Blast waves in a non-ideal self-gravitating gas with magnetic field
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Blast waves in a non-ideal self-gravitating gas with magnetic field Kajal Sharmaa , Rajan Arorab Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India Received: 28 June 2020 / Accepted: 31 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The propagation of the blast wave in self-gravitating non-ideal gas under the influence of axial magnetic field is investigated. The magnetic pressure and density are considered to be varying according to the power law. The approximate analytical solutions are obtained by expanding the flow variables in the form of power series using Sakurai’s technique. The zeroth- and first-order approximate solutions of self-gravitating non-ideal gas with magnetic field are discussed in detail. Solutions for zeroth-order approximation are constructed in analytical form. The effect of the flow parameters, namely parameter of non-idealness, adiabatic exponent, ambient density variation exponent and gravitational parameter on the flow variables, is discussed in detail. The results obtained in this work are compared with the results obtained by Sakurai and Nath, which are in good agreement
1 Introduction In this paper, we present the mathematical model of cylindrical ionizing shock wave in a selfgravitating non-ideal gas under the influence of magnetic field. When a strong cylindrical shock propagates through the non-ionized gas, it converts the inert quiescent gas into an electrical conductor. This type of shock wave is called ionizing shock [1]. When the ionized shock wave propagates through the non-ionized neutral gas, it ionizes the neutral gas by making it electrically conducting. The gas is non-conducting below the critical temperature and becomes highly conducting at the critical temperature. Above the critical temperature the gas is considered as perfect conductor. Thus, the behavior and the motion of the shock wave get affected by the magnetic field. These shocks are intermediate species between hydromagnetic shocks and gas shocks. It is assumed that the gas behind the shock front is a perfect conductor, while the gas ahead of the shock front is assumed to be perfectly non-conductor. Therefore, the condition of no precursor ionization is considered. The propagation of ionizing shock waves has been studied by many investigators like Greenspan [2] has obtained the similarity solution for a cylindrical shock in magnetic field. The dynamics of ionizing shock waves has been explained by Chu [3]. Rangarao and Ramana [4] investigated the self-similar cylindrical magnetogasdynamic and ionizing shock waves.
a e-mail: [email protected] b e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:773
The explosion of long thin wire, exploding wire, experiments on pinch effects and missile [5] is the applications of the cylindrical shock waves. Magnetic field plays an important role in astrophysical situation
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