本文以單相與混合模型探討Al2O3/water奈米流體於均勻等熱通量中斷式微渠道散熱器，不同肋條之層流流場與熱傳特性的數值模擬。所考慮的五種不同肋條形狀是矩形(R)、橢圓形(E)、菱形(D)、前向三角形(FT)以及梯形(TR)。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(181 ≤ Re ≤ 701)、奈米粒子體積濃度(2 % ≤ ϕ ≤ 4 %)和奈米粒子粒徑(13 nm ≤ dp ≤59 nm)，並詳細討論參數對速度分布、溫度分布、平均紐賽數和平均摩擦因子的影響。
首先以純水與參考文獻中可用的數據作驗證，再進一步擴展到Al2O3/water奈米流體。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，且混合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35.5%，但奈米粒子粒徑的影響並不明顯。此計算結果顯示奈米流體在單相模型與混合模型中，在流場表現近乎相同，而熱傳特性上卻有明顯的差異。整體而言，改變肋條形狀能有效提升熱傳效果，但同時卻也大幅增加平均摩擦因子。
其次，選出熱性能係數最好的肋條形狀(IMCHS-TR)進行尺寸形狀之數值模擬，並討論無因次化參數與奈米粒子體積濃度對該流場和熱傳之特性。研究的無因次化參數包括梯形肋條上下底之比值(0.4 ≤ α ≤ 0.6)、高度和上下底差之比值(1.075 ≤ β ≤ 3.125)和奈米粒子體積濃度(ϕ)。數值模擬結果顯示，平均紐賽數最高在α=0.6、β=3.125和ϕ = 4 %，平均摩擦因子最低在α=0.4、β=1.075和ϕ = 4 %。
在比較單相與混合模型的數值結果後，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)設計中斷式微渠道散熱器之奈米流體層流強制對流問題。定義熱性能係數為目標函數並發展出具有三個設計參數之迴歸函數α、β和ϕ。由數值最佳化結果顯示，單相模型與混合模型之最佳組較原尺寸，熱性能係數η增益可達到約15.4 % 與41.3 %。

Numerical simulations by single-phase model and mixture model of Al2O3/water nanofluids for the laminar flow and heat transfer characteristics in the interrupted microchannel heat sink with different ribs are investigated. Five different rib geometries are considered: rectangular (R), ellipsoidal (E), diamond (D), forward triangular (FT) and trapezoid (TR). The effects of the parameters, including Reynolds numbers, the nanoparticle volume concentrations (ϕ) and the nanoparticle diameters (dp), on the velocity contour, temperature distribution, average Nusselt number and the average friction factor are discussed in detail. Further, the different geometric shape of the ribs with the best thermal coefficient is selected (i.e. IMCHS-TR), and the flow field and heat transfer characteristics are discussed for the dimensionless parameters, i.e., the ratio of upper width and lower width of the microchannel (α), the ratio of the height of the microchannel to the difference between the upper and lower width of the microchannel (β) and the nanoparticle volume concentrations (ϕ). The multi-parameter constrained optimization procedure integrating the design of experiments (DOE), response surface methodology (RSM), genetic algorithm (GA) and computational fluid dynamics (CFD) are proposed to design the laminar forced convection of nanofluids for the interrupted microchannel heat sink. The objective function η is defined as the thermal performance factor has developed a regression function with three design parameters, α, β and ϕ. The numerical optimization indicates that the enhancement of thermal performance factor η with single-phase model and mixture model can achieve 15.4 % and 41.3 % in the optimization compared with the original case.

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