Similarity Solution for Magnetogasdynamic Shock Waves in a Weakly Conducting Perfect Gas by Using the Lie Group Invariance Method

Abstract

Under axial and azimuthal magnetic inductions, the similarity solutions for a cylindrical shock wave in a weakly conducting ideal gas are determined using the Lie group invariance method. The axial and azimuthal magnetic inductions and density are presumed to vary in an ambient medium. This study determines the form of expression for axial and azimuthal magnetic inductions in the ambient medium. The ambient density is considered to be varying according to the power law of the shock radius. The weakly conducting medium causes inadequate magnetic freezing. We have numerically solved the system of ordinary differential equations that resulted from applying the Lie group invariance method to the system of partial differential equations. The impact of the variation in the ambient density exponent, the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers on the shock strength and the flow variables behind the shock front is discussed. It is found that the shock strength decreases with an increase in the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers.