Self-similar dynamics of a cylindrical shock wave in a rotating, self-gravitating dusty gas under monochromatic radiation

The study explores the propagation of a cylindrical shock wave in a self-gravitating, rotat- ing axisymmetric dusty gas subjected to monochromatic radiation of constant intensity per unit area. The gas is considered grey and opaque, while the shock wave itself is transparent. The fluid velocity has variable azimuthal and axial components. The dusty gas is modeled as a mixture of a non-ideal gas and small solid particles, which are continuously distributed throughout. To capture key characteristics of shock propagation, the solid particles are treated as a pseudo-fluid, ensuring that equilibrium flow conditions are maintained across the entire flow field. Similarity solutions are derived, and the influence of various parame- ters—such as radiation, gravitation, gas non-idealness, mass concentration of solid particles, and the density ratio of solid particles to the initial gas density—is analyzed in detail. The similarity solution holds under the assumption of a constant initial angular velocity, and it is observed that shock strength remains unaffected by both the radiation and gravitation parameters. Additionally, the radiation parameter plays a dominant role in governing the effect of dusty gas parameters on radiation heat flux variation. Furthermore, the total en- ergy in the flow field behind the shock front is not conserved but instead varies as the fourth power of the shock radius.