Exact Solution for Isothermal Flow behind a Shock Wave in a Self-Gravitating Gas of Variable Density in an Azimuthal Magnetic Field

2020 ◽  
Vol 93 (5) ◽  
pp. 1247-1254
Author(s):  
G. Nath ◽  
Mrityunjoy Dutta ◽  
S. Chaurasia
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Exact Solution ◽  
Variable Density ◽  
Isothermal Flow ◽  
Azimuthal Magnetic Field

scholarly journals A Self-Similar Flow behind a Magnetogasdynamic Shock Wave Generated by a Moving Piston in a Gravitating Gas with Variable Density: Isothermal Flow

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
G. Nath ◽  
A. K. Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Ambient Medium ◽  
Initial Density ◽  
Power Laws ◽  
Variable Density ◽  
Ideal Gas ◽  
Piston Velocity ◽  
Azimuthal Magnetic Field ◽  
Initial Magnetic Field

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.

Approximate analytical solution for ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas: isothermal flow

2020 ◽  
Vol 98 (11) ◽  
pp. 1077-1089
Author(s):  
G. Nath ◽  
Sumeeta Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Total Energy ◽  
Fluid Velocity ◽  
Ideal Gas ◽  
Isothermal Flow ◽  
Adiabatic Exponent ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
Axis Of Symmetry

The propagation of an ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas under isothermal flow condition with an azimuthal magnetic field is investigated. The electrical conductivity is assumed to be negligible in the medium ahead of the shock wave, which after the passage of the shock wave becomes infinitely large. The magnetic pressure, azimuthal fluid velocity, and axial fluid velocity are assumed to be varying according to the power law with distance from the axis of symmetry in the undisturbed medium. The zeroth and first-order approximations are discussed by the aid of the power series method. Solutions for the zeroth-order approximation are constructed in analytical form. Distributions of hydrodynamical quantities are discussed. The effect of flow parameters, namely, shock wave Cowling number c∗, adiabatic exponent γ, rotational parameter L, and gas non-idealness parameter [Formula: see text] are studied on the flow variables. Due to the consideration of a rotating medium or due to the presence of magnetic field, the total energy of the disturbance increases, while with an increase in adiabatic exponent γ the total energy of the disturbance decreases. Density and pressure vanish near the axis of symmetry, thus forming a vacuum there.

scholarly journals Magnetogasdynamic Shock Waves in a Rotating Gas with Exponentially Varying Density

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. P. Vishwakarma ◽  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Ambient Medium ◽  
Variable Velocity ◽  
Perfect Gas ◽  
Azimuthal Magnetic Field ◽  
One Dimensional ◽  
Adiabatic Flow ◽  
Exponential Law ◽  
Nonsimilar Solutions

Nonsimilar solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating or nonrotating perfect gas in presence of a constant azimuthal magnetic field. The density of the gas is assumed to be varying and obeying an exponential law. In order to obtain the solutions, the angular velocity of the ambient medium is assumed to be decreasing exponentially as the distance from the axis increases. The shock wave moves with variable velocity and the total energy of the wave is nonconstant. The effects of variation of Alfven-Mach number and time are obtained. Also, a comparison between the solutions in the cases of rotating and non-rotating media with or without magnetic field is made.

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