Approximate Analytical Solution for Ionizing Cylindrical Magnetogasdynamic Shock Wave in Rotational Axisymmetric Self-Gravitating Perfect Gas: Isothermal Flow View Full Text


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Article Info

DATE

2021-04-30

AUTHORS

G. Nath, Sumeeta Singh

ABSTRACT

The propagation of ionizing cylindrical magnetogasdynamic shock wave in rotational axisymmetric self-gravitating perfect gas under isothermal flow condition is investigated. Mathematical model for the considered problem using system of PDEs is presented. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to power law with distance from the axis of symmetry in the undisturbed medium. The flow variables are expanded in power series and using that the zeroth and first order approximations are discussed. Solutions for zeroth order approximation are constructed in approximate analytical form. The effect of flow parameters namely: gravitational parameter G0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{0}$$\end{document}, shock Cowling number C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{0}$$\end{document}, rotational parameter L and ambient density variation index q are studied on the flow variables and total energy of disturbance. Distribution of gasdynamical quantities are discussed. Radial fluid velocity and mass tends to zero near the axis of symmetry in general; but magnetic pressure, axial fluid velocity, non-dimensional components of vorticity vector lθ(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{\theta }^{(0)}$$\end{document} and lz(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{z}^{(0)}$$\end{document} tend to positive infinity near the axis of symmetry. Azimuthal fluid velocity decreases as we move inwards from the shock to the axis of symmetry. Density and pressure vanish near the axis of symmetry thus forming a vacuum there. J0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{0}$$\end{document} decreases with increase in value of ambient density variation index q or gravitational parameter G0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{0}$$\end{document}; whereas it increases with increase in value of rotational parameter L or shock Cowling number C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{0}$$\end{document}. More... »

PAGES

1-27

References to SciGraph publications

  • 2020-08-07. Approximate analytical solution for the propagation of shock waves in self-gravitating perfect gas via power series method: isothermal flow in JOURNAL OF ASTROPHYSICS AND ASTRONOMY
  • 2015-12-18. Propagation of a spherical shock wave in mixture of non-ideal gas and small solid particles under the influence of gravitational field with conductive and radiative heat fluxes in ASTROPHYSICS AND SPACE SCIENCE
  • 1971-01. Strong cylindrical shocks in a rotating gas in FLOW, TURBULENCE AND COMBUSTION
  • 2014-06-05. Unsteady isothermal flow behind a magnetogasdynamic shock wave in a self-gravitating gas with exponentially varying density in JOURNAL OF THEORETICAL AND APPLIED PHYSICS
  • 1971-11. Converging spherical and cylindrical shocks with zero temperature gradient in the rear flow field in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 1983-09. Self-similar solutions in the theory of flare-ups in novae, I in ASTROPHYSICS AND SPACE SCIENCE
  • 2003-07. Self-similar analytical solutions for blast waves in inhomogeneous atmospheres with frozen-in-magnetic field in THE EUROPEAN PHYSICAL JOURNAL B
  • 2004-07. Detonation Wave Propagation in Rotational Gas Flows in JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS
  • 2000-07. Propagation of shock waves in a dusty gas with exponentially varying density in THE EUROPEAN PHYSICAL JOURNAL B
  • 2018-09. Exact Solution for a Magnetogasdynamical Cylindrical Shock Wave in a Self-Gravitating Rotating Perfect Gas with Radiation Heat Flux and Variable Density in JOURNAL OF ENGINEERING PHYSICS AND THERMOPHYSICS
  • 2019-12-02. Cylindrical ionizing shock waves in a self-gravitating gas with magnetic field: Power series method in JOURNAL OF ASTROPHYSICS AND ASTRONOMY
  • 2019-12-07. Approximate analytical solution for shock wave in rotational axisymmetric perfect gas with azimuthal magnetic field: Isothermal flow in JOURNAL OF ASTROPHYSICS AND ASTRONOMY
  • 2013-10-01. Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas in SHOCK WAVES
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    http://scigraph.springernature.com/pub.10.1007/s12591-021-00566-8

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