Selection of the optimal configuration of the frame and the form of the transverse cross section of a frame-type MHD channel

A solution is given to a variational problem of the distribution of the current and the potential in the plane of the transverse cross section of an MHD channel. It is shown that, for arbitrary distributions of the conductivity and the velocity in the transverse cross section of the channel, a maximum of the power is realized with an integral condition for the reversion of the longitudinal current to zero. An investigation is made of the effect of the form of the transverse cross section of a channel with flat frames on its characteristics. It is shown that channels of elliptical (or round) form have considerable advantages over rectangular channels.