Exact Similarity Solution for the Propagation of Spherical Shock Wave in a van der Waals Gas with Azimuthal Magnetic Field, Radiation Heat Flux, Radiation Pressure and Radiation Energy Under Gravitational Field

We investigated the exact similarity solutions for shock wave propagation in non-ideal gas with radiation heat flux under gravitational field by taking radiation pressure and radiation energy into account in the presence of azimuthal magnetic field for spherical geometry. The solutions are in terms of analytical expressions. Similarity method is used to transform the basic equation from a system of partial differential equation into a system of ordinary differential equations. The system of ODE yields exact solutions for initial magnetic field distributions as power law. Consideration of isothermal approximations, radiation pressure, radiation energy and adiabatic compressibility in gravitating medium into accounts leads to new insights into explosion problem in contrast to earlier model. Finally, the product solution of progressive wave given by Mc. Vittie is used to obtain the exact similarity solution under the consideration that the radiation pressure is not equal to zero and the energy loss due to radiation escape is significant. The Alfven–Mach number effect, the parameter of gravitational effect, the parameter of non-idealness of the gas, the radiation pressure number and the adiabatic exponent gamma of the gas are discussed in detail.