New Self Similar Solution of Spherical Radiative Gasdynamic Shock Wave With Increasing Density Under The Effect Of Axial And Azimuthal Magnetic Field

Author(s):  
Ajay Singh Yadav ◽  
Pravin Kumar Srivastava ◽  
Kishor Kumar Srivastava

In the present chapter we investigated the self similar flow behind a spherical shock wave propagating in a medium with increasing density, in the presence of magnetic fields. The medium is assumed to be non gravitational due to the heavy nucleus at origin. The medium ahead and behind the shock front are assumed to be inviscid. The initial density of gas is assumed to vary as some power of distance. It is assumed that gas is grey and opaque. The assumption of optically thick grey gas is physically consistant with the neglect of radiation pressure and radiation energy. Total energy of the flow field behind the spherical shock is assumed to be increasing with time, where the gas ahead of the shock is assumed to be at rest. The results of numerical calculations were shown in the form of graphs. A complete study was made for axial and azimuthal magnetic field. Also the effect of variation of initial density behind the shock, shock velocity and respective magnetic fields were investigated.

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
G. Nath ◽  
A. K. Sinha

The propagation of a cylindrical (or spherical) shock wave in an ideal gas with azimuthal magnetic field and with or without self-gravitational effects is investigated. The shock wave is driven out by a piston moving with time according to power law. The initial density and the initial magnetic field of the ambient medium are assumed to be varying and obeying power laws. Solutions are obtained, when the flow between the shock and the piston is isothermal. The gas is assumed to have infinite electrical conductivity. The shock wave moves with variable velocity, and the total energy of the wave is nonconstant. The effects of variation of the piston velocity exponent (i.e., variation of the initial density exponent), the initial magnetic field exponent, the gravitational parameter, and the Alfven-Mach number on the flow field are obtained. It is investigated that the self-gravitation reduces the effects of the magnetic field. A comparison is also made between gravitating and nongravitating cases.


2020 ◽  
Vol 17 (10) ◽  
pp. 2050148
Author(s):  
G. Nath ◽  
Arti Devi

In this paper, we have studied the propagation of cylindrical shock waves in a self-gravitating perfect gas under the influence of azimuthal magnetic field. The method of Lie group invariance is used to construct some special class of self-similar solutions in the presence of the azimuthal magnetic field. The different cases of solutions with a power law and exponential law shock paths are obtained with the choice of arbitrary constants appearing in the expressions for the infinitesimal generators. The similarity solution for cylindrical shock wave with power law shock path is discussed in detail. The effects of variation of Alfven-Mach number, gravitation parameter, initial density variation index and adiabatic exponent on the flow variables are analyzed graphically. It is obtained that the increase in the values of Alfven-Mach number, gravitation parameter and adiabatic exponent have decaying effect on the shock strength. Also, the shock strength increases with an increase in the values of initial density variation index. A comparison is also made between the solutions in gravitating and non-gravitating cases in the presence of magnetic field.


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