滑移邊界條件對於導電冪次型流體受勞倫茲力驅動時之流況分析

Magnetohydrodynamic pumping of power-law liquids subjected to boundary slip

黃士庭(Shih Ting Huang)

指導教授 ： 黃信富

國立臺灣大學/工學院/機械工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.11214

摘要

電磁流體動力學(magnetohydrodynamics, MHD)之非機械式微型泵，運用在微流體系統的發展越來越受重視。此類微型泵藉由與流體流動方向垂直的電場與磁場，產生勞倫茲力驅動流體。其中，勞倫茲驅動力的非線性磁力流速耦合項，在前人的研究中提出可忽略之結論。本研究驗證前人研究結果之合理性，並推廣至牛頓與非牛頓冪次型流體，交互搭配無滑移與滑移邊界條件之狀況，且在平板與圓管兩種幾何模型中，進行磁流體泵流況之案例分析。結果顯示，勞倫茲力中的非線性磁力流速耦合項，在不同邊界與哈特曼數(Hartmann number, Ha)條件下，對磁流力泵之流場有輕重不一的影響。因此，此非線性磁力流速耦合項並不能輕易忽略。前人文獻所得可忽略本項之結論，亦僅適用於低哈特曼數之情形，而非通則。

關鍵字

磁性流體力學 ； 勞倫茲力 ； 微型泵 ； 哈特曼數 ； 滑移邊界條件 ； 冪次型流體

並列摘要

Magnetohydrodynamic (MHD) liquid micro-pumps are widely applied in micro-electromechanical systems (MEMS), micro total analysis systems ( TAS), micro/nano-fluidic devices, and Lab-on-a-Chip devices. Due to the mutual interactions among the externally applied electric and magnetic fields as well as the current flow of the ionic species, Lorentz body force, which coupling the magnetic field intensity and the liquid flow velocity, is generated within the liquid medium and thus provides the driving force of the MHD liquid micro-pump. The coupling between the magnetic field intensity and the liquid flow velocity is non-linear and hinders the process of obtaining analytical solutions for further parametric studies on the flow conditions and performances of the MHD micro-pumps. As such, the importance of this non-linear term coupling the magnetic field intensity and the flow velocity is usually assumed insignificant and thus neglected in most previous investigations as found in the literature.
This thesis aims to investigate whether the assumption of neglecting the non-linear field intensity and flow velocity coupling term is indeed valid for general flow conditions or parametric regimes. We consider the MHD flow conditions of pumping Newtonian and non-Newtonian power-law liquids both subjected to slip and no-slip boundary condition. Moreover, both two-dimensional parallel plate and circular cylindrical geometries are examined. Our results show that the non-linear field intensity and flow velocity coupling term of the Lorentz body force has fundamental importance and significant influence on the flow behavior and responses of the MHD pumping liquid flow, and that this non-linear coupling term cannot be arbitrarily neglected for general flow conditions. The conclusion of neglecting this non-linear coupling term as found in previous literature is likely only valid when the MHD liquid flow is subjected to small Hartmann number and hydrodynamically no-slip conditions.

並列關鍵字

magnetohydrodynamic ； Lorentz force ； micropump ； Hartmann number ； slip boundary condition ； power-law fluid

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