On Analytical Solution of a Plasma over a Moving Rigid Plate under the Influence of Non-linear Non-uniform Applied External Magnetic Field

In this study, we mainly focus on the behavior of an electron gas produced by argon plasma that is bounded by a moving rigid flat plate. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are investigated. We used the BGK model of the Boltzmann kinetic equation, which is fundamental in the study of the gas dynamics from the continuum flow to the free-molecular regimes with Maxwellian velocity distribution functions of the various species. An exact analytical solution of the model equations for the unsteady flow is given using the moment and the traveling wave methods. The behavior of the mean velocity of electrons is illustrated, which compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying the principles of irreversible thermodynamics and Gibbs formula. It is found that the thermodynamic variables verify the Boltzmann’s H–theorem, the principle of Le Chatelier, and the Thermodynamics Second Law for the non-equilibrium processes of the system. Qualitative agreements with previous related papers are introducing. 3-Dimensional graphics for the calculating variables are offering, and their behavior is deeply discussed.