A self-similar solution for the flow behind an exponential cylindrical shock in a self-gravitating mixture of non-ideal gas and a pseudo-fluid of solid particles in a rotating medium

Although the shock wave propagation in the dusty gas medium is widely used in research, astrophysics, military, and industrial applications, the shock wave in a self-gravitating mixture of van der Waals gas and a pseudo-fluid of inert solid particles in a rotating medium, is not well understood. In the present paper, the strong exponential shock wave propagation in a selfgravitating mixture of non-ideal gas and a pseudo-fluid of small solid particles is modelled for unsteady adiabatic and isothermal flows in a rotating medium. In our model, the solid particles are considered as chemically inert pseudo-fluid, and the equilibrium flow conditions hold in the entire flow field region. The similarity solutions are derived for isothermal and adiabatic flows. The vorticity vector components, and isothermal and adiabatic compressibility's are also taken into account. It is shown that the zero-temperature gradient supposition brings the reflective changes in pressure, axial vorticity vector, density, and compressibility distributions in contrast to the adiabatic flow. The shock strength decreases, and the compressibility increases due to the zero-temperature gradient consideration. Also, the effects of the problem parameters on shock waves and the distributions of the flow variables velocity, density, etc., are discussed in detail. It is remarkable to note that due to the consideration of a self-gravitating mixture or with an increase in the ratio of the density of solid particles to the initial density of the gas, the shock strength increases; whereas due to the consideration of non-idealness of the gas or rotating medium the shock strength decreases.