Exact solutions of shock waves in non-ideal gas with magnetic field and radiation flux under the influence of gravitational field

Spherical shock waves in non-ideal gas with azimuthal magnetic field and radiation heat flux under the influence of gravitational field by taking into account the radiation energy and radiation pressure is investigated. The total energy of the shock wave increases with time. An exact similarity solution is obtained in the case when the radiation pressure is non-zero and the loss of energy because of radiation escape is significant. The effects of variation of the parameter of non-idealness of the gas, the Alfven-Mach number, the gravitational parameter, the radiation pressure number and the adiabatic exponent of the gas are workout in detail. It is shown that the presence of a magnetic field or with an increase in the value of the radiation pressure number or the ratio of specific heats of the gas or gravitational parameter or the non-idealness of the gas decreases shock strength. Also, it is obtained that an increase in the value of gravitational parameter or the parameter of non-idealness of the gas or the radiation pressure number has same effect on the flow variables.