Abstract
Abstract In this paper, we consider a quasilinear hyperbolic system of partial differential equations (PDEs) governing unsteady cylindrically symmetric motion of an inviscid, perfectly conducting and non-ideal gas in which the effects of magnetic field as well as gravitational field are significant. The ambient medium is assumed to have radial, azimuthal and axial components of fluid velocity. The fluid velocities and the initial magnetic field of the ambient medium are assumed to be varying and obeying exponential laws. The density of the ambient medium is assumed to be constant. Solutions are obtained for self-gravitating MHD shock in a rotating medium with the vorticity vector and its components in one-dimensional flow case. The numerical solutions are obtained using Runge-Kutta method of the fourth order. The effects of variation of the non-idealness parameter of the gas, gravitational parameter, the Shock Cowling number, and the adiabatic exponent of the gas are are worked out in detail. Further, a comparison between the solutions obtained in the case of isothermal and adiabatic flows is done. It is manifested that the non-idealness parameter of gas, presence of magnetic field (axial or azimuthal), and the adiabatic exponent of the gas have decaying effect on the shock wave however increase in the value of gravitational parameter has reverse effect on the shock strength. Further, it is shown that the consideration of isothermal flow or the presence of azimuthal magnetic field removes the singularity in the density distribution, the magnetic field distribution and the non-dimensional axial component of the vorticity vector distribution which arises in the case of adiabatic flow. It is investigated that the self-gravitation reduces the effects of the non-idealness of the gas. The obtained results are found in good agreement with the existing results.
Published Version
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