Isentropic one-dimensional magnetohydrodynamic channel flow

Summary

It is usual in the analysis of one-dimensional channel flows to study the behaviour of the analogous isentropic flow since, first, it retains the essential features of flows of practical interest and, secondly, it is simpler to describe. Although in conventional channel flows it is sufficient to neglect heat addition and friction to ensure isentropicity, in the MHD case it is in addition necessary to neglect Joule heating. This is accomplished by considering the fluid as having infinite electrical conductivity. However, this procedure does not necessarily imply infinite currents, since the external resistance will limit current flow. In the conventional problem, if we assume an isentropic flow, we are able to obtain a once integrated form of the governing equations. Such once integrated solutions are not possible in the present isentropic MHD channel flow, but equally simple solutions can be found and are presented. Examples of application of these results to the crossed field MHD generator and accelerator are also given.