Transient Magnetohydrodynamic Channel Flow with Axial Symmetry at a Supersonic Speed

Abstract

The transient supersonic flow of a slightly conducting gas in an MHD channel with axial symmetry is investigated assuming that the magnetic Reynolds number and the interaction parameter are small. The solutions to the linearized equations for supersonic flow show that in the asymptotic limit as t →∞, these solutions all tend to coincide with the solutions for the corresponding steady flow. This point is remarkably different as compared with the result for the transient subsonic flow in a channel. The reason for this discrepancy is made clear. The time for the transient flow to achieve the steady state is also evaluated.