MHD flow in conducting circular expansions with strong transverse magnetic fields

This paper treats the steady, inertialess flow of an incompressible, electrically conducting fluid through perfectly conducting, variable-area ducts of circular cross section in the presence of strong transverse magnetic fields. The problem is of fundamental importance in the design of liquid-lithium cooling systems for fusion reactors, of liquid-metal MHD generators and of MHD machinery in metallurgy. First we find that, if a straight pipe of radius r is joined to an expansion or contraction, then the disturbance of the fully developed flow in the pipe dies out like exp ($\text{? 12.16¦x¦r}{}^{\mathrm{?1}}$), where x is distance from the join. Next we consider the flow in conical expansions with end effects neglected; and find that the flow becomes concentrated near the plane of symmetry as the divergence increases. Finally numerical schemes for determining the flow in more general expansions and contractions are outlined. Extension of the present analysis to non-circular sections is also discussed.