Similarity solution via one-dimensional Lie subalgebras for shock waves in a self-gravitating and rotating gas with magnetic field and radiation heat flux

The dynamical effects of a cylindrically symmetric moving shock wave in a self-gravitating and rotating ideal gas medium influenced by a magnetic field and radiation heat flux are investigated. The dynamics of the shock wave are governed by the one-dimensional motion of the gas, and the energy equation contains the effect of thermal radiation in the setting of an optically thick limit. A mathematical model is established using the Lie symmetry method, and all possible cases of similarity solutions are obtained by choosing different subalgebras from the optimal system. The numerical computations are performed using a fourth-order Runge–Kutta method. For a power law shock path, the contour plots of flow variables such as density and velocity are presented for convenient visualization. The variations of the shock strength and the flow variables in the physical flow field region behind the shock front with changes in the values of the gravitational parameter, rotational parameter, adiabatic index, ambient magnetic field strength, similarity exponent, and radiative heat transfer parameter are investigated. It is found that increases in the ambient magnetic field strength and the radiative heat transfer parameter lead to decay of the shock wave. For a power law shock path, it is found that increases in the gravitational parameter and adiabatic index cause decay of the shock wave, whereas for an exponential law shock path, the shock strength is increased by increases in the values of these parameters.