Jump relations for magnetrohydrodynamic shock waves in a dusty gas atmosphere

Abstract

In this article, we have derived Rankine-Hugoniot (RH) jump conditions across a magnetohydrodynamic (MHD) shock front propagating in a dusty gas atmosphere. The dusty gas atmosphere is assumed to be a mixture of a perfect gas and small solid particles, in which small spherical solid particles are continuously distributed. The non-relativistic RH conditions for the pressure, the density, and the fluid velocity across an MHD shock front have been derived in terms of a compression ratio. The simplified forms of RH conditions have been written simultaneously for the weak and strong MHD shock waves in terms of the initial volume fraction of solid particles, the ratio of specific heats of the mixture, and the strength of the magnetic field. Further, the weak and strong shocks have been explored under two distinct conditions, viz., (i) when the applied magnetic field is weak and (ii) when the field is strong. Finally, the effects on the shock velocity and the pressure across the MHD shock front are studied due to the strength of the magnetic field, the concentration of dust particles in the mixture, and the volumetric parameter. This study presents an overview of the influence of the strength of the magnetic field and the dust loading parameters on the shock velocity, the pressure, the density, and the fluid velocity across the MHD shock front.