橫向磁化雙層平板多孔介質磁泊蘇葉-庫頁流之理論分析

本研究在於探討一維雙層平板通道內中上平板為移動平板通以外加橫向磁場，並在雙層平板間使用多孔介質作為磁性流體流經之媒介。上平板以均一速度向右移動，而下平板則靜止。其邊界條件針對上下平板壁面之導電性可分為上下平板皆絕緣與僅單一平板完全傳導的情況下，進而求解出統御方程式內之速度分佈、電流密度分佈、誘導磁場分佈及羅倫茲力分佈的理論解析解。本研究也藉由使用不同的哈曼數與達西數，探討流場受外加磁場與多孔介質影響下之內部流動情形。當多孔介質之達西數非常大時，表示多孔介質內部之滲透率變大，造成流體容易通過，其內部所造成的現象與單純加入磁場時情況相同。反之，達西數縮減至很小時，流體對流現象幾乎消失，僅剩靠近上平板移動端之區域。當上下平板皆絕緣時，其流場內部會產生一固定點，此點不會隨著磁場強度與速度變化而改變，但明顯會受到多孔介質滲透率的影響，其固定點逐漸往上平板移動。當上平板絕緣下平板完全傳導時，隨著Ha逐漸變大，接近下平板附近呈現減速效應，但在靠近上平板時又受到逐漸增加的負Z向羅倫茲力推動流體，導致上平板速度局部產生逆流現象。當上平板完全傳導下平板絕緣時，上平板附近電流量少，而下平板附近電流量多，因Ha增加造成下平板磁性流體流速提高之特殊現象。

關鍵字

多孔介質；哈曼數；達西數；滲透率；橫向磁場

並列摘要

The objective of this thesis is to investigate the steady magnetic flow field in an infinitely long double-layer porous structure subjected to an external transverse magnetic field. The upper wall moves at a constant moving speed whereas the lower wall remains stationary. The magnetic boundary conditions depend on the conductivity of the parallel-walls. In current study, either both walls are perfectly insulated or only one of them is perfectly insulated while the other is perfectly conducting. With these boundary conditions, the profiles for velocity, induced magnetic, current density, and Lorentz force were obtained. Based on different Hartmann and Darcy numbers, this thesis has investigated how the magnetic flow field responses to the change in externally applied magnetic field and permeability of the double-layer porous structure. At a large Darcy number, fluid can flow through the porous matrix more easily and its flow pattern is almost identical to that not in a porous medium. On the other hand, the flow field in the porous layers associated to a sufficiently small Darcy number becomes stagnant everywhere except in the vicinity of the upper moving wall. When both walls are perfectly insulated, there will be an invariant point independent of the strength of magnetic and flow fields. However, this point shifts towards the upper wall as the permeability increases. When the upper wall is insulated while the lower one is perfectly conducting, the velocity close to the lower wall decreases with Ha. At the same time, a reverse flow is found close to the upper wall after being pushed by its local Lorentz force. When the upper wall is perfectly conducting and the lower wall is insulated, the current density surrounding the upper wall reduces and that next to the lower wall increases leading to a special phenomenon which shows that the magnetic fluid actually flows faster as Ha increases.

並列關鍵字

Transverse magnetic field ； Porous medium ； Hartmann number ； Darcy number ； Permeability

參考文獻

[1] Langmuir, I., 1928, “Oscillations in Ionized Gases” Proceedings of the National Academy of Sciences of the United States of America, Volume 14, Issue 8, pp. 627-637.

[2] Setsuo, T., 1995, “Operation of the Thruster for Superconducting Electromagnetohydrodynamic Propu1sion Ship "YAMATO 1",” Bulletin of the M.E.S.J., Vo1. 23, No.1, pp. 46-55.

[6] Coles, D., 1965, “Transition in Circular Couette Flow,” Journal of Fluid Mechanics, Vol. 21, pp. 385-425.

[7] Taylor, G.I., 1923, “Stability of a Viscous Liquid Contained between Two Rotating Cylinders,” Philosophical Transactions of the Royal Society of London. Series A, Vol, 223, pp. 289-343.

[10] Shercliff, J.A., 1956, “The Flow of Conducting Fluids in Circular Pipes under Transverse Magnetic Fields,” Journal of Fluid Mechanics, Vol. 1, pp. 644-666.

國際替代計量

橫向磁化雙層平板多孔介質磁泊蘇葉-庫頁流之理論分析

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