A Self-similar Solution of a Shock Wave Propagation in a Perfectly Conducting Dusty Gas

Abstract

Self-similar solutions are obtained for unsteady, one-dimensional adiabatic (or isothermal) flow behind a strong shock in a perfectly conducting dusty gas in presence of a magnetic field. The shock wave is driven out by a piston moving with time according to power law. The initial magnetic field varies as some power of distance and the initial density of the medium is constant. The dusty gas is taken as the mixture of a perfect gas and small solid particles. 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. Effects of a change in the mass concentration of the solid particles in the mixture kp, in the ratio of the density of solid particles to the initial density of the gas G0 and in the strength of initial magnetic field are also obtained. It is shown that the presence of magnetic field has decaying effect on the shock wave, but this effect is decreased on increasing kp when G0 = 1. Also, a comparison is made between adiabatic and isothermal cases