本文研究的目的在於利用數值方法模擬分析三維封閉空間流場之對流，數值方法是以上風的有限體積法來求解Navier-Stokes equation，在連續方程式中加入人工壓縮因子（artificial compressibility ）及壓力對時間的微分項，其中對流項採用高階的上風有限體積法，進而利用DDADI數值法對時間積分，並加入隱式殘值平滑性（implicit residual smoothing）加速穩態計算的收斂性。
　　本篇的兩個物理問題則是應用三維封閉空間的自然對流原理，首先研究在垂直壁上有3×3排列與壁面齊平（未凸起）的分離熱源，相對的壁面為等溫的冷板，模擬利用液態電介質來冷卻電子系統的模式，所以採用Pr＝9，雷利數的範圍在104到107，展弦比為7.5。其次控制壁面上的凸起物為主要的熱源；熱源的相對面為等溫的冷板，其餘壁面為絕熱的條件，探討雷利數（Rayleigh number）、展弦比的改變對流場及溫度場的影響，以利在電子元件的散熱設計以及其它有著相同模式設備的熱處理參考。

　　A numerical method is applied to simulate the three-dimensional convection heat transfer in enclosure. The numerical method solves three- dimensional steady Navior-Stokes equation coupling with the nature convection equation. The artificial compressibility method, a third-order upwind finite volume method, a DDADI time integration and an implicit residual smoothing were applied in the numerical method to achieve a high-order accurate method.
　　This thesis presents a three-dimensional computational study of natural convection cooling of two models. First, a 3-by-3 array of discrete heat sources flush-mounted on one vertical wall. And in order to simulate dielectric cooling of electronic system, Pr=9 is used, the range of Rayleigh number varies from 104〜107 and aspect ratio is 7.5. The second model, one block is mounted on vertical wall of a rectangular enclosure filled with air and is cooled by the opposite wall. Remaining walls are adiabatic. Computations are performed for a range of Rayleigh number while the heat block aspect ratio varies. The effects of Rayleigh number and block aspect ratio on heat transfer characteristics are investigated. Then some empirical relations are established to provide the engineers with some references on the electronic packaging or other heat transfer problems.

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