| Summary: | 碩士 === 國立成功大學 === 機械工程學系 === 89 === A linear analysis for the stability of ferrofluid flow between two concentric rotating cylinders in the present of an axial magnetic field is implemented. The governing equations with respect to both axisymmetric and non-axisymmetric three-dimensional disturbances are derived. The eigenvalue problems, governing the onset of instability, are solved by a direct numerical procedure.
Detailed results for the critical Taylor number, the critical wavenumber, critical angular wave velocity, and the critical frequency of the oscillation are obtained. In addition, the critical mode transition of the onset of instability from non-axisymmetric modes to axisymmetric modes with increasing strength of magnetic field will be discussed in detail. Finally, the locus of the marginal states which separate stable from unstable regions is shown. It is demonstrated that the region of instability is reduced significantly by an applied axial magnetic field.
To analyze the stability of this flow, we consider the flow field including two different cases. Then the equations for the linear stability of this flow are derived and the eigenvalue problems are solved respectively. Both of the cases are
(1) the wide-gap case：
In this section we consider the full linear disturbance equations without making the small-gap approximation.
(2)the small-gap case：
If the gap is small compared to the inner radius , the small-gap approximation is made.
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