Magnetohydrodynamics at Small Magnetic Reynolds Numbers

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Abstract
Two problems are considered, each of which represents a class of flows. In the first problem the motion is induced by passage of electric current through an incompressible viscous electrically conducting fluid contained in an insulated axisymmetric tube. The solution is obtained in closed form by assuming small Reynolds numbers such that the electromagnetic forces are balanced by viscous forces. In the second problem incompressible inviscid electrically conducting fluid flows through an axisymmetric tube and the flow is modified due to passage of electric current. The complete solution of the resultant rotational flow is obtained in closed form for small changes in tube diameter. At appreciable rates of current flow the fluid in the central part of a contracting tube behaves as if the tube were expanding; the opposite is true for an expanding tube. This is shown to be the case quite generally even when the assumption of small magnetic Reynolds number is dropped. Further, at large rates of current flow there may develop a secondary flow.

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