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Differential Equations and Dynamical Systems

, Volume 27, Issue 1–3, pp 169–180 | Cite as

Similarity Solutions of Cylindrical Shock Waves in Non-Ideal Magnetogasdynamics with Thermal Radiation

  • Hariom SharmaEmail author
  • Rajan Arora
Original Research
  • 98 Downloads

Abstract

In the present work we have taken one-dimensional unsteady flow of non-ideal gas with magnetic effect under the presence of thermal radiation. The system is hyperbolic in nature and solved by similarity method using Lie Group of Transformations under the assumption that the system is constantly conformally invariant under the transformations. The similarity solutions are investigated behind a cylindrical shock which is a consequence of a sudden explosion or produced by an expanding piston. The shock is assumed to be strong and propagating into the medium which is at rest, with uniform density. The total energy of the shock is assumed to be time dependent and obeying the power law. By means of similarity method our system of PDEs transformed into the system of ordinary differential equations (ODEs), which in general are nonlinear. The effects of thermal radiation on the the flow variables velocity, density, pressure and magnetic field are investigated behind the shock.

Keywords

Shock waves Lie group of transformations Similarity solutions Non-ideal gas Magnetogasdynamics 

Mathematics Subject Classification

35Lxx 76Lxx 76Nxx 

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2017

Authors and Affiliations

  1. 1.Department of Applied Science and EngineeringIIT RoorkeeSaharanpurIndia

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