Jump relations for magnetrohydrodynamic shock waves in a dusty gas   atmosphere
  In this paper, jump relations for one dimensional magnetohydrodynamic (MHD) shock waves propagating in a dusty gas environment are expressed in a simple form in terms of dimensionless variables. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The jump relations across the MHD shock front for the pressure, the density and the velocity of mixture have been derived, respectively in terms of a compression ratio across the shock front in a gas-solid particle two-phase flow. The expressions for the speed of sound, adiabatic compressibility of mixture and the change-in-entropy across the MHD shock front have also been derived in terms of the compression ratio. Further, the handy forms of MHD shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is strong and, (ii) when it is weak. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The simplified MHD shock jump relations for dusty gas reduce to MHD shock jump relations for an idea gas when the mass fraction of solid particles in the mixture becomes zero. The effects due to the magnetic field, the mass fraction of solid particles in mixture, and the ratio of the density of solid particles to the initial density of gas are studied on the pressure, density, velocity of mixture, speed of sound, adiabatic compressibility of mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of magnetic field and dusty parameters affect the flow field behind the MHD shock front. 
R. K. Anand
astro-ph.HE