Fluid Mechanics

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Travelling Waves Solution of the Unsteady Flow Problem of a Collisional Plasma Bounded by a Moving Plate

Received: 21 September 2017    Accepted: 26 October 2017    Published: 15 March 2018
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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.

DOI 10.11648/j.fm.20180401.14
Published in Fluid Mechanics (Volume 4, Issue 1, March 2018)
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), 2024. Published by Science Publishing Group

Keywords

Rayleigh Flow Problem, Charged Gas, Boltzmann Equation, Maxwell Equations, Exact Solution, Boltzmann H-Theorem, Internal Energy, Extended Gibbs Formula

References
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[12] A. M. Abourabia and Taha Zakaraia Abdel Wahid " Solution of The Krook Kinetic Equation Model and Non-Equilibrium Thermodynamics of a Rarefied Gas Affected by a Nonlinear Thermal Radiation Field", J. Non-Equilibrium Thermodynamic, 36 (2011), 75–98.
[13] A. M. Abourabia and Taha Zakaraia Abdel Wahid " Kinetic and thermodynamic treatment for the Rayleigh flow problem of an inhomogeneous charged gas mixture", J. Non-Equilibrium Thermodynamic, 37, 1, (2012), 1–25.
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[17] Taha Zakaraia Abdel Wahid " Exact solution of the unsteady Krook kinetic model and nonequilibrium thermodynamic study for a rarefied gas affected by a nonlinear thermal radiation field. ", Canadian Journal of Physics (2013); 91(3):201-210.
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Author Information
  • Department of Basic Sciences, El-Gezeera High Institute for Engineering and Technology, Cairo, Egypt; Mathematic Department, Faculty of Science, Menofia University, Shebin El-Kom, Egypt

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    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

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    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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    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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  • @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://download.sciencepg.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}
    }
    

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  • 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
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    PB  - Science Publishing Group
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    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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