本文探討以矽做為基板並使用水為冷卻流體的矩形微渠道散熱器之三維不可壓縮層流流場與熱傳的數值模擬。在流體與固體區域皆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QUICK法與SIMPLE法來離散動量方程式與能量方程式。本研究中，數值計算的參數範圍為50≦Re≦600, 0.05W≦P≦0.25W, 100W/cm2≦q"≦300W/cm2。
首先將模擬結果與文獻中可用的實驗數據做仔細的驗證，且應用了反應曲面法(response surface methodology)、全因子法(full factorial design)配合基因演算法(genetic algorithm method)來最佳化微渠道散熱器的幾何形狀。文中定義兩設計參數分別為渠道深度與總深度的比η(Hc/Hb+Hc)，渠道寬度與總寬度的比ξ(Wc/Ww+Wc) 。在等熱通量與等泵浦功率的條件下，將微渠道散熱器的熱阻最小化，經由不同最佳化方法後的結果幾乎有一致最佳幾何形狀，基於最佳化結果，其最佳化情況為η=0.8和ξ=0.711。根據數值結果，進口熱阻隨著η增加而減少，但會隨著ξ增加而增加。另外平均紐賽數則隨著雷諾數或泵浦功率增加而變大。

Three-dimensional incompressible laminar fluid flow and heat transfer of a rectangular micro-channel heat sink is studied numerically using water as a cooling fluid in a silicon substrate. The control volume approach is developed for solving Navier-Stokes equations with conjugate energy equation for both fluid and solid regions. The QUICK and SIMPLE techniques are used for discretization of momentum and energy equations. In this studied, computations were performed for a range of 50≦Re≦600, 0.05W≦P≦0.25W, 100W/cm2≦q"≦300W/cm2.
Solutions are first carefully validated with available experimental results in the literature and the shape of the micro-channel is then optimization using response surface methodology, full factorial design and genetic algorithm method. Ratio of the depth of the micro-channel to the whole depth η(Hc/Hb+Hc) and the width of the micro-channel to the whole width ξ(Wc/Wb+Wc) are selected as design variables. The thermal resistance of a micro-channel is minimized for a constant heat flux and constant pumping power. The different optimum models yielded nearly the same optimum geometries. Based on the results derived by the optimization, the optimum condition is η=0.8 and ξ=0.711. According to the numerical results, the inlet thermal resistance decreases with increasing η but increases with increasing ξ in all cases. In addition, one can observes that averaged Nusselt number increases with increase in Reynolds number or pumping power.

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