Moatimid Galal M
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
J Colloid Interface Sci. 2002 Jun 1;250(1):108-20. doi: 10.1006/jcis.2002.8291.
The stability of two rigidly rotating magnetic fluids separated by a cylindrical interface and stressed by a timely oscillating axial magnetic field is investigated. Only axisymmetric disturbances are considered. The interface admits both mass and heat transfer. Weak viscous effects on the interface are taken into account so that their contributions are demonstrated in the boundary conditions. The solution of the boundary value problem leads to a transcendental differential equation. It includes a periodic coefficient together with modified Bessel functions of operators involved as their arguments. In the absence of rotation and under the assumption of small amplitude of the harmonic magnetic field, the characteristic equation is analyzed by means of Whittaker's perturbation technique to determine the transition curves which separate stable from unstable solutions. While in the presence of rotation, the method of multiple-time scales is adopted to investigate the necessary and sufficient conditions for stability. The analysis results in the resonance cases as well as the nonresonance cases. In order to simplify the analysis, the periodic solutions are only considered. Therefore, stability is discussed through the marginal state. Furthermore, the rotation is considered as small. The analytical results are numerically confirmed.
研究了由圆柱界面分隔并受时变振荡轴向磁场作用的两种刚性旋转磁流体的稳定性。仅考虑轴对称扰动。界面允许质量和热传递。考虑了界面上微弱的粘性效应，以便在边界条件中体现它们的贡献。边值问题的解导致一个超越微分方程。它包括一个周期系数以及以算子的修正贝塞尔函数作为自变量。在无旋转且谐波磁场振幅较小的假设下，通过惠特克微扰技术分析特征方程，以确定区分稳定解和不稳定解的过渡曲线。而在有旋转的情况下，采用多时间尺度方法研究稳定性的充要条件。分析得出共振情况和非共振情况。为了简化分析，仅考虑周期解。因此，通过边际状态讨论稳定性。此外，将旋转视为小量。分析结果得到了数值验证。
