Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method

The group invariance technique is used to investigate the similarity solution of one-dimensional, unsteady motion of cylindrically symmetric shock waves propagating in a rotating, axisymmetric perfect gas permeated with an azimuthal or axial magnetic field, under the effect of monochromatic radiation, with or without self-gravitational effects. The density is considered to be varying with radiation flux moving through the gas. Considering the absorption coefficient to be variable and choosing different values for the arbitrary constants appearing in infinitesimal generators, all possible cases of similarity solutions with shock paths following the power law and exponential law are discussed in detail, and numerical solutions for both the power law and exponential law path is obtained. The effect of changes in the Alfven-Mach number, density exponent, adiabatic index, gravitational, and rotational parameters on shock formation and shock strength has been obtained for both the power law and the exponential law. Further, the effect of all these parameters on the behaviour of flow variables behind the shock is investigated in detail and the results are depicted graphically via figures. It has been found during the study that, the strength of the shock reduces considerably with an increase in the Alfven-Mach number, rotational parameter and adiabatic index, and it increases with increase in density index and gravitational parameter. Various computations involved in this article are carried out by using the MATLAB software.