Abstract
This paper treats periodic fluid transients in liquid metals contained in constant-area rectangular ducts with uniform, transverse, applied magnetic fields. The magnetic Reynolds and Mach numbers are assumed to be small, and the Reynolds number is assumed to be large. Two separate families of discrete wave numbers are found for ducts with perfectly conducting sides (parallel to the applied magnetic field) and either perfectly conducting or insulating top and bottom. The dispersion relation is found for the wave modes in fully insulating ducts, and its numerical solution is outlined. Solutions are also given for the viscous boundary layers which match the inviscid wave modes in fully conducting ducts, these being typical of boundary layers in any rectangular duct.
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