Effect of Gravitation on the Motion of Cylindrical Imploding Shock Wave in Dusty Gas

In the present paper, the propagation of cylindrical imploding strong shock waves in a self-gravitating
dusty gas has been investigated by Chester- Chisnell- Whitham method. The dusty gas is assumed to be a
mixture of small solid spherical particles and a perfect gas. The effect of overtaking disturbances on freely
propagating shock has been estimated by using Yadav technique [Mod. Mes. Cont. B, 46(4), 1(1992)].
Assuming an initial density distribution
o     log( r)
, where µ is the density at the axis of symmetry and φ
is a constant, the variation of shock velocity, shock strength, pressure and particle velocity with
propagation distance, density parameter (φ), mass concentration of solid particles in the mixture and the
ratio of solid particles to the initial density of gas have been computed and discussed through figures. The
effect of self-gravitation is also calculated. Maintaining equilibrium flow conditions, it is found that the
presence of dust particles in the gases medium has significant effects on the variation of flow variables
and the shock is strengthened under the influence of overtaking disturbances. The role of the acceleration
due to gravity on propagation of shock wave is also calculated numerically and depict through graphs.
Finally, the results obtained here have been compared with those for pure perfect gas as well as those for
freely propagating shock.