Propagation of strong cylindrical shock wave in a self-gravitating rotational axisymmetric mixture of small solid particles and perfect gas with density varying exponentially

The non-similarity solution for the propagation of a strong cylindrical shock wave in a self-gravitating and rotational axisymmetric dusty gas, having variable azimuthal and axial fluid velocities is obtained. The dusty gas is assumed to be a mixture of small solid particles of micro size and perfect gas. The equilibrium flow conditions are assumed to be maintained. The density of the mixture and the fluid velocities in the ambient medium are assumed to be varying and obeying an exponential law. The shock wave moves with variable velocity and the total energy of the wave is non-constant. The effects of variation of the mass concentration of solid particles in the mixture, the ratio of the density of solid particles to the initial density of the gas, and the gravitational parameter on the flow variables in the region behind the shock are investigated at a given time in both the rotating and non-rotating cases. Our analysis reveals that an increase in gravitational parameter or in the ratio of the density of solid particles to the initial density of the gas surprisingly the shock strength increases and remarkable differences are found in the distribution of flow variables in both the rotating and non-rotating cases. An increase in time also, increases the shock strength in the case of isothermal flow, but to decrease the shock strength in the case of adiabatic flow in general. Further, it is investigated that the consideration of isothermal flow increases the shock strength. A comparison is made between the solutions in isothermal and adiabatic flow cases with or without gravitational effects in both the rotating and non-rotating medium. The obtained solutions are applicable for arbitrary values of time.