Cylindrical shock wave generated by a moving piston in a rotational axisymmetric non-ideal gas with conductive and radiative heat-fluxes in the presence of azimuthal magnetic field

Abstract

The propagation of a cylindrical shock wave in a rotational axisymmetric non-ideal gas with heat conduction and radiation heat-flux, in the presence of a spatially decreasing azimuthal magnetic field, driven out by a moving piston is investigated. The fluid velocities and the azimuthal magnetic field in the ambient medium are assume to be varying and obeying power laws. The gas is assumed to be electrically conducting and obey a simplified van der Waals equation of state. The shock wave moves with variable velocity and the total energy of the wave is non-constant. Similarity solutions are obtained for the flow-field behind the shock and the effects of variation of Alfven Mach number, the conductive and radiative heat transfer parameters, the parameter of the non-idealness are worked out in detail. An increase in the value of Alfven Mach number or in the non-idealness parameter of the gas, decreases the compressibility of the gas and hence there is a decrease in the shock strength; whereas the reverse effects on compressibility and shock strength are obtained with an increase in conductive or radiative heat transfer parameter. It is shown that due to the consideration of rotating medium the compressibility of the gas and the shock strength increase. Further, it is investigated that with an increase in the parameters of conductive and radiative heat transfer the tendency of formation of maxima in the distribution of pressure and minimum in magnetic field and non-dimensional axial component of vorticity vector decreases. It is interesting to note that the pressure and density vanish at the inner surface (piston) and hence a vacuum is formed at the axis of symmetry, which is in excellent agreement with the laboratory conditions to produce a shock wave. A comparison between the cases of rotating and non-rotating medium is also made.