Lie symmetry approach for shock wave propagation in a self-gravitating non-ideal gas under the influence of monochromatic radiation and magnetic field in rotating medium

The propagation of cylindrical shock wave influenced by monochromatic radiation and magnetic field in a self-gravitating non-ideal gas for a rotating medium has been investigated by using the Lie symmetry method. Ahead of the shock front, the ambient density of the medium is taken as constant, while the magnetic field, azimuthal and axial velocities vary over time. By using the Lie symmetry approach, the optimal system for the governing equations, the similarity variable and transformations are obtained. By the use of derived similarity transformations, the governing equations change into a system of ODEs (ordinary differential equations). The software package “Mathematica” has been utilized to solve the system of ODEs numerically and to generate the graphs for the flow variables distribution. In this article, the strength of the shock wave and variations in the flow variables of the flow field region behind the shock front, which are influenced by the strength of the ambient magnetic field, gravitational parameter, non-idealness parameter, adiabatic exponent, and rotational parameter, are examined in detail. It has been demonstrated that the magnetic field, non-idealness parameter, adiabatic exponent, and rotational parameter have decaying effect on the shock wave. In contrast, the gravitational parameter has reversed impact on the shock strength.