Propagation of cylindrical shock waves in rotational axisymmetric dusty gas with magnetic field: Isothermal flow

Abstract

In this article, the effect of the dust particles is studied on the propagation of a cylindrical shock wave in rotational axisymmetric ideal gas under isothermal flow conditions with the magnetic field. Here, magnetic pressure, azimuthal fluid velocity, and axial fluid velocity are supposed to vary according to a power law in the undisturbed medium. With the help of Sakurai's technique, we obtain approximate solutions analytically by expanding the flow parameters in the form of a power series in ϕ=(CV)2. The power series method is used to derive the zeroth and the first-order approximations. The solutions for the zeroth-order approximation are constructed in analytical form. Distributions of the hydrodynamical quantities are analyzed graphically behind the shock front. Also, the effects of shock Cowling number (co), mass fraction of the solid particles in the mixture (kp), adiabatic exponent (γ), and rotational parameter (L) on the flow variables are discussed. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero, and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods. Furthermore, the results obtained in the present work are found to be in good agreement with those obtained from the study by Nath and Singh [Can. J. 98, 1077 (2020)].