本文以單相與兩相模型模擬奈米流體於等壁溫三維矩形/弧形肋條－凹槽渠道紊流強制對流之數值計算。應用控制體積法求解紊流強制對流奈米流體穩態、耦合三維統御橢圓偏微分方程式。採用標準 紊流模型求解紊流方程式。先以紊流奈米流體於平滑渠道之模擬結果與參考文獻數據作驗證，最大誤差在2%內，再進一步研究矩形/弧形肋條－凹槽渠道。矩形/弧形肋條－凹槽數值計算的研究參數範圍包括雷諾數 (5000 ≤ Re ≤ 20000)、體積濃度(2% ≤ ϕ ≤ 4%)、矩形肋條－凹槽高度(0.1875 ≤ e/H ≤ 0.5625)、矩形肋條－凹槽寬度(0.325 ≤ b/H ≤ 0.775)、矩形肋條－凹槽間距(0.25 ≤ p/H ≤ 0.75)。弧形肋條－凹槽高度(0.0825 ≤ r1/H ≤ 0.1875)、弧形肋條－凹槽寬度(0.04125 ≤ r2/H ≤ 0.09375)、弧形肋條－凹槽間距 (0.25 ≤ p/H ≤ 0.75)。
　　文中提供矩形/弧形肋條－凹槽幾何尺寸和奈米流體體積濃度參數間互相影響與平均紐賽數之比較。數值結果顯示加入矩形及弧形肋條－凹槽渠道的平均紐賽數優於平滑渠道。平均紐賽數在較小的肋條－凹槽高度、特定的肋條－凹槽間距時有較好增幅。除此之外，單相模型與兩相模型計算結果顯示在模擬流場與對流熱傳特性有些許不同。
　　此外本文利用反應曲面法(RSM)、基因演算法(GA)得到目標函數定義為熱性能係數E (Thermal Performance Factor)與四種設計參數，肋條－凹槽高度、肋條－凹槽寬度、肋條－凹槽間距、體積濃度之間關係式，並得到不同雷諾數下最佳矩形/弧形肋條－凹槽幾何外型。其中發現目標函數Ｅ在雷諾數(Re = 10000)時有較好的表現，矩形肋條－凹槽渠道有18.2%而弧形肋條凹槽渠道有42.1%的增益。

In this study, numerical simulations by single and two-phase models of nanofluids turbulent forced convection in a three-dimensional rectangular/arc rib-grooved channel with constant wall temperature are investigated. The elliptical, coupled, steady-state, three-dimensional governing partial differential equations for turbulent forced convection of nanofluids are solved numerically using the finite volume approach. The standard turbulence model is applied to solve the turbulent equations. Numerical simulations of turbulent nanofluids in a smooth channel are first validated with available results in the literature, the maximum discrepancy within 2%, and rectangular/arc rib-grooved channels are further studied.　Numerical computations are performed with rectangular/arc rib-grooved channel for the parameters studied include Reynolds number (5000 ≤ Re ≤ 20000), volume concentration (2% ≤ ϕ ≤ 4%), rectangular rib-grooved height ratios (0.1875 ≤ e/H ≤ 0.5625), rectangular rib-grooved width ratios (0.325 ≤ b/H ≤ 0.775), rectangular rib-grooved pitch ratios (0.25 ≤ p/H ≤ 0.75), arc rib-grooved height ratios (0.0825 ≤ r1/H ≤ 0.1875), arc rib-grooved width ratios (0.04125 ≤ r2/H ≤ 0.09375) and the rib-grooved pitch ratios (0.25 ≤ p/H ≤ 0.75).
　The interactive influences of rib-groove geometrical ratios and nanofluid volume concentration on the average Nusselt number are provided in this study. The numerical results show that average Nusselt number within rectangular/arc rib-grooved channels are enhanced compared to the smooth channel. The average Nusselt number of rib-grooved channel is found to improve better with smaller rib-grooved height ratios, and some ratios of rib-grooved pitch. Furthermore, the numerical results of the single and two-phase models show that it have some differences in simulated the flow filed and turbulent convective heat transfer characteristics.
In addition, the optimization of this problem is also presented by using response surface methodology (RSM) and genetic algorithm (GA) method. The objective function E is defined as thermal performance factor has developed a correlation function with four design parameters, rib-groove height ratios, rib-groove width ratios, rib-groove pitch, and the volume concentration. According to the optimal results, optimum rib-grooved geometrical conditions were obtained at four different Reynolds numbers.
It is found that the objective function E is better at Re = 10000, rectangular rib-grooved have 18.2% and arc rib-grooved have 42.1% enhancement.

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