磁性流體是強磁性超微粒子經界面活性劑的作用，安定分散於水、有機溶媒等液體中的膠體溶液。它雖然是液體，卻能像鐵、鎳等固態金屬材料一樣被磁鐵所吸引。經過近十幾年來的研究及製程改良後，磁流體逐漸被導入熱流工程領域中一些前瞻性的應用。磁流體的熱傳特性研究及外加磁場對自然對流現象的影響，不論是在科學界或者是工程應用領域都是非常令人感興趣的一門研究。例如在太空微重力的環境下，流場中重力加速度所扮演的角色可以被外加磁場所取代，而且磁流體中的熱磁自然對流效應(thermomagnetic free convection)也遠比一般重力環境下浮力誘導的自然對流(Benard convection)還要顯著。

　　本文中結合流體力學、熱質傳學以及靜磁學等科學知識，建立了一套完整而精確的理論模型。利用該理論模型，我們重建了Yamaguchi等人針對封閉的二維矩形空間中磁流體受到外加均勻垂直磁場作用的熱對流不穩定性理論研究的數值模擬與實驗結果；並且改變二維模型中磁場與重力的角度，以觀察其對熱傳效果的影響。未來，我們更希望進一步的探討邊界受磁極化效應對於封閉容器內自然對流效果的影響。

　　Magnetic fluids have many promising applications in thermo-fluid engineering. This is mainly because that, when magnetic fluids are in use, the effects of gravitational acceleration on the flow can then be augmented by a magnetic body force. It is also well known that thermo-magnetic free convection in a magnetic fluid is significantly stronger than Benard convection in non-magnetic fluids. Clearly, understanding the characteristics of natural convection of magnetic fluids is of fundamental importance in fluid science and engineering.

　　In this thesis, using a well-established theoretical model that combines theories of fluid mechanics, heat transfer, and electromagnetics, we study the stability and heat transfer characteristics of a magnetic fluid in a square cavity. Accurate numerical methods are employed to solve the resulting mathematical equations. In particular, the effects of the inclination angle between the gravitational field and the magnetic field on the flow are also taken into consideration. It is found that the flow and heat transfer characteristics are greatly influenced by both the strength of the magnetic flied and its inclination angle to the gravity.

[1] Berkovsky , B.M Magnetic Fluids Engineering Applications( Oxford Univ . Press , New York , 1933) pp.214.
[2] Sihiliomis , M.I. , “ Magnetic Fluids , “ Soviet Physics-Adv-ances in Physical Science , Vol . 17 , No.2 , 1974 , pp.153-169.
[3] Stiles , P.J. , and Kagan , M. , “ Thermoconvective Instabilityof a Ferrofluid in a Strong Magnetic Field , “ Journal of Collid and Interface science , Vol . 134 , No.2 , 1990 , pp.435-488.
[4] Blennerhasset , P . J. , Lin , and Stiles , P.J. , “ Heat Transfer Through Strongly Magnetized Ferrofluids , “ Proceeding of the Royal Society of London , Series A:Mathematical and Physical Science , Vol.433 , No . 1887 , 1991 , pp.165-177 .
[5] Kato , Y . , Kawai H . , and Tanahashi , T . , “ Numerical Flow Analysis in a Cubic Cavity by the GSMAC Finite-EleMent Method , “ Japan Society of Mechanical Engineers International Journal , Vol.33 , No.41990 , pp.649-658.
[6] Blums , E . , Cebers , A . , and Maiorov , M.M. , Magnetic Fluids , ed . , Walter de Gruyter , New York , 1997 , pp.289-341 .
[7] Finlayson , B.A. , “Convective Instability of Ferromagnetic Fluids” , Journal of Fluid Mech . , Vol.40 , Pt. 4 , 1970 ,pp.753-767.
[8] Schwab , L . , Magnetic Benard Convection , Doctoral Dissertation , University of Munich , Germany , 1989 .
[9] Schwab , L . , Hildebrandt , U . , Stierstadt , K . , “Magnetic Benard Convection , “Journal of Magnetism and Magnetic Material“, Vol.39 , 1983 , pp.113-114 .
[10] Schwab , L . , Stierstadt , K . , “ Field - Induced Wave vector Selection by Magnetic Benard Convection , “ Journal of Magnetism and Magnetic Material,Vol.65 ,1987, pp.315-316 .
[11] Gotoh , K . , Yamada , M . , “ Thermal Convection in a HorizontalLayer of Magnetic Fluids , “ Journal of the PhysicalSociety of Japan , Vol.51 No.9 , 1982 , pp.3042-3048 .
[12] Yamaguchi , H . , Kobori , I . , Uehata , Y . , Shimada , K . , “ Natural Convection of Magnetic Fluids , “ Journal of Thermophysics and Heat Transfer ,Vol.13,No4,1999 , pp.501-507.
[13] Adrian Bejan , Convection Heat Transfer ( Department of Mechanical Engineering and Materials Science Duke University Durham , North Carolina , 1984 ) pp.159-195 .