Similarity solution for the flow behind a magnetogasdynamic exponential shock wave in a perfect gas with varying density, heat conduction and radiation heat flux

TL;DR

This paper derives similarity solutions for the propagation of an exponential shock wave in a magnetized perfect gas with variable density, heat conduction, and radiation, analyzing how magnetic and thermal parameters influence shock behavior.

Contribution

It presents new similarity solutions considering magnetic fields, heat conduction, and radiation effects with variable density and temperature-dependent properties, extending previous shock wave models.

Findings

Shock strength decreases with increasing magnetic field strength.

Shock wave properties are unaffected by heat transfer parameters.

Total flow energy varies as a power of shock radius.

Abstract

Similarity solutions are obtained for one dimensional, unsteady, adiabatic propagation of an exponential shock wave in a perfect gas with heat conduction and radiation heat flux, in the presence of azimuthal magnetic field. The shock wave is driven out by a piston moving with time according to an exponential law. The equilibrium flow conditions are maintained. The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to power law. The density and magnetic field ahead of the shock front, are assumed to vary as an exponential law. The effects of the variation of the strength of ambient magnetic field, heat transfer parameters, adiabatic exponent, ambient density variation index on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. The similarity solution exists only when the sum of shock radius and ambient magnetic field exponent is equal to the half of the ambient density exponent. It is manifested that the shock strength decreases by increasing the strength of ambient magnetic field but it is independent from the heat transfer parameters. The total energy of the flow field behind the shock front is not constant but varies as power of shock radius. The compressibility of the medium is increased in the non-magnetic field. Also, the presence of the magnetic field have significant effects on the shock wave.