Exact Self-similar Solution for Spherical Shock Wave in a Non-ideal Gas with Azimuthal Magnetic Field under Isothermal Flow Condition

Abstract

In the present paper the exact similarity solution for spherical shock wave propagation in a non-ideal gas in the case of isothermal flow with azimuthal magnetic field is studied. In the ambient medium the initial density is assumed to be constant and the magnetic field is taken to be varying according to power law. Exact self-similar solutions are obtained using Mc. Vittie method in the case of isothermal flow in non-ideal gas with magnetic field first time. To obtain the solution similarity transformations are used to transfer the system of PDE's into a system of ODE's. The product solution of Mc Vittie is used to obtain the exact self-similar solution of the problem under consideration. The effects of an increase in the values of the ratio of the gas specific heats , the parameter of the nonidealness of the gas and the strength of initial magnetic field −2 are discussed in detail. It is shown that the shock strength decreases and isothermal compressibility increases with an increase in the values of these parameters. The total energy of the shock wave increases with time. The solutions obtained show that the density, fluid velocity, magnetic field and pressure tend to zero as the point of symmetry is reached.