本研究是以數值模擬方式分析平行板流道之散熱片在層流情況下的對流熱傳效果。不僅對於流道壁上之單一散熱片在強制對流情況下與不同傾斜角之混合、自然對流情況下加以分析，亦對平行流道兩壁的散熱片排列成一直線或交錯形式之對流情況下進行探討。

在分析與計算之過程中，採用控制體積計算方法及非均勻網格點方式，將系統之統御方程式轉置成流線函數、渦度方程式與能量方程式進行解析與模擬計算。首先，討論關於流體雷諾數、散熱片與流體之熱傳導性能的比值、流道入口距離、散熱片之間距等變數的影響。進而，探討單一散熱片與散熱片列之最佳化的形狀比例與雷諾數、散熱片與流體熱傳導性能之比值，以及散熱片之剖面積的關聯性。更進一步，分析在平行板流道中，不同強度之浮力以及流道傾斜角變化的影響。

結果顯示，固定散熱片剖面積之條件下，在強制對流與混合對流情況時，代表具最大散熱性能之散熱片最佳化形狀因子隨雷諾數之提升而增大，但隨散熱片與流體熱傳導性能之比值降低而減小。在強制對流下，散熱片列之最佳化形狀因子隨散熱片間距變大而增加，但隨入口到第一散熱片之距離變長而減小。然後，提出散熱片的最佳化形狀因子與雷諾數、傳導性能比值或散熱片數目之關係式。

最後，在混合對流中，浮力效應之增強，有助於提升散熱片的熱傳性能。單一散熱片與交錯式散熱片列之最佳化形狀因子不僅隨流道傾斜角增加而增大，且隨浮力強度增加而增大。

Numerical study of laminar convective cooling of ribs in a parallel plate channel is investigated. Single rib mounted on one channel wall in forced, mixed and free convection is analyzed. Furthermore, the series ribs array with in-line and staggered mounted on channel walls are considered.

Through the use of a stream function vorticity transformation, solution of the transformed governing equations for the system is obtained using the control volume method with non-uniform grid. The effects of the Reynolds number, thermal conductivity ratio of rib to fluid and rib’s profile area on heat transfer rate of single rib and rib array are presented. In addition, the effects of the length from inlet to the first rib and the space between ribs for rib array are carried out. A correlation for single and rib array in forced convection is presented to estimate the optimum aspect ratio of rib with various Reynolds number, thermal conductivity ratio of rib to fluid, rib’s profile area. Furthermore, the results of different Gr/Re2 and various channel inclination angle in mixed convection are also examined numerically.

The results indicate that both in forced and mixed convection, the optimum aspect ratio of a rib corresponding to the rib with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed rib profile area. In forced convection the optimum aspect ratio of rib array increases with rib’s space but decreases with the length from inlet to the first rib of channel. Then, numerical correlations to predict the optimum aspect ratio of single rib and rib array are developed for fixed rib’s area with various Re, K and rib number. In mixed convection, the optimum aspect ratios of single rib and staggered rib array increase with not only the inclination angle but also Gr/Re2.

Contents

List of Tables………………………………..……..…....……..…………..…...v
List of Figures……………………………….……..………………….………vi
摘要 …………………………………….…………..…………………….…xi
Abstract……………………….....…………………..……...…………………xii
Nomenclature………………………….………..………………..…………xiii

Chapter 1 Introduction………………………………………………………1
1.1 Numerical in forced convection…………..…………………………….2
1.2 Numerical in mixed convection…………..………..…………….……11
1.3 Experimental in convection ……………..…..…………………...…...23

Chapter 2 Analysis and Formulation…..……….…….……………………31
2.1 Analysis ………………………….…………..…………………………..31
2.1.1 Forced convection with single rib .…………...………..…….……31
2.1.2 Forced convection with rib array .………...………………………32
2.1.3 Mixed convection with single rib .…………...…………………….32
2.1.4 Mixed convection with rib array .…..………...…………………….33

2.2 Governing equations…………………………………………………..33
2.2.1 In forced convection .…………...………..………….….………..33
2.2.2 In mixed convection.…………...…….…….…………..…………35

2.3 Boundary conditions…………..……...…………………….…....……36
2.3.1 Channel with single rib.…………….……………....…...…....36
2.3.2 Channel with rib array.……………...…………..……..….…37

2.4 Evaluations of heat transfer and pressure drop.…………..……………...39
Chapter 3 Numerical Method………...…….….…………………………...43
3.1 The Discretization of the convection-diffusion equation.……….....…..43
3.1.1 Vorticity transport equation.………...…...………………...…….…..45
3.1.2 Stream function.…………...………………………………….….…..46
3.1.3 Energy equation of the flow..………………………………………..46
3.1.4 Energy equation of the solid rib.…………...….………………….....47
3.1.5 Relaxation factor.…………...………………………………………..48

3.2 Numerical solution procedures.……...…...…………………………...49
3.2.1 Forced convection …………..……..………………...….………….49
3.2.2 Mixed convection ………………….…………...….…….…....……50

3.3 Validation………..........................................................………….........…52
3.3.1 Forced convection with single rib……..…………………...………52
3.3.2 Forced convection in a channel with rib array ………………….....52
3.3.3 Mixed convection in a channel with single rib …………………….53
3.3.4 Mixed convection in various inclined angle channel……......…….53
3.3.5 Experimental data verification……………………………….......…54

3.4 Grid independence ................................................................................ 55
3.4.1 Single rib in forced convection........................................................ 55
3.4.2 Rib array in forced convection…..............................…................…56
3.4.3 Single rib in mixed convection……..............................................…56
3.4.4 Rib array in mixed convection ..............................….................…57

Chapter 4 Results and Discussions……………………………….…………73
4.1 Forced convection with single rib.…………...………….……………..73
4.1.1 Effect of Re………..……......………………………….…………..77
4.1.2 Effect of K ……….…………………..………….……….………..77
4.1.3 Effect of A.……….…………………………………………....……..78
4.1.3 Pressure drop…………...……………..…..……...……….………..78

4.2 Forced convection with in-line rib array ……………..………………..80
4.2.1 Effect of Re …………….…………………………………....……..81
4.2.2 Effect of K…………….....…………………………….……….…..83
4.2.3 Effect of S………...……..……………………………...…………..83
4.2.4 Effect of Li…………….....……………………………..…………..84

4.3 Forced convection with staggered rib array …………..……...………..86
4.3.1 Effect of K…………..…….……….…………….………….……..88
4.3.2 Effect of Re ……………………….…………….…..……………..90
4.3.3 Effect of Li…………..………….….……………..………………..90
4.3.4 Effect of A…………..………………..………….……………….. 91
4.3.5 Comparison of heat transfer and pressure drop……………...…..91

4.4 Mixed convection with single rib …….…….……..……….…………..93
4.4.1 Effect of Gr/Re2..……..………..……………….……….……...…..94
4.4.2 Effect of inclined angle………………...…………………….….....97
4.4.3 Effect of K …………...…………………………………………..97
4.4.4 Effect of A……………………..………...………………..………..97

4.5 Mixed convection staggered rib array…….……………….…………..98
4.5.1 Effect of inclined angle………………...…………………….…...100
4.5.2 Effect of Gr/Re2..…..………..……………….……….……...…..101
4.5.3 Effect of K …………...…………………………………………101

Chapter 5 Conclusions and Recommendations……..…...…….....………151
5.1 Conclusions…………………………..………….………….…………..151
5.2 Recommendations……………………………...…..…….….………...153

Reference………………….…………………….............……….…………154

Publication List ……….…………………….............……….…..……...…169

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