Propagation of shock waves in a dusty gas with heat conduction, radiation heat flux and exponentially varying density

Abstract

The propagation of shock waves in a dusty gas with heat conduction and radiation heat flux, in which density varies exponentially, is investigated. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. The equilibrium flow conditions are assumed to be maintained, and the heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient αR are assumed to vary with temperature and density. The shock wave moves with variable velocity and the total energy of the wave is non-constant. Non-similar solutions are obtained and the effects of variation of the heat transfer parameters and time are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are also investigated at given times.