Similarity solution using group theoretic method for unsteady flow behind shock wave in a self-gravitating dusty gas

Abstract

In this article, the similarity solution using the Lie group theoretic method for unsteady isothermal and adiabatic flows behind cylindrical or spherical shock wave in a mixture of self-gravitating real gas and small solid particles is discussed. The Lie group theoretic method gives out different cases, i.e., exponential law and power-law shock paths. The similarity solution exists only when the shock path varies according to an exponential law. The dispersal of the flow variables with the variations of the solid particles’ mass concentration in the mixture kp, gravitational parameter g0, the ratio of the density of solid particles to the initial density of the gas μ1, non-idealness parameter b¯ and the geometry index ν are discussed graphically. It is found that an increase in the value of μ1 or g0 or ν leads to an increase in the shock strength, but the shock wave decay with an increase in b¯. A comparison between the solutions for cylindrical and spherical symmetry, and for adiabatic and isothermal flows is also made.