Exact solutions of plasma flow on a rigid oscillating plate under the effect of an external non-uniform electric field

Abstract

The paper is concerned with the flow behavior of a helium-plasma bounded by a rigid, oscillating flat plate. The influences of an unsteady nonlinear external electric field (NEEF) on the plasma fluid were investigated. Attention has been focused on the Bhatnagar-Gross-Krook (BGK)–type of the Boltzmann kinetic equation (BKE) to study the gas dynamics with the Maxwellian velocity distribution function (VDF). An analytical solution of the model equations was given using the moment and the traveling wave methods. The role of the mean velocity, shear stress, viscosity coefficient, and electromagnetic fields are investigated. We found that the effect of the NEEF is powerful in plasma. It made it fluctuate and perturbed strongly compared to the effect of the nonlinear external magnetic field (NEMF). So, in the plasma controlling process, we should use NEMF instead of NEEF to save the equilibrium state (ES) for a plasma fluid. The thermodynamic properties were investigated, and qualitative agreements with previous related papers were demonstrated using 3-Dimensional graphics for the calculating variables. This study's significance was due to its vast applications in numerous fields, such as in physics, electrical engineering, micro-electro-mechanical systems (MEMS), or Nano-electro-mechanical systems (NEMS) devices, and various commercial-industrial applications.