Propagation of shock waves in a non-ideal gas under the action of magnetic field

摘要

In this paper, we use power series method to study the propagation of cylindrical shock waves produced on account of a strong explosion in a non-ideal gas under the influence of azimuthal magnetic field. Here, the density is assumed to be uniform and magnetic pressure is assumed to vary according to power law with distance from the symmetry axis in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in(a(0)/V)(2), wherea(0)andVare the velocities of sound in the undisturbed medium and shock front, respectively. The first-order and second-order approximate solutions to the considered problem are discussed with the help of the said method. We construct solutions for the first-order approximation in closed form. Distributions of the flow variables such as fluid velocity, density, pressure, and magnetic pressure for the first-order approximation are analyzed graphically behind the shock front. Also, the effects of non-ideal parameter and shock Cowling number on the flow variables are discussed. It is observed that an increase in the value of non-ideal parameter causes fluid velocity to increase, and density, pressure, and magnetic pressure to decrease. Increase in the shock Cowling number causes decrease in density and pressure, whereas increase in fluid velocity and magnetic pressure behind the shock. Also, it is found that numerical results obtained in the absence of magnetic field recover the existing results in the literature. Further, these results are found to be in good agreement with those obtained by the Runge-Kutta method of fourth-order.