https://doi.org/10.11648/j.fm.20180401.14
ACS Style
Taha Zakaraia Abdel Wahid. Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate. Fluid Mech. 2018, 4(1), 27-37. doi: 10.11648/j.fm.20180401.14
AMA Style
Taha Zakaraia Abdel Wahid. Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate. Fluid Mech. 2018;4(1):27-37. doi: 10.11648/j.fm.20180401.14
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Download@article{10.11648/j.fm.20180401.14,
author = {Taha Zakaraia Abdel Wahid},
title = {Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate},
journal = {Fluid Mechanics},
volume = {4},
number = {1},
pages = {27-37},
doi = {10.11648/j.fm.20180401.14},
url = {https://doi.org/10.11648/j.fm.20180401.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20180401.14},
abstract = {The extension of the previous paper [Can. J. Phys. Vol. 88, (2010), 501–511] has been made. Therefore, the effect of the neutral atoms collisions with electrons and with positive ions is taken into consideration, which was ignored, for the sake of simplicity, in the earlier work. Thus, we will have multi-collision terms (electron–electron, electron–ion, electron– neutral) instead of one term, as was studied before for the sake of facilitation. These collision terms are needed to obtain the real physical situation. The new procedures will increase the ability of the research applications. This study is based on the solution of the BGK (Bhatnager–Gross–Krook) model of the nonlinear partial differential Boltzmann equations coupled with Maxwell’s partial differential equations. The initial-boundary value problem of the Rayleigh flow problem applied to the system of the plasma (positive ions + electrons+ neutral atoms), bounded by a moving plate, is solved. For this purpose, the traveling wave solution method is used to get the exact solution of the nonlinear partial differential equations system. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both dia-magnetic and para-magnetic plasma. The results are applied to a typical model of laboratory argon plasma. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.},
year = {2018}
}
TY - JOUR T1 - Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate AU - Taha Zakaraia Abdel Wahid Y1 - 2018/03/15 PY - 2018 N1 - https://doi.org/10.11648/j.fm.20180401.14 DO - 10.11648/j.fm.20180401.14 T2 - Fluid Mechanics JF - Fluid Mechanics JO - Fluid Mechanics SP - 27 EP - 37 PB - Science Publishing Group SN - 2575-1816 UR - https://doi.org/10.11648/j.fm.20180401.14 AB - The extension of the previous paper [Can. J. Phys. Vol. 88, (2010), 501–511] has been made. Therefore, the effect of the neutral atoms collisions with electrons and with positive ions is taken into consideration, which was ignored, for the sake of simplicity, in the earlier work. Thus, we will have multi-collision terms (electron–electron, electron–ion, electron– neutral) instead of one term, as was studied before for the sake of facilitation. These collision terms are needed to obtain the real physical situation. The new procedures will increase the ability of the research applications. This study is based on the solution of the BGK (Bhatnager–Gross–Krook) model of the nonlinear partial differential Boltzmann equations coupled with Maxwell’s partial differential equations. The initial-boundary value problem of the Rayleigh flow problem applied to the system of the plasma (positive ions + electrons+ neutral atoms), bounded by a moving plate, is solved. For this purpose, the traveling wave solution method is used to get the exact solution of the nonlinear partial differential equations system. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both dia-magnetic and para-magnetic plasma. The results are applied to a typical model of laboratory argon plasma. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed. VL - 4 IS - 1 ER -
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