本研究使用冪次流體為工作流體，探討一個具迴流之非對稱固定壁溫度二行程平板式熱交換器，改變其上下板溫度比例、格拉茲數與隔板位置以獲得最有效率之熱傳效果。此熱傳系統之統制方程式屬於共軛格拉茲問題 (conjugated Graetz problem)，本研究應用分離變數法、重疊原理 (superposition)及正交展開法(orthogonal expansion technique)求其解析解，求得於壁固定溫度比例下，兩平板間流體的溫度分佈與平均納塞數 (average Nusselt number)。此外，亦探討改變冪次定律指數、不同壁溫度比例、迴流比值、隔板位置和迴流型式等參數下的熱傳現象之改善效率，並與單行程熱交換器作比較。結果顯示，本研究之實驗數據與理論模擬結果趨勢相符合，且可發現預混效應與滯留時間為影響熱傳效率之主要因素，並可發現冪次指數愈小的流體所獲得出口溫度較低。

The conjugated Graetz problem of a double-pass parallel-plate heat exchanger under asymmetric wall temperatures improvement is investigated theoretically and experimentally to enhance the device performace improvement.  The theoretical mathematical model is solved analytically using the separation of variables, superposition principle and an orthogonal expansion technique in extended power series.  The analytical predictions show that the power-law fluids in such a double-pass operation results in the significant heat-transfer efficiency improvement as compared with those in an open conduit (without an impermeable resistless sheet inserted), especially when the double-pass device was operated in a larger Graetz number.  The results show that the good agreement between the experimental results and theoretical prediction is obtained.  The effects of the ratio of top and bottom wall temperatures, impermeable-sheet position, recycle ratio and power consumption increment for power-law fluids have also been presented.

中文摘要......................................................................................................I
英文摘要.....................................................................................................II
目錄...............................................................................................III
圖目錄...............................................................................................V
表目錄.....................................................................................................XIII
符號說明................................................................................................XIV
第一章 緒論................................................................................................1
1.1	前言................................................................................................1
1.2	迴流效應對系統之影響................................................................2
1.3	研究動機與目的............................................................................3
1.4	研究架構........................................................................................4
第二章 文獻回顧........................................................................................5
2.1	文獻回顧........................................................................................5
2.2	格拉茲問題....................................................................................7
第三章 基本理論......................................................................................10
3.1	二行程無迴流模型之理論分析..............................................17
3.2	管末端出口迴流模型之理論分析..............................................24
3.3	出口迴流至末端模型之理論分析..............................................30
3.4	末端迴流至入口模型之理論分析..............................................36
3.5	出口迴流至入口模型之理論分析..............................................43
3.6	平均納塞數及熱傳導效率..........................................................49
3.7	能量消耗增益率..........................................................................51
第四章 實驗分析......................................................................................55
4.1	冪次流體溶液配製......................................................................55
4.2	流變儀操作..................................................................................55
4.3	物理性質檢測..............................................................................57
4.4	實驗裝置說明..............................................................................60
4.5	實驗步驟......................................................................................63
第五章 結果與討論..................................................................................65
5.1	二行程無迴流模型之結果討論..................................................70
5.2	管末端出口迴流模型之結果討論..............................................85
5.3	出口迴流至管末端模型之結果討論........................................100
5.4	管末端迴流至入口模型之結果討論........................................116
5.5	出口迴流至入口模型之結果討論............................................130
5.6	實驗結果與討論........................................................................144
第六章 結論與建議................................................................................148
6.1	二行程無迴流模型....................................................................148
6.2	管末端出口迴流模型................................................................148
6.3	出口迴流至管末端模型............................................................149
6.4	管末端迴流至入口模型............................................................149
6.5	出口迴流至入口模型................................................................150
6.6	五種模型之比較........................................................................150
6.7	未來的研究方向........................................................................151
參考文獻..........................................................................153
附錄(一)冪次流體速度分佈式...............................................................160
附錄(二)正交性質...................................................................................166
附錄(三)積分公式證明...........................................................................169
附錄(四)單行程之理論分析...................................................................173
附錄(五)五次方多項式展開法...............................................................178

 
圖目錄
圖(3.1.1)	無迴流之二行程熱交換系統……………………………...20
圖(3.2.1)	管末端出口迴流之二行程熱交換系統…………………...26
圖(3.3.1)	出口迴流之二行程熱交換系統…………………………...32
圖(3.4.1)	管末端迴流至入口之二行程熱交換系統………………...38
圖(3.5.1)	出口迴流至入口之二行程熱交換系統…………………...45
圖(4.2.1)	黏度隨剪率變化圖形……………………………………...56
圖(4.3.1)	瑞典Hot Disk TPS 2500[61]………….......………….58
圖(4.3.2)	量測時熱量擴散示意圖[61]………………….....………...59
圖(4.4.1)	二行程無迴流實驗裝備簡圖……………………………...60
圖(4.4.2)	管末端出口迴流實驗裝備簡圖…………………………...60
圖(4.4.3)	出口迴流至末端實驗裝備簡圖…………………………...61
圖(4.4.4)	末端迴流至入口實驗裝備簡圖…………………………...61
圖(4.4.5)	出口迴流至入口實驗裝備簡圖…………………………...61
圖(4.4.6)	平板式熱交換器模組分解圖……………………………...62
圖(4.4.7)	平板式熱交換器實驗裝備實際圖………………………...62
圖(5.1.1)	二行程無迴流模型，冪次指數0.4時，格拉茲數 與出口無因次溫度於壁溫度比例不同之關係............................................…73
圖(5.1.2)	二行程無迴流模型，冪次指數0.8時，格拉茲數 與出口無因次溫度於壁溫度比例不同之關係……………………........……74
圖(5.1.3)	二行程無迴流模型，冪次指數0.4及壁溫度比例3時，格拉茲數 與出口無因次溫度於中間隔板位置不同之關係..............75
圖(5.1.4)	二行程無迴流模型，冪次指數0.8及壁溫度比例3時，格拉茲數 與出口無因次溫度於中間隔板位置不同之關係..............76
圖(5.1.5)	二行程無迴流模型，冪次指數0.4及中間隔板位置0.5時，格拉茲數 與出口無因次溫度於壁溫度比例不同之關係..........77
圖(5.1.6)	二行程無迴流模型，冪次指數0.8及中間隔板位置0.5時，格拉茲數 與出口無因次溫度於壁溫度比例不同之關係……..78
圖(5.1.7)	二行程無迴流模型，冪次指數0.4時，格拉茲數 與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係	…….........….79
圖(5.1.8)	二行程無迴流模型，冪次指數0.8時，格拉茲數 與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係…….…….....80
圖(5.1.9)	二行程無迴流模型，冪次指數0.4時，格拉茲數 與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係…….......81
圖(5.1.10)	二行程無迴流模型，冪次指數0.8時，格拉茲數 與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係……..….82
圖(5.1.11)	二行程無迴流模型，冪次指數0.4時，格拉茲數 與 於壁溫度比例不同及中間隔板位置不同之關係……..............….83
圖(5.1.12)	二行程無迴流模型，冪次指數0.8時，格拉茲數 與 於壁溫度比例不同及中間隔板位置不同之關係………..….……84
圖(5.2.1)	管末端出口迴流模型，冪次指數0.4時，格拉茲數 與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係….......…88
圖(5.2.2)	管末端出口迴流模型，冪次指數0.8時，格拉茲數 與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係	….......…89
圖(5.2.3)	管末端出口迴流模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係...90
圖(5.2.4)	管末端出口迴流模型，冪次指數0.8時，格拉茲數 與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係...…91
圖(5.2.5)	管末端出口迴流模型，冪次指數0.4及壁溫度比例3且中間隔板位置0.5時，格拉茲數 與出口無因次溫度於不同迴流比之關係.......................................................................................................92
圖(5.2.6)	管末端出口迴流模型，冪次指數0.8及壁溫度比例3且中間隔板位置0.5時，格拉茲數 與出口無因次溫度於不同迴流比之關係……………………………………..................……………….…93
圖(5.2.7)	管末端出口迴流模型，冪次指數0.4且迴流比R=1時，格拉茲數 與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係………………………………………………………….....…..…94
圖(5.2.8)	管末端出口迴流模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係……………......……………………………………………….…95
圖(5.2.9)	管末端出口迴流模型，冪次指數0.4且迴流比R=1時，格拉茲數 與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係…………………………………………………..............….…96
圖(5.2.10)	管末端出口迴流模型，冪次指數0.8且迴流比R=1時，格拉茲數 與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係………………………………..............…………………….…97
圖(5.2.11)	管末端出口迴流模型，冪次指數0.4且迴流比R=1時，格拉茲數 與 於壁溫度比例不同及中間隔板位置不同之關係………………………………………………………………...…98
圖(5.2.12)	管末端出口迴流模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係………………………………….………………………….….…99
圖(5.3.1)	出口迴流至管末端模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係……………………………………………………….………....102
圖(5.3.2)	出口迴流至管末端模型，冪次指數0.8時，格拉茲數Gz與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係.....103
圖(5.3.3)	出口迴流至管末端模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係…………………….………………………………………….....104
圖(5.3.4)	出口迴流至管末端模型，冪次指數0.8時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係………………………………………………….………….…..105
圖(5.3.5)	出口迴流至管末端模型，冪次指數0.4及壁溫度比例3且中間隔板位置0.5時，格拉茲數Gz與出口無因次溫度於不同迴流比之關係………………………….........……………………….…..106
圖(5.3.6)	出口迴流至管末端模型，冪次指數0.8及壁溫度比例3且中間隔板位置0.5時，格拉茲數Gz與出口無因次溫度於不同迴流比之關係……………………………….........………………….…..107
圖(5.3.7)	出口迴流至管末端模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係……………………………………….………………….…..108
圖(5.3.8)	出口迴流至管末端模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係…………………………………………………….…….…..109
圖(5.3.9)	出口迴流至管末端模型，冪次指數0.4且固定中間隔板位置0.5時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及迴流比不同之關係………………………….............…………………….…..110
圖(5.3.10)	出口迴流至管末端模型，冪次指數0.8且固定中間隔板位置0.5時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及迴流比不同之關係………………………………………….............….……..111
圖(5.3.11)	出口迴流至管末端模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係…………………………………………………..........…..112
圖(5.3.12)	出口迴流至管末端模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係………………………….........……………………….…..113
圖(5.3.13)	出口迴流至管末端模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係………………………………………………….…….………..114
圖(5.3.14)	  出口迴流至管末端模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係………………………………………………………….….…..115
圖(5.4.1)	管末端迴流至入口模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係....................................................................................................118
圖(5.4.2)	  管末端迴流至入口模型，冪次指數0.8時，格拉茲數Gz與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係………………………………………………….………….…..119
圖(5.4.3)	  管末端迴流至入口模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係...................................................................................................120
圖(5.4.4)	  管末端迴流至入口模型，冪次指數0.8時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係...................................................................................................121
圖(5.4.5)	  管末端迴流至入口模型，冪次指數0.4及壁溫度比例3且中間隔板位置0.5時，格拉茲數Gz與出口無因次溫度於不同迴流比之關係...........................................................................................122
圖(5.4.6)	管末端迴流至入口模型，冪次指數0.8及壁溫度比例3且中間隔板位置0.5時，格拉茲數Gz與出口無因次溫度於不同迴流比之關係...........................................................................................123
圖(5.4.7)	  管末端迴流至入口模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係...............................................................................................124
圖(5.4.8)	  管末端迴流至入口模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係...............................................................................................125
圖(5.4.9)	  管末端迴流至入口模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係..........................................................................................126
圖(5.4.10)	管末端迴流至入口模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係..........................................................................................127
圖(5.4.11)  	管末端迴流至入口模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係..................................................................................................128
圖(5.4.12)	  管末端迴流至入口模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係..................................................................................................129
圖(5.5.1)	出口迴流至入口模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係......132
圖(5.5.2)	出口迴流至入口模型，冪次指數0.8時，格拉茲數Gz與出口無因次溫度於壁溫度比例不同於與迴流比不同之關係......133
圖(5.5.3)	出口迴流至入口模型，冪次指數0.4時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係..................................................................................................134
圖(5.5.4)	出口迴流至入口模型，冪次指數0.8時，格拉茲數Gz與出口無因次溫度於中間隔板位置不同與壁溫度比例不同之關係...................................................................................................135
圖(5.5.5)	出口迴流至入口模型，冪次指數0.4及壁溫度比例3且中間隔板位置0.5時，格拉茲數Gz與出口無因次溫度於不同迴流比之關係...............................................................................................136
圖(5.5.6)	出口迴流至入口模型，冪次指數0.8及壁溫度比例3且中間隔板位置0.5時，格拉茲數Gz與出口無因次溫度於不同迴流比之關係...............................................................................................137
圖(5.5.7)	出口迴流至入口模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係...................................................................................................138
圖(5.5.8)	出口迴流至入口模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與納賽數Nu於壁溫度比例不同及中間隔板位置不同之關係...................................................................................................139
圖(5.5.9)	出口迴流至入口模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係..............................................................................................140
圖(5.5.10)	出口迴流至入口模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與熱量傳送效率於壁溫度比例不同及中間隔板位置不同之關係.............................................................................................141
圖(5.5.11)	  出口迴流至入口模型，冪次指數0.4且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係.................................................................................................142
圖(5.5.12)	  出口迴流至入口模型，冪次指數0.8且迴流比R=1時，格拉茲數Gz與Ih/Ip於壁溫度比例不同及中間隔板位置不同之關係..................................................................................................143 


表目錄
表(3.7.1)	二行程無迴流模型以中間隔板為參數能源消耗增加率...53
表(3.7.2)	管末端出口迴流模型以中間隔板為參數能源消耗增加率........................................................................................................53
表(3.7.3)	出口迴流至管末端模型以中間隔板為參數能源消耗增加率........................................................................................................54
表(3.7.4)	管末端迴流至入口模型以中間隔板為參數能源消耗增加率........................................................................................................54
表(3.7.5)	出口迴流至入口模型以中間隔板為參數能源消耗增加率........................................................................................................54
表(4.3.1)	熱傳導係數與比熱量測結果[61]...........................................58
表(4.3.2)	物質標準狀況下比熱對照表[61]...........................................59
表(5.0.1)	二行程無迴流模型，級數解收斂情形，於隔板位置0.5、壁溫度比例3.........................................................................................66
表(5.0.2)	管末端出口迴流模型，級數解收斂情形，於隔板位置0.5、 及壁溫度比例3.........................................................................66
表(5.0.3)	出口迴流至管末端模型，級數解收斂情形，於隔板位置0.5、 及壁溫度比例3.........................................................................66
表(5.0.4)	管末端迴流至入口模型，級數解收斂情形，於隔板位置0.5、 及壁溫度比例3.........................................................................67
表(5.0.5)	出口迴流至入口模型，級數解收斂情形，於隔板位置0.5、 及壁溫度比例3.........................................................................67
表(5.0.6)	二行程無迴流模型，特徵值收斂情形，於隔板位置0.5、壁溫度比例3.........................................................................................67
表(5.0.7)	管末端出口迴流模型，特徵值收斂情形，於隔板位置0.5、 及壁溫度比例3.........................................................................68
表(5.0.8)	出口迴流至管末端模型，特徵值收斂情形，於 、 及壁溫度比例3................................................................................68
表(5.0.9)	管末端迴流至入口模型，特徵值收斂情形，於 、 及壁溫度比例3................................................................................68
表(5.0.10)	出口迴流至入口模型，特徵值收斂情形，於 、 及壁溫度比例3....................................................................................69
表(5.6.1)	二行程無迴流模型實驗值與理論值之平均誤差.............145
表(5.6.2)	管末端出口模型實驗值與理論值之平均誤差.................145
表(5.6.3)	出口回流至管末端模型實驗值與理論值之平均誤差.....146
表(5.6.4)	管末端迴流至入口模型實驗值與理論值之平均誤差.....146
表(5.6.5)	出口回流至入口模型實驗值與理論值之平均誤差.........147

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