Effect of Gravitation on the Motion of Cylindrical Imploding Shock Wave in Dusty Gas (International Journal of Emerging Trends in Science and Technology, 2017)
In the present paper, the propagation of cylindrical imploding strong shock waves in a self-gravitatingdusty gas has been investigated by Chester- Chisnell- Whitham method. The dusty gas is assumed to be amixture of small solid spherical particles and a perfect gas. The effect of overtaking disturbances on freelypropagating shock has been estimated by using Yadav technique [Mod. Mes. Cont. B, 46(4), 1(1992)].Assuming an initial density distributiono     log( r), where µ is the density at the axis of symmetry and φis a constant, the variation of shock velocity, shock strength, pressure and particle velocity withpropagation distance, density parameter (φ), mass concentration of solid particles in the mixture and theratio of solid particles to the initial density of gas have been computed and discussed through figures. Theeffect of self-gravitation is also calculated. Maintaining equilibrium flow conditions, it is found that thepresence of dust particles in the gases medium has significant effects on the variation of flow variablesand the shock is strengthened under the influence of overtaking disturbances. The role of the accelerationdue 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 forfreely propagating shock.