Analysis of the flow in a thermo-acoustic MHD generator with conducting walls

This paper is devoted to the analysis of a pulsating MHD flow in a rectangular channel, submitted to an applied DC magnetic field and an imposed harmonically oscillating thermo-acoustically generated pressure gradient. The resulting AC current is collected by two electrodes placed on one either side of the channel. The walls of the channel are assumed electrically conducting. The channel is considered sufficiently long to justify the hypothesis of a fully developed flow. The analytical solution proposed is based on a simultaneous resolution of the Navier–Stokes and induction equations. This solution is limited to moderate values of the magnetic Reynolds number.