A self-similar solution for unsteady isothermal and adiabatic flows behind the shock wave in a dusty non-ideal rotating medium under the action of magnetic field

Abstract

In this paper, the similarity solutions using Lie group analysis for shock wave propagation in a rotational axisymmetric mixture of small solid particles of micro-size and a non-ideal gas with azimuthal magnetic field are obtained. In the mixture, the solid particles are distributed uniformly. For isothermal and adiabatic flows, the Lie group analysis is used to discuss all possible cases of similarity solutions. The local Lie group generator’s arbitrary constants generate a range of solutions with power and exponential law shock paths. A detailed discussion of the similarity solution for isothermal and adiabatic flows with a power-law shock path is presented. The constant density for the ambient medium has been assumed. The effect of changing the Alfven Mach number, non-idealness parameter, and other parameters on shock wave strength and flow variables is explored. These parameters are observed to have a decaying impact on shock waves. The effect of varying the Alfven Mach number, non-idealness parameter and other parameters on shock wave strength and flow variables is investigated. The parameter of non-idealness and Alfven Mach number are noted to have a decaying effect on shock waves.