Generalized Poiseuille profiles in plasma flows in a stabilized region of a plasma generator

The equations of motion and energy balance in view of Joule heat release and temperature dependence of the coefficient of viscosity are used to generalize the Poiseuille solution to the case of stabilized laminar flow of low-temperature plasma in the channel of a plasma generator. Analytical relations are convenient for use in estimating various effects associated with a flow of plasma in channels and in processing the experimental results. The effect of the nonmonotonic temperature dependence of dynamic viscosity on the velocity profile is investigated. It is demonstrated that the nonmonotonic variation of viscosity over the channel cross section in the general case causes the emergence of two inflection points in the velocity profile; this, in turn, may cause the emergence of an instability due to the hydrodynamic mechanism of Kelvin–Helmholtz rather than to the mechanism of superheating. The numerical solutions of the Poiseuille and Elenbaas–Heller equations in a wide range of the working parameters of a plasma generator support the conclusions based on analytical solutions of these equations.