Shock waves in an ideal gas with variable density, the radiative and conductive heat fluxes in the presence of gravitational force and magnetic field via the Lie group technique

Abstract

In our study, we have investigated the spherical (or cylindrical) shock waves propagation in an ideal gas with heat conduction and radiation heat flux in the presence of gravitational force and azimuthal magnetic field via the Lie group transformation technique. In this article, the heat conduction is described using Fourier’s law for heat conduction. In the case of thick gray gas model, the radiation is treated as of the diffusion type. The absorption coefficient and the thermal conductivity are considered to depend on some specific powers of density and temperature. By utilizing the Lie group transformation technique, four potential similarity solution cases were identified, in which the similarity solution exist in only one case (i.e., Case I). In this case, the shock radius follows a power law dependence on time. For this case, the similarity solutions are derived for the flow region behind the shock front, and the impact of problem physical parameters on the flow variables and on the shock strength are studied in detail. The results of this study offer a clear understanding of the influence of radiative and conductive heat transfer parameters, the gravitational parameter, the similarity exponent, and the magnetic field on the shock and on the flow dynamics behind the shock front. It is found that the shock wave decays with an increment in shock Cowling number or the heat transfer parameters or gravitational parameter. On increasing the value of similarity exponent, the strength of the shock wave increases in the non-magnetic case; whereas in the magnetic case, the shock strength reduces. It is also observed that, the shock strength is enhanced, when we change the geometry from cylindrical to spherical.