Travelling waves solution of the unsteady flow problem of a rarefied nonhomogeneous charged gas bounded by an oscillating plate
type: Item
instance of: scholarly article
title: Travelling waves solution of the unsteady flow problem of a rarefied nonhomogeneous charged gas bounded by an oscillating plate
zbMATH Open document ID: 1299.76228
DOI: 10.1155/2013/503729
author: Taha Zakaraia Abdel Wahid
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: The extension of the previous paper [the author and \textit{S. K. Elagan}, Can. J. Phys. 90, No. 10, 987--998 (2012; \url{doi:10.1139/p2012-095}] has been made for a nonhomogeneous charged rarefied gas mixture (two-component plasma) instead of a single electron gas. Therefore, the effect of the positive ion collisions with electrons and with each other is taken into consideration, which was ignored, as an approximation, in the earlier work. Thus, we will have four collision terms (electron-electron, electron-ion, ion-ion, and ion-electron) instead of one term, as was studied before. These collision terms are added together with a completely additional system of differential equations for ions. This study is based on the solution of the Bhatnager-Gross-Krook (BGK) model of the Boltzmann kinetic equation coupled with Maxwell's equations. The initial-boundary value problem of the Rayleigh flow problem applied to the system of the two-component plasma (positive ions + electrons), bounded by an oscillating plate, is solved. This situation, for the best of my knowledge, is presented from the molecular viewpoint for the first time. For this purpose, the traveling wave solution method is used to get the exact solution of the nonlinear partial differential equations. In addition, the accurate formula of the whole four-collision frequency terms is presented. The distinction and comparisons between the perturbed and the equilibrium velocity distribution functions are illustrated. Definitely, the equilibrium time for electrons and for ions is calculated. The relation between those times and the relaxation time is deduced for both species of the mixture. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma.
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 6372418
Wikidata QID: Q59028192
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/503729
OpenAlex ID: W2010799698
cites work: Kinetic treatment for the exact solution of the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas bounded by an oscillating plate
cites work: Direct methods for solving the Boltzmann equation and study of nonequilibrium flows
cites work: Q4188958
cites work: Q5842362
cites work: Understanding Non-equilibrium Thermodynamics
cites work: Solution of the Krook kinetic equation model and non-equilibrium thermodynamics of a rarefied gas affected by a non-linear thermal radiation field
cites work: The unsteady Boltzmann kinetic equation and non-equilibrium thermodynamics of an electron gas for the Rayleigh flow problem
cites work: Kinetic and thermodynamic treatment for the exact solution of the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas
cites work: Kinetic and thermodynamic treatment for the Rayleigh flow problem of an inhomogeneous charged gas mixture
cites work: Gas flow near a plate oscillating longitudinally with an arbitrary frequency
cites work: Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime
cites work: Oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes
cites work: Nonplanar oscillatory shear flow: From the continuum to the free-molecular regime
cites work: Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics
cites work: Analytical solutions of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles
cites work: Analytical solutions of the Rayleigh flow problem for a highly rarefied gas of nonhomogeneous system of charged particles
cites work: A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
cites work: The Physics of Plasmas
cites work: On the kinetic theory of rarefied gases
description: scientific article; zbMATH DE number 6372418