Exponential shock wave in perfectly conducting self-gravitating rotational axi-symmetric dusty gas with magnetic field, radiative and conductive heat fluxes

In the present paper, we study the exponential shock propagation in a self-gravitating rotational axisymmetric perfectly conducting mixture of van der Waal gas and solid particles with magnetic field either axial or azimuthal and radiative and conductive heat fluxes. In our model, the solid particles are distributed continuously in the mixture and are chemically inert, and the equilibrium conditions for flow are preserved in the entire region of flow field behind shock wave. In a thick gray gas model case, the radiation is assumed to be of diffusion type. The Fourier's heat conduction law is used to express the heat conduction. The effects of the problem parameters variations are discussed. It is shown that the density of micro size solid particles to the gas initial density ratio or the gravitational parameter or the rotational parameter or the gas adiabatic index has effects to enhance the shock wave strength. Also, it is derived that an increase in the nonidealness of the gas, Alfvén Mach number, and the mass concentration of solid particles in the mixture have decaying effects on the strength of shock wave. It is shown that the shock wave is stronger when magnetic field is axial and weaker for azimuthal magnetic field.