Self-similar flow of a mixture of a non-ideal gas and small solid particles behind a shock wave in presence of heat conduction, radiation heat flux and a gravitational field

Abstract

Similarity solutions are obtained for one-dimensional unsteady flow of a dusty gas behind a spherical shock wave with heat conduction and radiation heat flux under a gravitational field of heavy nucleus at the centre (Roche model). The dusty gas is assumed to be a mixture of small solid particles and a non-ideal 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. In order to obtain similarity solutions the density of the undisturbed medium is assumed to be constant. The effects of an increase in the value of the parameter of non-idealness of the gas in the mixture \(\bar{b}\), the mass concentration of the solid particles in the mixture Kp, the ratio of the density of the solid particles to the initial density of the gas G1 and the variation of the heat transfer parameters ΓR and Γc are obtained.