本研究是使用數值方法探討以奈米流體為冷卻流體之梯形微渠道之
三維不可壓縮層流的流場與熱傳特性。在流體計算區域以控制體積法求解
那維爾-史托克方程式(Navier-Stokes equations)與共軛能量方程式。以
SIMPLE法來離散動量方程式與能量方程式。網格設計則採用正交非均勻
的交錯式網格。本研究中，數值計算的參數為入口速度(V = 4 m/s、6 m/s、
10 m/s)，水力直徑Dh =106.66 μm，熱通量q"= 200 kW/ m2
將模擬結果與文獻中可用的模擬數據做仔細的驗證，且應用了全因子
法(full factorial design)配合基因演算法(genetic algorithm method)來最佳化微渠道的幾何形狀。文中定義三個設計參數分別為梯形上下底之比值(1.2 ≤α ≤ 3.6)、渠道深度與梯形上下底之差的比值(0.5 ≤ β ≤1.866)和奈米粒子體積分率(0% ≤φ ≤ 4%)。在等熱通量與固定入口速度的條件下，將
微渠道的系統總熵增最小化，經由最佳化方法後的結果獲得三組最佳幾何
形狀。數值結果可看出系統阻力熵增隨雷諾數增加而增加，而系統熱熵增
則降低，發現總熵增在入口速度Uin = 6 m/s 時有較小的結果。
此外，氧化銅/水奈米流體在層流強制對流下，由單相模型和兩相模
型的CFD 預測值進行比較。研究發現，單相模型和兩相模型預測幾乎有
著相同的流場表現，但在熱場則差異較大。對於研究的模型中，兩相模型
比單相模型在熱傳表現上有更高的提升。

This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow of a trapezoidal micro-channel heat sink using nanofluids as a cooling fluid. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method.
The coupling of the velocity and the pressure terms of momentum equations are solved by SIMPLE algorithm. Orthogonal non-uniform staggered grids are used for the establishment of mesh grids. In this study, numerical
computations are performed for inlet velocity ( Uin= 4 m/s、6 m/s、10 m/s)，hydraulic diameterDh =106.66 μm，heat flux ( q" = 200k W/m2)
The numerical results are first validated with the available results in the literature, and a good agreement has been found. The present study demonstrates the numerical optimization of a trapezoidal micro-channel heat sink design using full factorial design and genetic algorithm method
(GA).Three design variables are selected from the geometric variables, the ratio of upper width and lower width of the micro-channel(1.2 ≤α ≤ 3.6)、the ratio of the height of the micro-channel to the difference between the upper and lower width of the micro-channel (0.5 ≤ β ≤1.866) 、volume fraction (0 ≤φ ≤ 4%) . The dimensionless entropy generation rate of a trapezoidal micro-channel is minimized for a constant heat flux and constant inlet velocity. There are three optimal results by genetic algorithm method (GA). Numerical results for the system dimensionless entropy generation rate show that system dimensionless friction entropy generation rate’s increase is consistence with Reynolds number; on the contrary, the higher the Reynolds
number the lower the system dimensionless thermal entropy generation rate. It is found that system dimensionless entropy generation rate is smaller at Uin= 6 m/s.
In addition, CFD predictions of laminar forced convection of CuO/water nanofluids by single-phase model and two-phase model are compared. It is found that single-phase model and two-phase model predict almost identical hydrodynamic fields but very different for thermal fields. For the problem under consideration, the two-phase model gives the higher enhancement than that of single-phase model.

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