Exact Similarity Solution for Unsteady Isothermal Flow Behind a Shock Wave in Self-gravitating Non-ideal Gas

The propagation of strong spherical shock wave in non-ideal gas under the influence of gravitational field is discussed. The total energy of the shock wave increases with time. An exact similarity solution is obtained in the case when the medium is non-ideal under the influence of a central mass (m). The effects of variation of the parameter of nonidealness of the gas and the ratio of the specific heats of the gas are workout in detail. It is shown that the shock strength and the isothermal compressibility decrease with an increase in the value of the ratio of specific heats of the gas or the parameter of nonidealness of the gas. Also, it is obtained that an increase in the value of the parameter of non-idealness of the gas and the ratio of the specific heats has same effect on the flow variables and on the shock strength.