Similarity solutions for shock wave in reacting gases with magnetic field using Lie group invariance method

Abstract The Lie group analysis method is used to derive the similarity solutions for unsteady, one-dimensional flow of chemically reacting polytropic gases behind a shock wave in cylindrical geometry with axial or azimuthal magnetic field. The arbitrary constants present in the infinitesimal generators lead to three distinct cases with shock paths varying according to power law, exponential law, and a special case of the power law. For power-law shock paths, a particular analytical solution is obtained, whereas for exponential-law shock paths, analytical solution is not possible, so the numerical solution is obtained. We have seen that the consideration of Lie group analysis method provides all possible similarity solutions of the present problem. The adiabatic index and shock Cowling number have decaying effect on the shock wave for both the power-law and exponential-law shock path cases. Also, in power-law case shock wave strength is enhanced due to increase in the value of initial magnetic field exponent. Physically, the increase or decrease in the shock strength is due to the increase or decrease in the compression, i.e., the compressibility of the medium, respectively. Our findings provide a comprehensive understanding of the interplay between magnetic fields, chemical reactions, and shock dynamics in chemically reacting polytropic gases flow.