Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

Abstract

A similarity solution is presented for a cylindrical magnetogasdynamic shock wave in a rotating nonideal gas in the presence of a variable axial magnetic fi eld in the case where the radiation heat fl ux is of importance. The initial angular velocity of the medium is assumed to vary as some power of the distance from the symmetry axis. The radiation heat fl ux is evaluated from the equation of motion without explicit use of the radiation transfer equations. It is shown that the gas nonidealness increases the shock strength but decreases the shock velocity. On the other hand, the presence of a magnetic fi eld decreases the shock strength but increases the shock velocity. Moreover, the shock velocity increases with the ratio of specifi c heats. The total energy of the shock wave increases with time.Keywords: cylindrical shock waves, self-similar fl ow, rotating nonideal gas, radiation heat fl ux, axial magnetic fi eld.Introduction. Formulation of self-similar problems and some examples describing the adiabatic motion in the context of nonrotating gas models of stars are considered by Sedov [1], Zel'dovich and Raizer [2], Lee and Chen [3], and Summers [4]. Experimental studies and astrophysical observations show that the outer atmosphere of planets rotates due to their rotation. Macroscopic motion with a supersonic speed occurs in an interplanetary atmosphere, so that shock waves are generated there. Thus, rotation of planets or stars signifi cantly affects the processes occurring in their outer layers; therefore, questions connected with explosions in a rotating gas atmosphere are of defi nite astrophysical interest. Chaturani [5] studied the propagation of cylindrical shock waves through a gas with solid body rotation and obtained solutions by the similarity method adopted by Sakurai [6]. Nath, Ojha, and Takhar [7] derived similarity solutions for the fl ow behind spherical shock waves propagating in a nonuniform rotating interplanetary atmosphere with increasing energy. Gangualy and Jana [8] studied a theoretical model of propagation of strong spherical shock waves in a self-gravitating atmosphere with a radiation fl ux in the presence of a magnetic fi eld. They also considered that the medium behind the shock rotated, but neglected rotation of the undisturbed medium. In all the works mentioned, the medium is taken to be a gas satisfying the equation of state of a perfect gas.The radiation infl uence on a shock wave and on a fl ow fi eld behind the shock front has always been of great interest, for instance, in nuclear power and space research. Consequently, similarity models for classical blast wave problems have been extended taking into account radiation (see [8][9][10][11][12][13][14][15]). Elliot [9] considered the explosion problem, introducing a radiation fl ux in its diffusion approximation. Wang [10] discussed the piston problem with radiation heat transfer in the thin and thick limits, as well as in the general case with an idealized two-direction approximation. Ashraf and Sachdev [12] did not explicitl...

An exact solution for the propagation of cylindrical shock waves in a rotational axisymmetric non-ideal gas with axial magnetic field and radiative heat flux

“…The value = 0 corresponds to the ideal gas case. Our solution is the generalization of the solution obtained by Vishwakarma and Patel [21] by considering the components of vorticity vectors and the axial component of fluid velocity (see Figs. 1 (c, h, i).…”

“…To obtained the similarity solutions, the field variables describing the flow pattern can be written in terms of the dimensionless functions of such that (Vishwakarma et al [25], Vishwakarm and Patel [21]…”

“…In the present problem we have extended the problem treated by Vishwakarma and Patel [21] by taking into account the axial component of fluid velocity and components of vorticity vectors. Also, we have study the effect of adiabatic exponent of the gas on the flow variables.…”