Flow behind an exponential shock wave in a perfectly conducting mixture of micro size small solid particles and non-ideal gas with azimuthal magnetic field

Abstract Unsteady adiabatic and isothermal flow behind an exponential spherical or cylindrical shock wave in a perfectly conducting mixture of micro size small solid particles and non-ideal gas under the influence of azimuthal magnetic field is investigated. The moving piston drives the shock wave. The azimuthal magnetic field in the ambient medium is assumed to be varying according to an exponential laws. In our study, micro size solid particles are take to be pseudo-fluid with the supposition that the equilibrium conditions for flow are maintained in the entire flow- field region, and the heat conduction and the viscous-stress of the conducting mixture are negligible. In both the isothermal and adiabatic cases, similarity solutions are obtained by taking into consideration the magnetic field and compressibility. The effects on the shock wave propagation and on the flow variables by the ratio of the density of micro size solid particles to the initial density of the gas G a as well as by the non-idealness parameter δ of the gas in the conducting mixture, by the mass concentration λ p of micro size solid particles in the conducting mixture and by the adiabatic exponent γ are worked out in detail. A relationship between the solutions in the cases of isothermal and adiabatic flows is made. It is found that the due to the thought of zero temperature gradient the flow variables fluid velocity, density and magnetic field and shock strength decrease. Also, it is important to note down that the shock wave strength enhances with an increase in G a or due to change in geometry from cylindrical to spherical; whereas it decreases with an increase in the non-idealness parameter δ or the strength of ambient magnetic field M A − 2 or the adiabatic exponent γ .