本論文主要採用理想之Lennard-Jones勢能函數以及能模擬水分子電子對效應（pair effect）之TIP4P (transferable intermolecular potential with 4 points) 勢能函數模擬系統中分子彼此間之交互作用，利用該二種勢能函數並以分子動力學方法配合蛙跳法則（leap-frog method）分別探討空穴流（lid-driven cavity flow）、平板完全發展流（plane fully developed Poiseuille flow）及自然對流（natural convection）之流場、溫度場及邊界特性。於進行平板完全發展流問題研究時，並進一步探討當二種不同勢能函數被使用時，其系統之物理現象有何差別。其中各種模型之壁面邊界均模擬成原子結構，並模擬壁面呈現一種完全為水分子之所覆蓋之類似冰結構之平面，以更趨近真實情況。於研究中吾人發現系統整體之現象不論是採用Lennard-Jones勢能函數或是TIP4P勢能函數其結果均相當一致，但是在局部的現象則有明顯之不同。

　　本論文中首先比較Lennard-Jones與TIP4P勢能函數間特性之不同，觀察到TIP4P勢能函數因其電子對效應之故，其分子間之函數值會隨分子間之相對角度改變而產生變化，但Lennard-Jones勢能則無此一現象。

　　於問題模擬中，首先進行二種矩形與三角形之上側板拖曳空穴流問題，結果觀察到渦流隨時間演進之現象。當計算時間足夠長時，吾人可於較小之三角形空穴中觀察到類似紊流之現象發生。此外，於結果中可以明顯地檢視到在三角形空穴中之渦流強度遠較矩形空穴中之渦流強度較強。

　　其次，再進行平板完全發展流之研究，並分別以TIP4P與Lennard-Jones勢能函數模擬水分子間之交互作用。我們在研究中藉著液-壁界面上不同的邊界條件，及不同大小尺寸流道寬度之影響，觀察流場中之速度場及邊界上速度梯度變化之現象。我們能清楚的觀察到在液-壁界面上有明顯地速度落差（velocity jump），若有效流道寬度（effect channel width）小於一臨界值後，速度曲線即明顯地偏離古典速度曲線。且在此發現”滑動條件”(slip condition)存在於虛擬滑移界面（virtual slip plane）上。此外，在邊界的速度梯度隨著有效流道寬度及液-壁界面上碰撞條件f值之減少而增加。我們也合理的推測出表面效應應存在於奈米流道之中而且對應力將會有所影響。於奈米尺度下，本研究率先使用真實之物理參數及TIP4P勢能函數並以分子動力學進行水的三維平板完全發展流模擬，以了解水在奈米流道內之各種現象。

　　最後，本論文將致力於以分子動力學方法探討自然對流之基礎熱傳現象。研究中以一高寬比（aspect ratio）為2之矩形空穴為基礎模型，其邊界條件設定為上下邊界保持一固定溫差，並逐漸增大溫度差。結果觀察到系統之溫度分布分為熱邊界層（thermal boundary layer）及等溫分布層（isothermal layer），此結果與巨觀之實驗相當一致。但隨著 之增加，其最大流線函數 並未有明顯之變化。換言之，當奈米系統在此尺寸大小時因溫差所造成之熱浮力並不足以驅動自然對流。系統溫度分佈主要之形成原因是由於界面熱傳之界面熱落差（thermal jump）所造成，並非由自然對流形成。

　　本論文期望能將模擬方法應用於奈米系統上，能預測其熱流現象，更進一步分析其物理意義，最終有助於奈米系統熱流理論之建立。

　　The TIP4P and Lennard-Jones potentials are used to predict the velocity profiles in the 3-D liquid water heat and mass transfer problems. These problems are investigated by the leap-frog method in the field of molecular dynamics. In these works, the wall boundary condition is considered to be the situation that the water is absorbed on the metal wall and is then formed to be flat ice. And, the periodic boundary condition is used under the infinite condition.

　　First, the TIP4P potential is used to predict the velocity profiles in the 3-D （about 100,000 molecules）liquid water lid-driven cavity flow. The vortices in the cavity are generated with the upper side wall moving with a constant speed. Two kinds of problems are investigated in this paper to demonstrate the feature of the velocity profiles and traced the particle in the system, one is the cavity flow problem with square cavity and the other is with V-shape cavity. The realistic parameters of the water molecule are adopted in this research.

　　In a very short time, the velocity profiles are evident that the vortices are driven by the moving top plate in all cases. And, the blow-up phenomena is observed in the small triangular cavity when the calculating time is long enough. In addition, the vortex-like profiles in the triangular cavity is stronger and more obvious than the ones in the rectangular cavity. Therefore, the strength of vortex would be affected by the variation of the geometry. It emerges from that the dynamic transport properties like the thermal conductivity, diffusion coefficient and shear stress, et al. would be varied by the variation of the geometry.

　　Next, the flow characteristics of the 3-D plane fully developed Poiseuille flow in the nano-channel driven by a constant external force are studied by the Lennard-Jones and TIP4P potentials. Both global effect （effective channel width） and local effect （wall boundary types） are examined to demonstrate the features of the distributions of velocity and its gradient in the system. When the effective channel width is less than a critical value, the numerical results show that the Navier-Stokes theory would be fail to predict the velocity distribution. Furthermore, the velocity profile at a virtual slip plane presents the slip condition. And, we can reason that the surface effect exists and will affect the shear stress in the nano-channel.

　　Finally, to understanding and treating the heat transfer problem is the most important purpose of this study. And, it will be a molecular dynamic analysis for Bernad convection across rectangular enclosures. The temperature drop between the top and bottom wall is applied to this model, i.e., the temperature of the top plate is lower than the bottom plate. The numerical result shows that the distribution of the temperature consists of the boundary layer and the isothermal layer. This result agrees with the earlier experimental study. But, the value of the maximum stream function does not change obviously since increases. Namely, the natural convection could not be driven by the buoyancy force induced by the temperature difference in nano-system. The thermal-jump is the reason of the formation of the temperature gradient in the solid-liquid interface. To get the reliable results of the heat transfer problem of Benard convection is the purpose of this research in order to build the basis of the work of molecular dynamics.

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