本文是利用晶格波茲曼法模擬低雷諾數二維穩態不可壓縮的背向階梯流場，模擬介質為空氣，為了確保二維流場的適用性，所模擬的雷諾數最大值為Re=200。並利用場協同理論來證明增加流場的擾動可使得速度場與溫度梯度場之間的協同角減少，進而增加熱傳效率。流場的擾動可經由置放不同幾何形狀的阻礙物而產生，本文考慮了3種不同幾何形狀的阻礙物，分別是寬度為 的矩形阻礙物、不同傾斜角度的雙翅片阻礙物及直徑為 的圓柱形阻礙物，也考慮了圓柱阻礙物在流場中不同位置其增加的流場擾動對熱傳係數的影響。除了圓柱阻礙物被動的產生擾動以外，也模擬了圓柱阻礙物其旋轉效應對熱傳係數的主動影響。
本文所得到的數值流場和溫度場與已發表的實驗值和數值解相當吻合。使用場協同理論來驗證所得到的數值解，說明透過速度場與溫度梯度場之間的相互配合可使熱傳係數增加，速度場與溫度梯度場之間的協同角越小其協同程度越好，因而得到較佳的熱傳係數。成功的利用簡化熱模型模擬低雷諾數不可壓縮的熱流場，也證明了在晶格波茲曼法領域裡，簡化熱模型是一個準確而簡單的模型。

This study applies the Lattice Boltzmann Method (LBM) to simulate incompressible steady low Reynolds number backward-facing step flows. In order to restrict the simulations to two-dimensional flows, the investigated Reynolds number range is limited to a maximum value of Re=200. In addition, the field synergy principle is applied to demonstrate that the increased interruption within the fluid reduces the intersection angle between the velocity vector and the temperature gradient. The interruption within the fluid is induced by different type of obstacles: square blockage, double plates aligned at angle to flow direction and cylinder. A cylinder is inserted into the flow and the effects on the heat transfer coefficient of different cylinder positions examined. This study considers both the passive heat transfer effect produced by a stationary cylinder and the active heat transfer effect produced by a rotating cylinder.
The present results obtained for the velocity and temperature fields are found to be in good agreement with the published experimental and numerical results. Furthermore, the numerical results confirm the relationship between the velocity and temperature gradient predicted by the field synergy principle. The results have shown that inserting obstacle to the flow direction enhances the convective heat transfer as a result of flow interruption and thermal boundary layer compression effects. The simplified thermal model applied in this study is therefore an appropriate LBM thermal model for performing accurate simulations of incompressible thermal fluid flows.

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