Lie symmetry analysis and optimal system for shock wave in a self-gravitating rotating ideal gas under the effect of magnetic field and monochromatic radiation

Abstract

The lie group invariance method is used to study a cylindrical shock wave in a self-gravitating, rotating perfect gas in the presence of monochromatic radiation and an azimuthal or axial magnetic field. The density of the ambient medium is taken as variable according as the law of shock path. For the system of equations of motion, the one-dimensional optimal system of subalgebra is determined by using Lie group analysis. We have utilized optimal classes of infinitesimal generators to acquire the flow variable transformation and the similarity variable, which are important prerequisites for obtaining the system of ordinary differential equations from the system of partial differential equations. In detail, we have numerically solved and discussed the results in two cases: with power and exponential laws shock path. The effects of variation of the rotational parameter, gravitational parameter, Alfvén Mach number, adiabatic exponent, and dimensionless parameter that characterize the interaction between incident radiation flux and gas are studied in depth. A comparative study is done between power law and exponential law in respect of the strength of shock wave and the flow variables distribution in the flow-field region behind the shock front. The shock is stronger with an axial magnetic field in a power law case; whereas shock is stronger with an azimuthal magnetic field in an exponential law case. The shock strength is observed to decline when the adiabatic index of the gas or the Alfvén Mach number increases. The shock decay with rotational parameter in case of exponential law, but it strength enhanced in case of power law. Also, the rotational parameter and gravitational parameter have an exact opposite impact on the strength of shock in power law and exponential law cases.