The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.
The unsteady free convection flow from an infinite vertical plate, under the action of a transverse magnetic field, is analysed in the case when the plate temperature undergoes a thermal transient. The solution is obtained by Laplace transform technique. The applied field is found to induce a wave‐dominated flow pattern. The flow within the viscous and thermal boundary layers is also considered. At all stages of the motion the shearing stress at the plate is found to be larger than the corresponding value in the non‐magnetic case, although the viscous part is smaller.
Fluid motion induced by the rotational vibrations of an infinite disc rotating with angular velocity
Ω
(
a
+
b
cos
ωT
) in contact with an incompressible viscous fluid of semi-infinite extent is analysed when the amplitude parameter
α
( =
b/a
) varies from zero to infinity. Composite solutions valid over the whole of the flow régime and specific expressions for the shearing stress components at the disc and for the axial flow in the far region are obtained for low and high frequencies of periodic fluctuations. An attempt is made to calculate the frequency of overlap of the two solutions. Using the method of matched asymptotic expansions, we find that the thickness of the region of mean flow increases with
α
. New estimates of the thickness of the outer region are obtained for the fluid motion induced by torsional oscillations of a plane lamina.
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