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.
Similarity Solutions of Cylindrical Shock Waves in Magnetogasdynamics With Thermal Radiation
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.
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Arora, R., and Sharma, A. (October 23, 2015). "Similarity Solutions of Cylindrical Shock Waves in Magnetogasdynamics With Thermal Radiation." ASME. J. Comput. Nonlinear Dynam. May 2016; 11(3): 031001. https://doi.org/10.1115/1.4031651
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