## Abstract

One-dimensional self-similar unsteady flows behind a spherical or cylindrical shock wave driven out by a piston moving with time according to a power law in a dusty gas is investigated. The medium is assumed to be the mixture of small solid particles of micro-size and a non-ideal gas. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by the inner surface (piston). It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock waves in non-ideal dusty gas can be important for the description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, the central part of starburst galaxies, nuclear explosion, rupture of the pressurized vessel, in the analysis of data from exploding wire experiments, and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry vehicles, etc. The findings of the present work provided a clear picture of whether and how the non-idealness of the gas and the presence of the magnetic field affect the propagation of shock and the flow behind it. It is interesting to note that in the presence of azimuthal magnetic field, the pressure and density vanish at the piston and hence a vacuum is formed at the center of symmetry for both the isothermal and adiabatic flows, which is in excellent agreement with the laboratory condition to produce the shock wave.

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## Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgments

The author is thankful to **Prof. M. K. Verma**, Department of Physics, Indian Institute of Technology Kanpur, Kanpur–208016, India for valuable suggestions and fruitful discussions.

## Funding

This research was supported by the research grant no. **TAR/2018/000150** under **Teachers Associateship for Research Excellence (TARE)** scheme from the **Science and Engineering Research Board (SERB)**, India. The author gratefully acknowledges the financial support of **SERB**.

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Sahu, P.K. Shock Wave Driven Out by a Piston in a Mixture of a Non-ideal Gas and Small Solid Particles Under the Influence of Azimuthal or Axial Magnetic Field.
*Braz J Phys* (2020). https://doi.org/10.1007/s13538-020-00762-x

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### Keywords

- Fluid-solid interactions
- Magnetogasdynamics
- Similarity method
- Shock wave
- Non-ideal gas
- Adiabatic and isothermal flows