Effect of electrode nonuniformities along the magnetic field in MHD generators

Abstract

The current distribution in an MHD channel with a working fluid characterized by a tensor electrical conductivity is computed for electrodes that are finely segmented in the flow direction but do not extend entirely across the channel. Fundamentally, this electrode geometry increases the normal internal impedance of the channel by an amount that is proportional to the aspect ratio of the channel, the quantity $\text{[1+(ωτ)}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and a factor that increases monotonically with the ratio of channel width to electrode width. The circuit characteristics as well as the efficiency characteristics of both normal current generators and Hall current generators based on this channel are worked out. The effects of electrodes segmented coarsely in the magnetic field direction, but finely along the flow, are deduced from the fundamental solution. A comparison with the effects of course segmentation along the flow indicates that these latter nonuniformities may be more than four times as effective in increasing the channel impedance.