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Research Papers

Similarity Solutions of Cylindrical Shock Waves in Magnetogasdynamics With Thermal Radiation

[+] Author and Article Information
Rajan Arora

Department of Applied Science and Engineering,
IIT Roorkee,
Saharanpur Campus,
Saharanpur, Uttar Pradesh 247001, India
e-mail: rajan_a100@yahoo.com

Ankita Sharma

Department of Applied Science and Engineering,
IIT Roorkee,
Saharanpur Campus,
Saharanpur, Uttar Pradesh 247001, India
e-mail: ankitasharma.iitr@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 27, 2013; final manuscript received September 22, 2015; published online October 23, 2015. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 11(3), 031001 (Oct 23, 2015) (6 pages) Paper No: CND-13-1303; doi: 10.1115/1.4031651 History: Received November 27, 2013; Revised September 22, 2015

Using Lie group of transformations, here we consider the problem of finding similarity solutions to the system of partial differential equations (PDEs) governing one-dimensional unsteady motion of an ideal gas in the presence of radiative cooling and idealized azimuthal magnetic field. The similarity solutions are investigated behind a cylindrical shock wave which is produced as a result of a sudden explosion or driven out by an expanding piston. The shock is assumed to be strong and propagates into a medium which is at rest, with nonuniform density. The total energy of the wave is assumed to be time dependent obeying a power law. Indeed, with the use of the similarity solution, the problem is transformed into a system of ordinary differential equations (ODEs), which in general is nonlinear; in some cases, it is possible to solve these ODEs to determine some special exact solutions.

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Figures

Grahic Jump Location
Fig. 1

The 3D-profiles of density, velocity, pressure, and magnetic field in (a), (b), (c), and (d), respectively, for ρc = 1 , δ = 3/2 , θ =−4, and hc = 1

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