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Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents

  • Swati Chauhan , Antim Chauhan and Rajan Arora EMAIL logo
Published/Copyright: September 20, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 12

Abstract

In this work, we consider the system of partial differential equations describing one-dimensional (1D) radially symmetric (i.e., cylindrical or spherical) flow of a nonideal gas with small solid dust particles. We analyze the implosion of cylindrical and spherical symmetric strong shock waves in a mixture of a nonideal gas with small solid dust particles. An evolution equation for the strong cylindrical and spherical shock waves is derived by using the Maslov technique based on the kinematics of 1D motion. The approximate value of the similarity exponent describing the behavior of strong shocks is calculated by applying a first-order truncation approximation. The obtained approximate values of similarity exponent are compared with the values of the similarity exponent obtained from Whitham’s rule and Guderley’s method. All the above computations are performed for the different values of mass fraction of dust particles, relative specific heat, and the ratio of the density of dust particle to the density of the mixture and van der Waals excluded volume.

Keywords: dust particles; first-order approximation (FOA); Guderley’s exact solution; non-ideal gas; strong shocks; Whitham’s approximation
Corresponding author: Rajan Arora, Department of Applied Science and Engineering, Indian Institute of Technology, Roorkee, India, E-mail:

Funding source: Ministry of Human Resource Development

Funding source: University Grant Commission

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

  2. Research funding: The first author, Swati Chauhan, acknowledges the financial support from the Ministry of Human Resource Development, New Delhi. The second author, Antim Chauhan, acknowledges the research support from the University Grant Commission (Govt. of India) (Sr. No. 2121541039 with Ref No. 20/12/2015 (ii) EU-V).

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

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Received: 2021-02-23
Revised: 2021-08-07
Accepted: 2021-09-05
Published Online: 2021-09-20
Published in Print: 2021-12-20

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents
  4. Nonlinear excitations and dynamic features of dust ion-acoustic waves in a magnetized electron–positron–ion plasma
  5. Bifurcation analysis in a predator–prey model with strong Allee effect
  6. Hydrodynamics
  7. Mixed initial-boundary value problems describing motions of Maxwell fluids with linear dependence of viscosity on the pressure
  8. Quantum Theory
  9. Spin coherent states, Bell states, spin Hamilton operators, entanglement, Husimi distribution, uncertainty relation and Bell inequality
  10. Solid State Physics & Materials Science
  11. Tailoring the optical properties of tin oxide thin films via gamma irradiation
  12. Thermodynamics & Statistical Physics
  13. Impact of partially thermal electrons on the propagation characteristics of extraordinary mode in relativistic regime
  14. The first-order phase transition of melting for molecular crystals by Frost–Kalkwarf vapor- and sublimation-pressure equations
  15. Mathieu-state reordering in periodic thermodynamics
  16. Corrigendum
  17. Corrigendum to: Study of ferrofluid flow and heat transfer between cone and disk
https://doi.org/10.1515/zna-2021-0049
Keywords for this article
dust particles; first-order approximation (FOA); Guderley’s exact solution; non-ideal gas; strong shocks; Whitham’s approximation

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents
  4. Nonlinear excitations and dynamic features of dust ion-acoustic waves in a magnetized electron–positron–ion plasma
  5. Bifurcation analysis in a predator–prey model with strong Allee effect
  6. Hydrodynamics
  7. Mixed initial-boundary value problems describing motions of Maxwell fluids with linear dependence of viscosity on the pressure
  8. Quantum Theory
  9. Spin coherent states, Bell states, spin Hamilton operators, entanglement, Husimi distribution, uncertainty relation and Bell inequality
  10. Solid State Physics & Materials Science
  11. Tailoring the optical properties of tin oxide thin films via gamma irradiation
  12. Thermodynamics & Statistical Physics
  13. Impact of partially thermal electrons on the propagation characteristics of extraordinary mode in relativistic regime
  14. The first-order phase transition of melting for molecular crystals by Frost–Kalkwarf vapor- and sublimation-pressure equations
  15. Mathieu-state reordering in periodic thermodynamics
  16. Corrigendum
  17. Corrigendum to: Study of ferrofluid flow and heat transfer between cone and disk
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