Similarity solutions for unsteady flow behind an exponential shock in a self-gravitating non-ideal gas with azimuthal magnetic field

Nath, G.; Pathak, R. P.; Dutta, Mrityunjoy

doi:10.1016/j.actaastro.2017.10.029

Cited by 29 publications

(9 citation statements)

References 43 publications

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“…We are able to obtain self‐similarity solutions for three cases, out of all possible four cases using Lie group theory. The similarity solution in terms of power law shock path which we have obtained in the first case is similar to the solution described in Nath et al; 33 also, we have similarity solutions in terms of exponential law shock path in the second case. The solution obtained by us is more general as compared with the solution obtained in Nath et al 33 The third case, which we have obtained, is a particular case of the first case.…”

Section: Introductionsupporting

confidence: 86%

“…The similarity solution in terms of power law shock path which we have obtained in the first case is similar to the solution described in Nath et al; 33 also, we have similarity solutions in terms of exponential law shock path in the second case. The solution obtained by us is more general as compared with the solution obtained in Nath et al 33 The third case, which we have obtained, is a particular case of the first case. In the present work, we studied the effects of the non‐ideal parameter, the strength of the ambient magnetic field, adiabatic exponent, ambient magnetic field variation index, and gravitational parameter on the distribution of flow variables.…”

Section: Introductionsupporting

confidence: 86%

“…To the best of the authors knowledge, such a problem has not been studied yet. Also, similarity solutions for unsteady flow behind a strong exponential shock under the effect of an azimuthal magnetic field with adiabatic or isothermal flow condition in a self‐gravitating non‐ideal gas using the technique described in Sedov 31 were determined in Nath et al 33 In the present work, to obtain the solutions, we used Lie group of transformations, and we have taken the effect of an axial magnetic field. We are able to obtain self‐similarity solutions for three cases, out of all possible four cases using Lie group theory.…”

Section: Introductionmentioning

confidence: 99%

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Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

Gupta

Sharma

Arora

2021

Math Methods in App Sciences

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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.

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Section: Introductionsupporting

confidence: 86%

Section: Introductionsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

Gupta

Sharma

Arora

2021

Math Methods in App Sciences

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“…Similarly, with a right state U + = ( + , u + , B + ), under the inequality 3 (U + ) > 3 (U), we use (10) to deduce a 3-rarefaction wave curve,…”

Section: Smooth Solutionsmentioning

confidence: 99%

“…Nath discussed a spherical shock wave propagation in a non‐ideal dusty gas under the effect of gravitational field with monochromatic radiation. As pointed out in Nath et al, at high temperature, a gas will be ionized, and the influence of electromagnetic is significant. This motivates us to study the motion of the dusty gas with a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

Pang

Yang

et al. 2020

Math Meth Appl Sci

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This paper deals with Riemann problem for one‐dimensional inviscid, isentropic, and perfectly conducting ideal dusty gas flow with a transverse magnetic field. The explicit expressions of elementary waves are derived in terms of the density, velocity, and transverse magnetic induction of an ideal dusty gas flow. The analytical properties of elementary wave curves and the influence of parameter on the elementary waves are discussed. A new approach is proposed to resolve the Riemann problem. By applying this approach, we obtain 10 kinds of exact solutions and their corresponding criteria.

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Lie group of invariance technique for analyzing propagation of strong shock wave in a rotating non‐ideal gas with azimuthal magnetic field

Yadav

Singh

Arora

2022

Math Methods in App Sciences

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In this manuscript, the propagation of strong shock wave in a non-ideal gas in the presence of azimuthal magnetic field with rotational effect is examined by using the Lie group of invariance technique with an assumption of uniform density in the undisturbed medium, whereas the azimuthal component of the fluid velocity and magnetic field are supposed to vary. The main advantage of this method is to reduce the number of independent variables by one. We obtained a special class of self-similar solutions to the problem, and the flow profiles are depicted graphically behind the shock followed by a brief discussion on the behavior of solutions through graphs. The effects of variation in non-ideal parameter, adiabatic index of the gas, Alfven-Mach number and ambient azimuthal velocity exponent on the flow variables are presented. All numerical calculations have been done using the "Mathematica"software.

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Similarity solutions for unsteady flow behind an exponential shock in a self-gravitating non-ideal gas with azimuthal magnetic field

Cited by 29 publications

References 43 publications

Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

Lie group of invariance technique for analyzing propagation of strong shock wave in a rotating non‐ideal gas with azimuthal magnetic field

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