Self similar flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux

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Abstract

One-dimensional unsteady adiabatic flow behind an exponential shock wave propagating in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux, which has exponentially varying azimuthal and axial fluid velocities, is investigated. The shock wave is driven out by a piston moving with time according to an exponential law. The dusty gas is taken to be a mixture of a non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The equilibrium flow conditions are maintained and energy is varying exponentially, which is continuously supplied by the piston. The heat conduction is expressed in the terms of Fourier’s law, and the radiation is assumed of diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to a power law. The effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. It is interesting to note that the similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the self gravitation, heat conduction and radiation heat flux.

Keywords

Exponential shock wave Self similar solution Dusty gas Self gravitation Conduction and radiation heat flux 

PACS Nos.

47.40.-X 47.55.Kf 47.70.Mc 47.32.Ef 

Notes

Acknowledgements

The research of the author (Ruchi Bajargaan) is supported by CSIR, New Delhi, India vide letter No. 09/045(1264)/2012-EMR-I. The second author (Arvind Patel) thanks to the University of Delhi, Delhi, India for the R&D grant vide letter No. RC/2015/9677 dated October 15, 2015.

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Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiDelhiIndia

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