臺灣博碩士論文加值系統

二維穩態無熱源的複合壁問題中，所有的熱傳教科書和參考文獻，都是利用類似並聯電阻迴路（PERC）的並聯熱阻迴路（PTRC）模型來分析求解。當應用相似於電阻串聯迴路（SERC）的熱阻串聯迴路（STRC）模型來求解一維穩態無熱源的複合壁熱傳問題時，由於兩者之本質完全相似，因此其結果是正碓的。但是，對複合壁二維穩態問題，利用誤以為類似PERC的PTRC模型來求解，其本質上有顯著的不同。因為一維PTRC模型其在二維複合壁交界面（PTRC的節點）的界面溫度並不相同，並不相似於PERC在節點上是有相同電壓。故此，以往應用上將之視為有相似性是非常不正確的。
為了獲得足夠的證據以證實應用PTRC模型於複合壁二維穩態問題之不正確性，本論文將對複合壁二維穩態問題，包括平面複合壁和圓管複合壁在在不同的邊界條件下，利用CFD軟體來分析所得熱傳率和溫度分佈的結果，與使用簡單的一維PTRC模型的結果作比較，由兩者之間產生極大的誤差以證明其不正確性。此外，本論文發展出之一維各自串聯熱阻迴路（SSTRC）模型作為取代PTRC模型作簡單可靠的工程計算。由SSTRC模型所生結果與數值解比較所得的誤差率，來尋求SSTRC模型在何種條件下的適用性。

For the two-dimensional steady heat-transfer problems of composite walls without heat source, all the heat transfer textbooks and research papers have applied the one-dimensional Parallel Thermal Resistance Circuit (PTRC) model to analyze and solve those problems. Undoubtedly, applying the Series Thermal Resistance Circuit (STRC) model, whose essential characteristics are totally identical to Series Electrical Resistance Circuit (PERC), to solve the one-dimensional steady heat-transfer problems of composite walls is accurate. For the two-dimensional steady heat-transfer problems of composite walls, applying the PTRC model, whose essential characteristics are totally not identical to PERC model, to solve those problems is inaccurate. Thus, their solutions will generate big errors.
This thesis proves that two-dimensional steady-state heat-transfer problems of composite walls should not be appropriately solved by the one-dimensional PTRC model. Because we found out that the interface temperatures (node points of PTRC) of the composite walls are not the same. It is a big different to the Parallel Electric Resistance Circuits (PERC) with the same voltage at the same node point. Thus, the conventional thinking of there is similarity between PTRC and PERC is absolutely wrong. In order to prove such theory, two typical composite wall examples are used to analyze by CFD software. We found that conventional one-dimensional PTRC model for two-dimensional steady-state heat-transfer problems of composite walls will generate very great errors by comparing with the numerical results.
Additionally, the alternative one-dimensional Separately Series Thermal Resistance Circuit (SSTRC) model is developed in this study. From the errors generated by the SSTRC model, we can figure out under what conditions the SSTRC model can be suitable applied to solve the two-dimensional steady-state heat-transfer problems of composite walls.

壹、緒論...................................................1
貳、理論與分析基礎.........................................7
2-1例子1：典型二維垂直熱流向三層四區域平板複合壁...........7
2-1-1、例子1之PTRC模型的分析過程...........................8
2-1-2、一維各自串聯熱阻迴路（SSTRC）在例子1的應用..........9
2-2例子2：典型二維垂直熱流向四層六區域平板複合壁..........10
2-2-1、一維各自串聯熱阻迴路（SSTRC）在例子2的應用.........11
2-2-2、PTRC模型與SSTRC模型的誤差率........................13
2-3例子3：典型二維垂直熱流向三層四區域平板複合壁當有熱對流影響時......................................................14
2-3-1、例子3之PTRC模型的分析過程..........................15
2-3-2、一維各自串聯熱阻迴路（SSTRC）在例子3的應用.........15
2-4例子4：典型二維垂直熱流向四層六區域平板複合壁當有熱對流影響時......................................................17
2-4-1、一維各自串聯熱阻迴路（SSTRC）在例子4的應用.........18
2-4-2、PTRC模型與SSTRC模型的誤差率........................20
2-5、圓管複合壁熱阻之理論基礎.............................21
2-5-1例子5：典型二維水平三層四區域的圓管複合壁............25
2-5-2、一維各自串聯熱阻迴路（SSTRC）在典型例子5的應用.....26
2-6例子6：典型二維水平四層六區域的圓管複合壁..............27
2-6-1、一維各自串聯熱阻迴路（SSTRC）在典型例子6的應用.....29
2-6-2、圓管複合壁PTRC模型與SSTRC模型的誤差率比............31
參、網格與邊界之正確性分析................................32
3-1、典型二維垂直熱流向三層四區域平板複合壁之FLUENT正確性模擬分析....................................................32
3-2、典型二維垂直熱流向四層六區域平板複合壁之FLUENT正確性模擬分析....................................................33
3-3、典型二維水平三層四區域的圓管複合壁之FLUENT正確性模擬分析........................................................34
3-4、典型二維水平四層六區域的圓管複合壁之FLUENT正確性模擬分析........................................................35
肆、結果與討論............................................37
4-1、典型二維垂直熱流向三層四區域平板複合壁之結果與討論...37
4-2、典型二維垂直熱流向四層六區域平板複合壁之結果與討論...38
4-3、典型二維垂直熱流向三層四區域平板複合壁當有熱對流影響時之結果與討論..............................................40
4-4、典型二維垂直熱流向四層六區域平板複合壁當有熱對流影響時之結果與討論..............................................43
4-5、典型二維水平三層四區域的圓管複合壁之結果與討論.......46
伍、結論..................................................49
5-1、平板與圓管複合壁邊界為等溫的條件下之結論.............49
5-2、平板複合壁有熱對流影響時之結論.......................49
參考文獻 ................................................52
附錄1....................................................109
附錄2....................................................114
表目錄
表1、如圖5（a）例子1所示複合壁在不同熱傳導係數組合五種情況下之熱傳率誤差圖表，其中Ka＝200 Wm-1℃-1、Kc＝350 Wm-1℃-1、Kd=80 Wm-1℃-1、T1＝100℃ 和 T2＝0℃ 及 L1=L2=L3=0.1m。...57
表2、如圖8（a）例子2所示複合壁在不同熱傳導係數組合五種情況下之熱傳率誤差圖表，其中Ke＝200 Wm-1℃-1、Kg＝350 Wm-1℃-1、Kh=350 Wm-1℃-1、Kj=80 Wm-1℃-1 T3＝100℃ 和T4＝0℃ 及 L1=L2=L3=L4=0.1m。........................................58
表3、如圖8（a）例子2所示複合壁在不同熱傳導係數組合五種情況下之熱傳率誤差圖表，其中Ke＝200 Wm-1℃-1、Kg＝350 Wm-1℃-1、Kh=350 Wm-1℃-1、Ki=0.035 Wm-1℃-1Kj=80 Wm-1℃-1 T3＝100℃ 和T4＝0℃ 及 L1=L2=L3=L4=0.1m。...........................59
表4、如圖9例子3所示平板複合壁當有熱對流影響時，在不同熱傳導係數組合情況下之熱傳率誤差圖表，其中Ka＝200 Wm-1℃-1、Kc＝350 Wm-1℃-1、Kd=80 Wm-1℃-1、T1＝100℃ 和 T2＝0℃ 及 L1=L2=L3=0.1m。...........................................60
表5、如圖9例子3所示平板複合壁當有熱對流影響時，在不同熱傳導係數組合情況下之熱傳率誤差圖表，其中Ka＝200 Wm-1℃-1、Kc＝350 Wm-1℃-1、Kd=0.7 Wm-1℃-1、T1＝100℃ 和 T2＝0℃ 及 L1=L2=L3=0.1m。...........................................61
表6、如圖9例子3所示平板複合壁當有熱對流影響時，在不同熱傳導係數組合情況下之熱傳率誤差圖表，其中Ka＝200 Wm-1℃-1、Kc＝350 Wm-1℃-1、Kd=0.035 Wm-1℃-1、T1＝100℃ 和 T2＝0℃ 及L1=L2=L3=0.1m。...........................................62
表7、如圖12例子4所示平板複合壁當有熱對流影響時，在不同熱傳導係數組合情況下之熱傳率誤差圖表，其中Ke = 200 Wm-1℃-1、Kg = 350 Wm-1℃-1、Kh = 350 Wm-1℃-1、Kj = 80 Wm-1℃-1、L1=0.1m、L2=0.2m、L3=0.3m、L4=0.4m、H=1m、Ti=100℃、To=0℃.........63
表8、如圖12例子4所示平板複合壁當有熱對流影響時，在不同熱傳導係數組合情況下之熱傳率誤差圖表，其中Ke = 200 Wm-1℃-1、Kg = 350 Wm-1℃-1、Kh = 350 Wm-1℃-1、Kj = 0.7 Wm-1℃-1、L1=0.1m、L2=0.2m、L3=0.3m、L4=0.4m、H=1m、Ti=100℃、To=0℃....................................................64
表9、如圖12例子4所示平板複合壁當有熱對流影響時，在不同熱傳導係數組合情況下之熱傳率誤差圖表，其中Ke = 200 Wm-1℃-1、Kg = 350 Wm-1℃-1、Kh = 350 Wm-1℃-1、Kj = 0.035 Wm-1℃-1、L1=0.1m、L2=0.2cm、L3=0.3m、L4=0.4m、H=1m、Ti=100℃、To=0℃....................................................65
表10、如圖17例子5所示圓管複合壁在不同熱傳導係數組合五種情況下之熱傳率誤差圖表，其中Ka = 200 Wm-1℃-1 Kc = 350 Wm-1℃-1 Kd = 80 Wm-1℃-1 r1= 0.20m, r2=0.23m, r3=0.26m, r4=0.29m, Ti=100℃, To=0℃..........................................66
表11、如圖20例子6所示圓管複合壁在不同熱傳導係數組合五種情況下之熱傳率誤差圖表，其中Ke = 200 Wm-1℃-1 Kg = 350 Wm-1℃-1 Kh = 350 Wm-1℃-1 Kj = 80 Wm-1℃-1 r1= 0.2m r2=0.23m r3=0.26m r4=0.29m r5=0.32m Ti=100℃To=0℃.................67
圖目錄
圖1、（a）簡單壁面的熱傳問題圖（b）電路迴路...............68
圖2、（a）電阻串聯迴路（b）一維複合壁熱阻串聯迴路.........69
圖3、例子1：典型二維垂直熱流方向三層四區域平板複合壁模型..70
圖4、（a）例子Ⅰ的PTRC模型（b）例子Ⅰ相對的電路並聯迴路...71
圖5、（a）例子1的一維SSTRC模型的假設......................72
圖6、例子2典型二維垂直熱流方向四層六區域復合璧............73
圖7、（a）例子2的PTRC模型（b）例子2相似電路並聯迴路.......74
圖8、（a）例子2的一維SSTRC模型（b）例子2的SSTRC模型.......75
圖9、例子3：二維垂直熱流向三層四區域平板複合壁當有熱對流影響時的典型例子..............................................76
圖10、（a）例子3的PTRC模型（b）例子3相對的電路並聯迴路....77
圖11、（a）二維垂直熱流向三層四區域平板複合壁當有熱對流影響時運用二維SSTRC模型的例子（b）二維垂直熱流向三層四區域平板複合壁當有熱對流影響時SSTRC模型.............................78
圖12、例子4二維垂直熱流向四層六區域平板複合壁當有熱對流影響時之典型例子..............................................79
圖13、（a）二維垂直熱流向四層六區域平板複合壁當有熱對流影響時之PTRC模型（b）例子4相似電路並聯迴路....................80
圖14、（a）二維垂直熱流向四層六區域平板複合壁當有熱對流影響時運用二維SSTRC模型的例子（b）二維垂直熱流向四層六區域平板複合壁當有熱對流影響時SSTRC模型.............................81
圖15、（a）簡單圓形圓管面的熱傳問題（b）電阻迴路（c）一維穩態熱阻迴路................................................82
圖16、（a）電阻串聯迴路（b）複合圓管一維熱阻串聯迴路......83
圖17、例子5典型二維水平三層四區域複合圓管模型.............84
圖18、（a）例子5的典型二維水平三層四區域複合圓管的PTRC模型（b）例子3之電阻並聯迴路..................................85
圖19、（a）例子5典型二維水平三層四區域SSTRC模型應用複合圓管的例子（b）例子5之典型二維水平三層四區域複合圓管之SSTRC模型........................................................86
圖20、例子6典型二維水平四層六區域複合圓管模型.............87
圖21、（a）例子6的典型二維水平四層六區域複合圓管PTRC模型（b）例子6之電阻並聯迴路..................................88
圖22、（a）例子6典型二維水平四層六區域複合圓管SSTRC模型應用的例子（b）例子6的典型二維水平四層六區域複合圓管SSTRC模型.89
圖23、使用FLUENT建立如圖5（a）典型二維垂直熱流向三層四區域平板複合壁之網格............................................90
圖24、典型二維垂直熱流方向三層四區域平板複合壁模型之Lab VIEW程式......................................................91
圖25、使用FLUENT建立如圖8（a）典型二維垂直熱流向四層六區域平板複合壁模型之網格........................................92
圖26、典型二維垂直熱流方向四層六區域平板複合壁模型之Lab VIEW程式......................................................93
圖27、使用FLUENT建立如圖19（a）典型二維水平三層四區域複合圓管模型之網格..............................................94
圖28、典型二維水平三層四區域複合圓管模型之Lab VIEW程式....95
圖29、使用FLUENT建立如圖22（a）典型二維水平四層六區域的圓管複合壁模型之網格..........................................96
圖30、典型二維水平四層六區域複合圓管模型之Lab VIEW程式....97
圖31、圖5例子1典型二維垂直熱流向三層四區域複合壁模型溫度流場分佈圖....................................................98
圖32、圖8例子2典型二維垂直熱流向四層六區域複合壁模型溫度流場分佈圖....................................................99
圖33、圖8例子2典型二維垂直熱流向四層六區域複合壁模型溫度流場分佈圖...................................................100
圖34、（a）CaseⅣ-3（b）CaseⅣ-6（c）CaseⅣ-9之溫度分佈圖.......................................................101
圖35、（a）CaseV-4（b）CaseV-7（c）CaseV-10之溫度分佈圖..102
圖36、（a）CaseVI-3（b）CaseVI-6（c）CaseVI-9之溫度分佈圖。.....................................................103
圖37、（a）CaseVII-3（b）CaseVII-6（c）CaseVII-9之溫度分佈圖.......................................................104
圖38、（a）CaseVIII-3（b）CaseVIII-6（c）CaseVIII-9之溫度分佈圖.....................................................105
圖39、（a）CaseIX-3（b）CaseIX-6（c）CaseIX-9之溫度分佈圖.......................................................106
圖40、圖19例子9典型二維水平熱流向三層四區域圓管複合壁模型溫度流場分佈圖.............................................107
圖41、圖22例子10典型二維水平熱流向四層六區域圓管複合壁模型溫度流場分佈圖.............................................108

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