Unsteady isothermal flow behind a magnetogasdynamic shockwave in a self-gravitating gas with exponentially varying density

The propagation of spherical (or cylindrical)shock wave in an ideal gas with or without gravitationaleffects in the presence of a constant azimuthal magneticfield is investigated. Non-similarity solutions are obtainedfor isothermal flow between the shock and the piston. Thenumerical solutions are obtained using the Runge–Kuttamethod of the fourth order. The density of the gas isassumed to be varying and obeying an exponential law.The shock wave moves with variable velocity, and the totalenergy of the wave is non-constant and varies with time.The effects of variation of the Alfven-Mach number,gravitational parameter and time are obtained. It is investigatedthat the presence of gravitational field reduces theeffect of the magnetic field. Also, the presence of gravitationalfield increases the compressibility of the medium,due to which it is compressed and, therefore, the distancebetween the inner contact surface and the shock surface isreduced. The shock waves in conducting perfect gas can beimportant for description of shocks in supernova explosions,in the study of central part of star burst galaxies,nuclear explosion, rupture of a pressurized vessel andexplosion in the ionosphere. Other potential applications ofthis study include analysis of data from exploding wireexperiments and cylindrically symmetric hypersonic flowproblems associated with meteors or re-entry vehicles etc.A comparison is made between the solutions in the cases ofthe gravitating and the non-gravitating medium with orwithout magnetic field. The obtained solutions are applicablefor arbitrary values of time.