Calculation of the flow of an electrically conducting liquid in a duct of rectangular cross section with electrodes

Abstract

A numerical solution is given for the problem of the flow of an electrically conducting liquid in a duct of rectangular cross section whose walls in the direction at right angles to the applied magnetic field are nonconducting, whereas those parallel to the field are perfect conductors. It is assumed that all the quantities except the pressure are independent of the coordinate along the axis of the duct, that the applied magnetic field is homogeneous, and that the induced current is diverted into an external circuit. The total current in the external circuit and the difference of the potentials of the conducting walls are found as functions of the external load, the Hartmann number, and the ratio of the lengths of the sides of the duct. It should be noted that problems of this kind have already been considered on many occasions and by many different approximate methods. The most complete bibliography on this question can be found in [1].