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A Self-Similar Solution of Shock Propagation in a Mixture of Non-ideal Gas and Small Solid Particles in Magnetogasdynamics


J. P. Vishwakarma and Reena Shrivastava


Similarity solutions are obtained for unsteady, one-dimensional, self-similar
flow of a perfectly conducting mixture of a non-ideal gas and small solid particles, behind a strong shock (cylindrical or spherical) driven by a piston moving according to power law in the presence of an azimuthal magnetic field. The small solid particles are considered as pseudo-fluid and assumed to be continuously distributed in the mixture. Effects of change in the values of parameters Kp, Ga (dust parameters), b (non-idealness parameter of the gas) and M−2A (magnetic parameter) on the shock strength, piston position and on the flowvariables in the flow-field behind the shock front are obtained. It is found that there is a decrease in the shock strength and the value of piston position due to the non-idealness of gas as well as due to the presence of dust-particles and the magnetic field. This decrease in the shock strength and the value of piston position is interpreted as a result of decrease in the compressibility of the mixture. Mutual effects of parameters are also obtained to investigate the deviations in the effects of parameters Kp, Ga and b due to the presence of magnetic field. It is observed that effects of parameters Kp, Ga and b on the shock strength and on the piston position are reduced due to the presence of magnetic field while the effects of these parameters on the flow-variables are enhanced due to the presence of magnetic-field.

Keywords and Phrases : Shock waves, piston problem, self-similar solutions, perfectly conducting mixture of non-ideal gas and small-solid particles, magnetic-field.
AMS Subject Classification : : 76L05, 35L67

Received date : February 9, 2017

Accepted date: May 21, 2017

cited by: J.T.S. Vol. 10 (2016), pp.49-68

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