本文以單相與兩相模型模擬奈米流體於均勻等壁溫三維波形渠道紊流強制對流之數值計算。應用控制體積法數值求解紊流強制對流奈米流體之橢圓、耦合、穩態之三維統御偏微分方程式。統御方程式則使用標準 紊流模型求解。研究參數包含雷諾數 、奈米粒子體積濃度、波形之振幅與波長。首先以參考文獻中紊流奈米流體於平滑渠道之數據作驗證，其結果相當吻合，最大誤差在2%內，再進一步延伸應用至波型渠道。
文中比較兩種不同波形渠道在等溫壁面時的平均紐賽數，模擬結果顯示對稱式渠道之平均紐賽數較對齊式渠道來的好。數值結果顯示，單相與兩相模型模擬結果在流場與紊流對流熱傳特性有些許的不同。三種兩相模型模擬所得熱場，除了尤拉模型外，幾乎相同；而兩相模型所得數值結果與單相模型則有些微的差異。在研究範圍內，波形渠道之平均紐賽數，會隨著雷諾數、振幅與波長增加而增加。
此外，比較單相與兩相模型的數值結果後，最佳化以多重參數並結合實驗設計(DOE)、反應曲面法(RSM)，藉由基因演算法(GA)及計算流體力學(CFD)設計三維波形渠道中紊流對流問題。選擇三個無因次設計參數分別為波形之振幅、波長與體積濃度。以熱性能係數E為目標函數，並與三設計參數產生關係式。此後利用迴歸函數預測對齊與對稱式渠道之熱性能係數，其結果與數值結果相當接近，其誤差分別在6.3%和3.3%內。而所得設計參數的組合即為最佳解。

In this study, numerical calculations by single-phase and two-phase models of nanofluid turbulent forced convection in a three-dimensional wavy channel with uniform 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 governing equations are solved with the standard turbulent model. The parameters studied include Reynolds number, nanoparticle volume concentration, wavy channel amplitude and wavy length. The numerical results are validated with the turbulent nanofluids in a smooth channel in the literature first, the maximum discrepancy within 2%, and then further extend to a wavy channel.
Two different types of wavy channels are considered and their average Nusselt number for a constant wall temperature is compared. The predicted average Nusselt number of the symmetric wavy channel shows better than that in-line wavy channel. The numerical results of the proposed models indicate the flow field and turbulent convective heat transfer characteristics have some differences for single and two-phase models. The thermal field predictions by the three two-phase models are essentially the same except the Eulerian model but very far from the numerical results of single-phase model. In the range of parameters in the study, the average Nusselt number of the wavy channel considered is found to improve with increase in Reynolds number, the wave amplitude, and the wavelength. In addition, after the comparisons of the numerical results with single and two-phase models, 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 nanofluid turbulent convection of three-dimensional wavy channel. Three non-dimensional variables, namely wavy amplitude, wavy length, and volume concentration are chosen as design variables. The objective function E which is defined as thermal performance factor has developed a correlation function with three design parameters. The thermal performance factors predicted by regression function for in-line and symmetric channel cases are in good agreement with the numerical results of CFD by the difference within 6.3% and 3.3%, respectively. The combination of parameters is considered as the optimum solution.

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