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Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles

  • G. Nath EMAIL logo
Published/Copyright: June 30, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 9

Abstract

The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

Keywords: analytical solution; blast and shock waves; dusty gas; interstellar matter; rotating medium
MSC 2010: 76J20; 76L05; 76M55; 76N15; 76T05; 76U05; 80A60; 85A20
Corresponding author: G. Nath, Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211004, India, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-01-29
Revised: 2021-05-01
Accepted: 2021-05-30
Published Online: 2021-06-30
Published in Print: 2021-09-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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  2. Atomic, Molecular & Chemical Physics
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  16. Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles
https://doi.org/10.1515/zna-2021-0022
Keywords for this article
analytical solution; blast and shock waves; dusty gas; interstellar matter; rotating medium

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
  3. Chirp waveform control to produce broad harmonic plateau and single attosecond pulse
  4. Dynamical Systems & Nonlinear Phenomena
  5. Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetized electron–positron–ion plasma
  6. Nonlinear forced vibration of rotating composite laminated cylindrical shells under hygrothermal environment
  7. Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion
  8. Hydrodynamics
  9. Curvilinear flow of micropolar fluid with Cattaneo–Christov heat flux model due to oscillation of curved stretchable sheet
  10. Quantum Theory
  11. Accuracy of the typicality approach using Chebyshev polynomials
  12. Solid State Physics & Materials Science
  13. Impact of Sn ions on structural and electrical description of TiO2 nanoparticles
  14. The effect of non-bridging oxygen on the electrical transport of some lead borate glasses containing cobalt
  15. Thermodynamics & Statistical Physics
  16. Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles
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