Magnetic field effect on the onset of Soret-driven convection of a nanofluid confined within a Hele-Shaw cell

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• 作者：Min Chan Kim
• 关键词：Soret ; driven Convection ; Nanoparticle Suspension ; Magnetic Field Effect ; Hele ; shaw Cell ; Linear Stability Analysis ; Non ; linear Analysis
• 刊名：Korean Journal of Chemical Engineering
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：34
• 期：1
• 页码：189-198
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Industrial Chemistry/Chemical Engineering; Catalysis; Materials Science, general; Biotechnology;
• 出版者：Springer US
• ISSN：1975-7220
• 卷排序：34

文摘

The effect of a magnetic field on the early stages of Soret-driven convection of a nanoparticle suspension with large negative separation ratio χ confined within a Hele-Shaw cell, heated from above, was analyzed. Taking the Lorentz force into account, new stability equations were formulated in a similar (τ, ζ)-domain as well as in a global (τ, z)-domain by introducing the Hele-Shaw Rayleigh number based on the Soret flux (Rs_H) and the Hele-Shaw Hartmann number (Ha_H). With and without the quasi-steadiness assumptions, the resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions, and also the numerical shooting method was used. The critical time of the onset of convection and the corresponding wave number were obtained as a function of Rs_H and Ha_H. It was found that the magnetic field plays a critical role in the onset of convective instability. The onset time increases with increasing Ha_H and decreasing Rs_H. The linear stability limits are independent of the solution methods, if the trial functions for the disturbance quantities are properly chosen. Based on the results of the linear stability analysis, a non-linear analysis was conducted using direct numerical simulations. The non-linear analysis revealed that the convective motion can be apparent far after the linear stability limit.