本研究以多目標參數並使用實驗設計(DOE)裡的全因子設計方法(FFED)，藉由基因演算法(GA)及計算流體力學(CFD)來設計三維矩形渠道內部設置多孔性材質柱狀鰭片的問題。統御方程式使用了雙方程式能量模型和Forchheimer-Brinkman extended Darcy model 來描述多孔性材質區域的流場與熱傳特性。應用控制體積法的數值方法求解矩形渠道內部設置多孔性材質柱狀鰭片的三維穩態、耦合、橢圓微分方程式的層流強制對流問題。
研究的參數包含雷諾數(Re = 1000~2300)、多孔性材質柱狀鰭片的高度(h = 6 mm、8 mm、10 mm)以及鰭片間距(p = 4.52 mm、5.52 mm、6.52 mm)。首先將得到的數值結果與參考文獻的數據進行驗證，發現非常吻合。除了參數上的改變，對於圓柱多孔性材質柱狀鰭片以對齊式排列與交錯式排列的熱性能作比較。在數值結果上，可以明顯的發現鰭片高度是流道整體熱傳效率的關鍵參數─不論是在對齊式或是交錯式排列，鰭片高度的增加都會造成流阻的劇烈上昇以及熱阻的急遽下降。而對齊式或是交錯式排列方式的不同對整體熱效益的影響並不十分明顯。
此外，完成數值結果的驗證後，使用基因演算法來完成圓柱多孔性鰭片的最佳化。選擇的兩個最佳化設計變數，分別是無因次化的鰭片高度(α)以及無因次化的鰭片間距(β)。利用基因演算法求得通過多孔性圓柱鰭片的整體熱傳效率的最大值，其中整體熱傳效率的大小是由熱通量與壓降決定。透過最佳化設計的過程得到的結果，相較於參考的幾何形狀，目標函數已成功地達到改善的效果。所以數值最佳化對於矩形流道內設置多孔性材質柱狀鰭片陣列這樣的熱傳問題，提供了一個可信賴且經濟的方法。

In this study, the multi-parameter constrained optimization procedure integrating the design of experiments (DOE), full factorial experimental design (FFED), genetic algorithm (GA) and computational fluid dynamics (CFD) is proposed to design three-dimensional porous pin fins in a Rectangular Channel. The Forchheimer-Brinkman extended Darcy model and two-equation energy model are adopted to describe the fluid flow and heat transfer characteristics in the porous media. The elliptical, coupled, steady-state, three-dimensional governing partial differential equations for laminar forced convection with porous pin fins in a rectangular channel are solved numerically using the finite volume approach.
The parameters studied include Reynolds number (Re = 1000~2300), the height of porous pin fins (h = 6 mm、8 mm、10 mm), and the pitch of porous pin fins (p = 4.52mm、5.52 mm、6.52 mm). The numerical results are first validated with the available data in the literature, and a good agreement has been found. Circular porous pin fins both are in-line and staggered arrangements are compared in the thermal performance. The numerical results show that the fin height is a key flow parameter and the flow resistance increases significantly and the thermal resistance decrease significantly for both in-line and staggered arrangements. The influences of in –line versus staggered array on the overall heat transfer efficiencies are not noticeable.
In addition,after the validation of the numerical results, genetic algorithm (GA) is applied for the optimization of the porous pin-fin. Two nondimensional variables, pin fin height-to-channel height ratio(α) and pin-fin pitch-to-channel height ratio (β) are chosen as design variables.
The overall heat transfer efficiency due to heat flux and pressure drop across the porous pin fins is maximized by using GA. Through optimization, the objective function is successfully improved with respect to the reference geometry. The numerical optimization provides a reliable and economic means of designing a heat transfer channel with porous pin fin arrays.

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