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SIMILARITY SOLUTIONS FOR CYLINDRICAL SHOCK WAVE IN SELF-GRAVITATING NON-IDEAL GAS WITH AXIAL MAGNETIC FIELD: ISOTHERMAL FLOW
  • Nandita Gupta,
  • Kajal Sharma,
  • Rajan Arora
Nandita Gupta
Indian Institute of Technology Roorkee

Corresponding Author:nandita@as.iitr.ac.in

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Kajal Sharma
Indian Institute of Technology Roorkee
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Rajan Arora
Indian Institute of Technology Roorkee
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Abstract

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.
15 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
16 Apr 2021Submission Checks Completed
16 Apr 2021Assigned to Editor
24 Apr 2021Reviewer(s) Assigned
31 Jul 2021Review(s) Completed, Editorial Evaluation Pending
31 Jul 2021Editorial Decision: Revise Major
31 Aug 20211st Revision Received
31 Aug 2021Submission Checks Completed
31 Aug 2021Assigned to Editor
01 Sep 2021Reviewer(s) Assigned
01 Sep 2021Review(s) Completed, Editorial Evaluation Pending
03 Sep 2021Editorial Decision: Accept
Feb 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 3 on pages 1259-1275. 10.1002/mma.7850