Theoretical model of a DC magnetohydrodynamic generator in annular geometry

We developed a theoretical model of a liquid metal magnetohydrodynamic (MHD) generator in annular geometry operating in
direct current (DC) mode. The geometrical concept of the MHD generator consists of a very thin annular duct where the conducting
fluid flows due to a constant pressure gradient in an imposed azimuthal magnetic field. We have supposed negligible effects
of the induced magnetic field which is characteristic of MHD flows at very low magnetic Reynolds numbers. These assumptions
reduce the MHD equations to one dimensional fully developed flow where the induced current is given only by Ohm’s law. The
theoretical performance of the generator is analyzed as a function of the external electrical load for different operating conditions.
The electrical output power depends on the imposed magnetic field, the electrical conductivity of the fluid, its velocity and the
external electrical load. The maximum output power occurs when the external resistance equals the internal resistance of the
generator. We found that the internal resistance depends on the imposed magnetic field and geometrical parameters as in the case
of the classical MHD generator in rectangular geometry, in spite of the absence of Hartmann layers. We analyze the isotropic
electrical efficiency of the MHD generator for an external electrical load ranging from negligible resistance (short circuit) to very
large resistance (open circuit) conditions. For a given external load the higher efficiencies of the generator can be achieved by
increasing the imposed magnetic field.