本文以單相與兩相模型探討Al2O3/water奈米流體於均勻等熱通量三維複雜的微流道散熱器強制對流之數值模擬。在流體與固體區域皆以控制體積法求解納維-斯托克斯方程式(Navier-Stokes equations)與共軛能量方程式，以QUICK法及SIMPLE法來離散動量方程式與能量方程式。本文研究參數包括雷諾數、奈米粒子體積濃度、奈米粒子粒徑以及複雜結構幾何尺寸。雷諾數、奈米粒子體積濃度、奈米粒子粒徑以及複雜結構幾何尺寸對壓降與平均紐賽數的影響也作了詳細地討論。
首先以參考文獻中水與Al2O3/water奈米流體的可用數據作驗證，其結果相當吻合。數值模擬結果顯示，平均紐賽數會隨著奈米粒子體積濃度與雷諾數的增加而提高，且兩相模型之平均紐賽數均高於單相模型，整體平均紐賽數增加約29%到39%，然而壓降最大提升率為4.68% 。此計算結果顯示奈米流體在單相模型與兩相模型中，流場與層流對流熱傳特性上有所不同，在流場表現近乎相同，而熱傳特性上卻有明顯的差異。此外，奈米體積濃度對熱傳性能有較大的影響，但奈米粒徑的影響並不明顯。
在比較單相與兩相模型的數值結果後，並提出以多重參數結合實驗設計(DOE)及反應曲面法(RSM)進行最佳化，藉由基因演算法(GA)與計算流體力學(CFD)設計三維複雜的微散熱器之對流問題。定義熱性能因子為目標函數並發展出具有三個設計參數之迴歸函數，三個設計參數即奈米粒子粒徑，奈米粒子體積濃度和複雜結構的尺寸。由數值最佳化結果顯示，相比於原始尺寸，熱性能係數η可達到約9-16%的增益。

Numerical simulations by single-phase and two-phase models of Al2O3/Water nanofluid forced convection in a complex micro heat sink with uniform heat flux are investigated. The parameters studied include the dimensions of complex structure, the particle volume fractions and the nanoparticle diameters. The different values of Reynolds numbers are considered and the thermal performance factor are compared. In the range of parameters in the study, the Nusselt number of the complex micro heat sink considered is found to be increase with the increase of the particle concentration and Reynolds number. The multi-parameter constrained optimization procedure integrating the design of experiments (DOE), response surface methodology (RSM), genetic algorithm (GA) and computational fluid dynamics (CFD) is proposed to design the geometric configuration for the complex micro heat sink. The objective function (η) defined as the thermal performance factor has developed a regression function with three design parameters, i.e. diameter of nanoparticle, nanoparticle volume concentrations and the dimensions of the complex structure. The numerical optimization indicates that the enhancement of thermal performance factor η can achieve 9%-16% in the optimization compared with the original case.

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