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One-dimensional self-similar unsteady flow behind a strong exponential shock driven out by a piston moving with time according to an exponential law is investigated. The medium is assumed to be a mixture of small solid particles and a perfect gas. In order to get some essential features of the shock propagation, small solid particles are considered as pseudo-fluid and it is assumed that the equilibrium flow condition is maintained in the flow-field, and that the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained, in both cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compared to that of the adiabatic case. Effects of a change in the mass concentration of the solid particles in the mixture Kp and the ratio of the density of solid particles to that of initial density of the gas G1 are also obtained.

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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 α R 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.