Self similar flow under the action of monochromatic radiation behind a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas

TL;DR

This paper derives similarity solutions for cylindrical shock waves in a rotating, self-gravitating dusty gas influenced by monochromatic radiation, highlighting the dominant role of radiation in heat flux variation.

Contribution

It introduces new similarity solutions for shock propagation in dusty gases considering rotation, self-gravity, and radiation effects, with detailed analysis of parameter influences.

Findings

Radiation parameter dominates heat flux variation.

Shock strength is unaffected by radiation and gravity parameters.

Flow energy varies with the fourth power of shock radius.

Abstract

The propagation of a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas under the action of monochromatic radiation with a constant intensity per unit area, which has variable azimuthal and axial components of fluid velocity, is investigated. The gas is assumed to be grey and opaque, and the shock is assumed to be transparent. The dusty gas is considered as a mixture of non-ideal gas and small solid particles, in which solid particles are continuously distributed. To obtain some essential features of shock propagation, small solid particles are considered as a pseudo-fluid, and it is assumed that the equilibrium flow condition is maintained in the entire flow-field. Similarity solutions are obtained as well as the effects of the variation of the radiation parameter, the gravitation parameter, the non-idealness parameter of the gas, the mass concentration of solid particles in the mixture, the ratio of the density of solid particles to the initial density of the gas are worked out in detail. The similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the radiation parameter and the gravitation parameter. It is found that radiation parameter dominates the effect of dusty gas parameters on the variation of radiation heat flux. The total energy of the flow-field behind the shock front is not constant but varies as fourth power of the shock radius.