本研究以多目標函數並結合全因子實驗設計方法，藉由基因演算法及計算流體力學設計奈米流體(銅/水、氧化鋁/水以及氧化銅/水)於二維波形渠道的問題。應用控制體積法求解穩態、耦合二維橢圓偏微分方程式，奈米流體的層流強制對流。
影響奈米流體熱傳增益的重要參數為：雷諾數、奈米粒子體積濃度、波形之振幅與波形之個數。首先以單相模型所得的數值結果與參考文獻的可用數據作確認，最大誤差在8%內，接著再進一步延伸應用至兩相模型(two-phase model)。
數值模擬結果顯示，體積濃度為φ= 3%與φ= 5%的銅/水奈米流體(100 nm)相較於純水分別有15%、24%的熱增益。平均紐賽數隨著奈米粒子體積濃度 與雷諾數Re的增加而提高。而就氧化鋁/水、銅/水及氧化銅/水三種奈米流體而言，銅/水奈米流體的熱傳增益優於氧化鋁/水及氧化銅/水。另一方面，由奈米流體之摩擦阻抗的結果顯示，幾何外型對於摩擦阻抗的影響較奈米粒子體積濃度的影響來得顯著。而後發現兩相模型在溫度場上與單相模型有很大的差異，但流場方面和單相模型所得到曲線幾乎重合。
此外，在數值驗證後，並利用全因子實驗設計方法(full factorial experimental design)和基因演算法 (genetic algorithm method)得到目標函數熱性能係數E (thermal performance factor) 與三個設計參數波形振幅、波形之個數、奈米粒子體積濃度 之間的關係式。

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 two-dimensional wavy channel with nanofluids (Cu/water, /water and CuO/water). The elliptical, coupled, steady-state, two-dimensional governing partial differential equations for laminar forced convection of nanofluids are solved numerically using the finite volume approach.
Some important parameters for the influences of heat transfer enhancement such as Reynolds number, the particle volume concentration, the wavy channel amplitude and the wavy numbers on the enhancement of nanofluid(100 nm) heat transfer have been investigated. The numerical results with single-phase model are first validated with the available data in the literature, the maximum discrepancy within 8%, and then further extend to two phase model.
The numerical results indicates that the thermal enhancement can achieve 15%、24% in the wavy channel flow compared with pure fluid, with the particle volume concentrationφ= 3% and φ= 5% of Cu/water nanofluids. The averaged Nusselt number increases with the increase of the particle concentration and Reynolds number. Among the mixtures studied, the Cu/water nanofluid appears to offer a better heat transfer enhancement than Al2O3/water and CuO/water. On the other hand, the friction factor of the nanofluids is also discussed, and it seems that the friction factor mainly depends on the amplitude of the wavy wall rather than the nanoparticle volume concentration. Furthermore, two-phase model predict almost identical hydrodynamic fields but different thermal ones.
In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using full factorial experimental design and genetic algorithm (GA) method. The objective function E which is defined as Thermal Performance Factor has developed a correlation function with three design parameters, wave amplitude, wavy numbers and the particle volume concentration.

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