Propagation of cylindrical converging shock wave in rotating ideal gas containing dust particles

In this article, the propagation of strong converging cylindrically symmetric shock waves in ideal dusty gas is studied using the Lie group technique while considering the effect of an axial magnetic field in a rotating gas atmosphere. The constant density in an undisturbed medium is assumed, whereas the magnetic field, the azimuthal, and axial components of fluid velocity are considered to be varying. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations bring about three different cases of solutions, i.e., with power-law shock path, exponential-law shock path, and a particular case of power-law shock path. Numerical solutions are obtained in the cases of the power-law shock path. The self-similar solutions to the problem are obtained, and the effect of the Shock Cowling number, the mass concentration of solid dust particles, the relative specific heat, the ratio of the density of solid particles, and the ambient azimuthal velocity exponent on the shock evolution are depicted through graphs.