Exact Solution for an Unsteady Isothermal Flow Behind a Cylindrical Shock Wave in a Rotating Perfect Gas with an Axial Magnetic Field and Variable Density

2020 ◽  
Vol 93 (6) ◽  
pp. 1538-1547
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Exact Solution ◽  
Axial Magnetic Field ◽  
Variable Density ◽  
Isothermal Flow ◽  
Perfect Gas ◽  
Cylindrical Shock Wave

scholarly journals SIMILARITY SOLUTIONS FOR CYLINDRICAL SHOCK WAVE IN SELF-GRAVITATING NON-IDEAL GAS WITH AXIAL MAGNETIC FIELD: ISOTHERMAL FLOW

2021 ◽  
Author(s):  
Nandita Gupta ◽  
Kajal Sharma ◽  
Rajan Arora
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Lie Group ◽  
Axial Magnetic Field ◽  
Similarity Solutions ◽  
Ideal Gas ◽  
Isothermal Flow ◽  
Field Variation ◽  
Cylindrical Shock Wave ◽  
Lie Group Of Transformations

The purpose of this study is to obtain the solution using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self-gravitating non-ideal gas with the magnetic field which is taken to be axial. Here, isothermal flow is considered. In the undisturbed medium, varying magnetic field and density are taken. Out of four different cases, only three cases yield the similarity solutions. Numerical computations have been performed for the cases of power-law and exponential law shock paths, to find out the behavior of flow variables in the flow-field immediately behind the shock. Similarity solutions are carried out by taking arbitrary constants in the expressions of infinitesimals of the Lie group of transformations. Also, the study of the present work provides a clear picture of whether and how the variations in the non-ideal parameter of the gas, Alfven-Mach number, adiabatic exponent, ambient magnetic field variation index and gravitational parameter affect the propagation of shock and the flow behind it. Software package “MATLAB” is used for all the computations.

Similarity solutions for magnetogasdynamic cylindrical shock wave in rotating ideal gas using Lie Group theoretic method: Isothermal flow

2020 ◽  
Vol 17 (08) ◽  
pp. 2050123
Author(s):  
G. Nath ◽  
Sumeeta Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Power Law ◽  
Azimuthal Velocity ◽  
Isothermal Flow ◽  
Index Formula ◽  
Shock Strength ◽  
Cylindrical Shock Wave ◽  
Exponential Law ◽  
Variation Index

The propagation of cylindrical shock wave under the influence of axial magnetic field in rotating medium under isothermal flow condition is investigated. The density, magnetic field and azimuthal and axial components of fluid velocity are assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations bring about three different cases of solutions, i.e. with power law shock path, exponential law shock path and a particular case of power law shock path. Numerical solutions are obtained in the cases of power law and exponential law shock paths. Distribution of gasdynamical quantities are discussed through figures. The effects of variation in values of Alfven-Mach number [Formula: see text], ambient azimuthal velocity index [Formula: see text] and ambient density index [Formula: see text] are studied on flow variables and on shock strength. The numerical integration is done using software Mathematica. It is obtained that magnetic field has a decaying effect on shock strength. Also, increase in value of ambient density or ambient azimuthal velocity variation index in the case of power law shock path and increase in value of ambient density variation index in case of exponential law shock path have the decaying effect on shock strength.

Cylindrical shock wave in a self-gravitating perfect gas with azimuthal magnetic field via Lie group invariance method

2020 ◽  
Vol 17 (10) ◽  
pp. 2050148
Author(s):  
G. Nath ◽  
Arti Devi
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Initial Density ◽  
Density Variation ◽  
Shock Strength ◽  
Adiabatic Exponent ◽  
Perfect Gas ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
Variation Index

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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