本研究以數值方法探討垂直等溫平板陣列之自然對流特性，共分為三個部分，第一部分探討不同計算域對二維單通道自然對流的影響：將進口邊界設在通道進口處會忽略下方進口處氣流轉折處形成的迴流區與流阻，將出口邊界設在通道出口處會忽略通道上方熱氣區(hot plume)提供的額外浮力，因此標準計算域應在平板陣列各方向具向外擴大的適當範圍。第二部分探討多通道平板陣列中的熱流場情況和各個通道間的熱對流係數，以及多通道與單通道的散熱特性的比較：多通道中愈靠近中央處通道上方的熱氣區愈高，提供較多額外浮力，且下方進口處氣流轉折流阻愈低，因此熱對流係數較大，反之亦然，且各通道彼此差異趨勢隨通道數增多而愈強烈；以單通道平板為比較基準，多通道平板陣列的總平均熱對流係數較高，且差異隨通道數增加而增大；多通道平板陣列的總平均熱對流係數相對於單通道平板的增加量比值(ho/hs)隨通道數N的增加而增大，原因在於通道數越多，通道上方熱氣區範圍越大進而產生更多額外的浮力，且靠近中央通道下方流場較為順暢使流阻下降。第三部分探討三維垂直平板自然對流散熱特性：針對單通道在固定板高及間距下有限寬度單通道平板的三維計算，顯示板邊緣受到側向引流而具甚高的區段熱對流係數，此係數向內急遽降低，卻在近中央區略有回升，寬度愈大時中間部分的熱氣區提供較多的額外浮力而形成較大的區段熱對流係數，造成回升現象，平板愈寬，三維狀況的散熱效果會趨近二維狀況。本研究亦顯示Elenbaas[1]將其三維平板數據轉換成二位數據時建議的修正比值q (≡ Q3D /Q2D)，在平板間距b > 5 mm時有顯著高估，原因在於在三維狀況之平板上方熱氣區範圍受側向流影響而變窄，提供的額外浮力低於二維狀況，反導致較低的散熱量。此外，亦針對三維多通道平板的流場、散熱特性及熱氣區的影響做討論。

In this study, the classical problems natural convection from vertical isothermal plate arrays is re-examined numerically. The dissertation is composed of three parts. In the first part, the effect of different computation domains on two-dimensional single channel is investigated. The results show that setting the inlet boundary at the entrance of the channel would ignore the recirculation flow formed near the entrance corner and the associated flow resistance; while setting the outlet boundary at the exit of the channel would miss the additional buoyancy provided by the hot plume above the channel. In the second part, the flow field and thermal performance of two-dimensional multi-channel fin arrays are analyzed. Multiple channels present higher average heat transfer coefficients (h) than a single channel, with h being highest at the central channel and decreasing to the lowest at the edge channel. The differences in h between the central and the edge channel increase with increasing number of channels. This phenomenon can be attributed to the greater hot plume regions which provide more additional buoyancy. The third part discusses the characteristics of three-dimensional natural convection from isothermal vertical plate arrays with a finite width under fixed height and spacing. The results of single-channel calculations demonstrate high h at the plate edge due to the effect of side flow. The value of h decreases inwardly but rebounds near the center of the plate as a result of higher additional plume buoyancy therein. As the plate width increases, the stronger plume buoyancy promotes the average h, which approaches the 2-D value when the plate is sufficiently wide. It is also found that the correction factors q (≡ Q3D /Q2D) used by Elanbaas [1] to correct his 3-D data into 2-D ones are considerably over-estimated for plate spacing b > 5 mm. The reason is that, with the presence of side flow, the 3-D plume region reduces and provides less buoyancy than the 2-D situation. The 3-D multi-channel conditions with finite plate width are also analyzed for their flow fields and the thermal performances with the configurations and effects of the 3-D plume regions discussed.

摘要 I
Abstract II
致謝 IV
目錄 VI
圖表目錄 VII
符號表 XI
第一章 緒論 1
1.1前言 1
1.2文獻回顧與基礎原理 1
1.3 研究動機與目的 4
第二章 理論基礎與模型建構 11
2.1數學模型 11
2.1.1 The Boussinesq Model 11
2.1.2統御方程式 11
2.2數值方法 12
2.2.1速度與壓力求解方式 13
2.2.2其餘離散化計算方式 13
2.2.3相關參數 13
2.3模擬參數 14
2.4流體計算網格與計算域建立 14
第三章 結果與討論 20
3.1計算域對單通道自然對流的影響 20
3.1.1不同計算域範圍 20
3.1.2邊界條件 21
3.1.3不同計算域對單通道自然對流的影響 22
3.2二維垂直平板陣列中各通道的散熱特性及多
通道與單通道散熱特性的比較 23
3.2.1邊界條件 23
3.2.2二維平板陣列中各通道的散熱量及不
同通道數的散熱特性 24
3.2.3不同Ra下二維多通道與單通道的散熱
效能比較 26
3.3 三維單通道垂直平板在不同寬度及不同間
距下的散熱量 28
3.3.1 邊界條件 29
3.3.2單通道垂直平板在不同寬度下的散熱量 29
3.3.3二維及三維散熱量的修正量探討 30
3.3.4三維多通道中流場與散熱特性 32
第四章 結論 56
參考文獻 59

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