本研究運用冪次流體作為工作流體，設計一可忽略熱阻之鋁板於兩平行板間並加入迴流裝置，使之成為一邊為固定壁溫度，另一邊為固定熱通量之二行程平板型熱交換器。此系統所推導之統制方程式屬於共軛格拉茲問題 (conjugated Graetz problem)，並運用分離變數法、重疊原理(superposition)及正交展開法(orthogonal expansion technique)，求得於一邊固定壁溫與另一邊固定熱通量混合型邊界條件下之解析解。此外，在理論推導過程中，另定義一包含兩端邊界條件之無因次數（β），其可明顯的影響熱交換器之出口溫度，其值主要決定於一端壁加熱功率以及進口流體溫度與另一邊壁溫差之比值。本研究探討流體冪次指數、迴流比大小、β值、隔板位置等參數對熱傳之影響。結果顯示實驗與理論計算值相符合，並且兩端邊界條件β值越大或流體冪次指數越小時，具有較高的熱傳效率。

The heat-transfer Graetz problem of a double-pass parallel-plate heat exchanger for the power-law flow subject to the hybrid boundary condition, was investigated theoretically. An impermeable barrier without thermal resistance was placed between two parallel plates, whose thermal boundaries were preset at constant temperature at one side, and constant heat flux at the other; it is called the hybrid boundary condition. In order to enhance the device performance, the recycle operation was designed between the flows in the two subchannels. The mathematical model was solved analytically using the separation of variables, together with the superposition principle and an orthogonal expansion in the power series. A dimensionless number (β) is defined as the ratio of the temperature difference between the inlet-flow and the wall at one side over the heat flux at the other side. Both theβvalue and the recycle ratio can render significant influences on the heat transfer efficiency and thus the outlet temperature from the heat exchanger. The experiments were conducted to justified the theoretical simulations. Both the theoretical and experimental results showed that the power law indices play little effect on the heat transfer of the double-pass heat exchanger in this study.

目錄
中文摘要	I
目錄	II
圖目錄	IV
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	出口迴流至入口模型之理論分析	25
3.3	管末端出口模型之理論分析	33
3.4	平均那塞數及熱傳導效率	41
3.5	能源消耗增益率	43
第四章  實驗分析	46
4.1	冪次流體溶液配製	46
4.2	流變儀操作	47
4.3	物理性質檢測	49
4.4	實驗裝置說明	52
4.5	實驗步驟	56
第五章  結果與討論	59
5.1	二行程無迴流之結果與討論	66
5.2	出口迴流至入口之結果與討論	89
5.3	管末端出口之結果與討論	117
第六章  結論與建議	146
6.1	二行程無迴流之模型	146
6.2	出口迴流至入口之模型	147
6.3	管末端出口之模型	148
6.4	二行程三種迴流系統之比較	149
6.5	未來研究方向	150
參考文獻	151
附錄(一) 冪次流體速度分佈式	159
附錄(二) 正交性質	164
附錄(三) 積分公式證明	167
附錄(四) 單通道之理論分析	170
附錄(五) 五次多項式展開法	176

圖目錄
圖(3.1.1)  二行程無迴流之熱交換系統	18
圖(3.2.1)  管末端出口之熱交換系統	26
圖(3.3.1)  管末端出口之熱交換系統	34
圖(4.2.1)  流變儀實際圖	47
圖(4.2.2)  黏度隨剪率變化圖形	48
圖(4.3.1)  瑞典Hot Disk TPS 2500	51
圖(4.3.2)  量測時熱量擴散示意圖	51
圖(4.4.1)  二行程無迴流實驗裝備簡圖	53
圖(4.4.2)  出口迴流至入口實驗裝備簡圖	53
圖(4.4.3)  管末端出口實驗裝備簡圖	54
圖(4.4.4)  平板式熱交換器實驗裝備實際圖	54
圖(5.1.1)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=0.5)，平均出口那塞數與格拉茲數關係	71
圖(5.1.2)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，平均出口那塞數與格拉茲數之關係	72
圖(5.1.3)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=2.0)，平均出口那塞數與格拉茲數之關係	73
圖(5.1.4)  二行程無迴流實驗，固定隔板位置(delta=0.5)，平均出口那塞數與格拉茲數之關係	74
圖(5.1.5)  二行程無迴流實驗，固定冪次指數(omega=0.4)及beta(beta=0.5)，平均出口那塞數與隔板位置之關係	75
圖(5.1.6)  二行程無迴流實驗，固定冪次指數(omega=0.4)及格拉茲數(Gz=10)，平均出口那塞數與隔板位置之關係	76
圖(5.1.7)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=0.5)，Ih與格拉茲數之關係	77
圖(5.1.8)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，Ih與格拉茲數之關係	78
圖(5.1.9)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=2.0)，Ih與格拉茲數之關係	79
圖(5.1.10)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=0.5)，Ih/Ip與格拉茲數之關係	80
圖(5.1.11)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，Ih/Ip與格拉茲數之關係	81
圖(5.1.12)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=2.0)，Ih/Ip與格拉茲數之關係	82
圖(5.1.13)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	83
圖(5.1.14)  二行程無迴流實驗，固定冪次指數(omega=0.4)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	84
圖(5.1.15)  二行程無迴流實驗，固定隔板位置(delta=0.5)及冪次指數(omega=0.4)，上通道壁無因次溫度與通道位置之關係	85
圖(5.1.16)  二行程無迴流實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，中間壁無因次溫度與通道位置之關係	86
圖(5.1.17)  二行程無迴流型式，固定beta(beta=1.0)及格拉茲數(Gz=1)，通道截面無因次溫度之關係	87
圖(5.1.18)  二行程無迴流型式，固定beta(beta=0.5)及冪次指數(omega=0.4)，流體無因次平均溫度與不同通道位置之關係	88
圖(5.2.1)  出口迴流至入口實驗實驗，固定隔板位置(delta=0.5)及beta(beta=0.5)，平均出口那塞數與格拉茲數之關係	94
圖(5.2.2)  出口迴流至入口實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，平均出口那塞數與格拉茲數之關係	95
圖(5.2.3)  出口迴流至入口實驗，固定隔板位置(delta=0.5)及beta(beta=2.0)，平均出口那塞數與格拉茲數之關係	96
圖(5.2.4)  出口迴流至入口實驗，固定隔板位置(delta=0.5)及冪次指數 (omega=0.4)，平均出口那塞數與格拉茲數之關係	97
圖(5.2.5)  出口迴流至入口實驗，固定冪次指數(omega=0.4)、beta(beta0.5)及迴流比(R=0.5)，平均出口那塞數與隔板位置之關係	98
圖(5.2.6)  出口迴流至入口實驗，固定冪次指數(omega=0.4)、格拉茲數 (Gz=10)及迴流比(R=0.5)，平均出口那塞數與隔板位置之關係	99
圖(5.2.7)  出口迴流至入口實驗，固定冪次指數(omega=0.4)及beta(beta=1.0)，平均出口那塞數與隔板位置之關係	100
圖(5.2.8)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、beta(beta=0.5)及迴流比(R=0.5)，Ih與格拉茲數之關係	101
圖(5.2.9)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、beta(beta=1.0)及迴流比(R=0.5)，Ih與格拉茲數之關係	102
圖(5.2.10)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、beta(beta=2.0)及迴流比(R=0.5)，Ih與格拉茲數之關係	103
圖(5.2.11)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、beta(beta=0.5)及迴流比(R=0.5)，Ih/Ip與格拉茲數之關係	104
圖(5.2.12)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、beta(beta=1.0)及迴流比(R=0.5)，Ih/Ip與格拉茲數之關係	105
圖(5.2.13)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、beta(beta=2.0)及迴流比(R=0.5)，Ih/Ip與格拉茲數之關係	106
圖(5.2.14)  出口迴流至入口實驗，固定冪次指數(omega=0.4)及隔板位置(delta=0.5)， 與格拉茲數之關係	107
圖(5.2.15)  出口迴流至入口實驗，固定迴流比 (R=1.5)、格板位置(delta=0.5)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	108
圖(5.2.16)  出口迴流至入口實驗，固定迴流比 (R=1.5)、冪次指數 (omega=0.4)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	109
圖(5.2.17)  出口迴流至入口實驗，固定格板位置(delta=0.5)、冪次指數 (omega=0.4)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	110
圖(5.2.18)  出口迴流至入口實驗，固定格板位置(delta=0.5)、冪次指數(omega=0.4)及迴流比(R=1.5)，上通道壁無因次溫度與通道位置之關係	111
圖(5.2.19)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、迴流比(R=1.5)及beta(beta=1.0)，中間壁無因次溫度與通道位置之關係	112
圖(5.2.20)  出口迴流至入口實驗，固定隔板位置(delta=0.5)、冪次指數(omega=0.4)及beta(beta=1.0)，中間壁無因次溫度與通道位置之關係	113
圖(5.2.21)  出口迴流至入口實驗，固定beta(beta=1.0)、迴流比(R=1.5)及格拉茲數(Gz=10)，通道截面無因次溫度之關係	114
圖(5.2.22)  出口迴流至入口實驗，固定beta(beta=1.0)、迴流比(R=1.5)及冪次指數(omega=0.4)，流體無因次平均溫度與不同通道位置之關係	115
圖(5.2.23) 出口迴流至入口實驗，固定beta(beta=1.0)、隔板位置(delta=0.5)及冪次指數(omega=0.4)，流體無因次平均溫度與不同通道位置之關係	116
圖(5.3.1)  管末端出口實驗實驗，固定隔板位置(delta=0.5)及beta(beta=0.5)，平均出口那塞數與格拉茲數之關係	122
圖(5.3.2)  管末端出口實驗實驗，固定隔板位置(delta=0.5)及beta(beta=1.0)，平均出口那塞數與格拉茲數之關係	123
圖(5.3.3)  管末端出口實驗實驗，固定隔板位置(delta=0.5)及beta(beta=2.0)，平均出口那塞數與格拉茲數之關係	124
圖(5.3.4)  管末端出口實驗，固定隔板位置(delta=0.5)及冪次指數 (omega=0.4)，平均出口那塞數與格拉茲數之關係	125
圖(5.3.5)  管末端出口實驗，固定冪次指數(omega=0.4)、beta(beta=1.0)及迴流比(R=0.5)，平均出口那塞數與隔板位置之關係	126
圖(5.3.6)  管末端出口實驗，固定冪次指數(omega=0.4)、格拉茲數(Gz=10)及迴流比(R=0.5)，平均出口那塞數與隔板位置beta之關係	127
圖(5.3.7)  管末端出口實驗，固定冪次指數(omega=0.4)、格拉茲數(Gz=10)及beta(beta=1.0)，平均出口那塞數與隔板位置之關係	128
圖(5.3.8)  管末端出口實驗，固定冪次指數(omega=0.4)、格拉茲數(Gz=1000)及beta(beta=1.0)，平均出口那塞數與隔板位置之關係	129
圖(5.3.9)  管末端出口實驗，固定隔板位置(delta=0.5)、beta(beta=0.5)及迴流比(R=0.5)，Ih與格拉茲數之關係	130
圖(5.3.10)  管末端出口實驗，固定隔板位置(delta=0.5)、beta(beta=1.0)及迴流比(R=0.5)，Ih與格拉茲數之關係	131
圖(5.3.11)  管末端出口實驗，固定隔板位置(delta=0.5)、beta(beta=2.0)及迴流比(R=0.5)，Ih與格拉茲數之關係	132
圖(5.3.12)  管末端出口實驗，固定隔板位置(delta=0.5)、beta(beta=0.5)及迴流比(R=0.5)，Ih/Ip與格拉茲數之關係	133
圖(5.3.13)  管末端出口實驗，固定隔板位置(delta=0.5)、beta(beta=1.0)及迴流比(R=0.5)，Ih/Ip與格拉茲數之關係	134
圖(5.3.14)  管末端出口實驗，固定隔板位置(delta=0.5)、beta(beta=2.0)及迴流比(R=0.5)，Ih/Ip與格拉茲數之關係	135
圖(5.3.15)  管末端出口實驗，固定冪次指數(omega=0.4)及隔板位置(delta=0.5)， 與格拉茲數之關係	136
圖(5.3.16)  管末端出口實驗，固定迴流比 (R=1.5)、格板位置(delta=0.5)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	137
圖(5.3.17)  管末端出口實驗，固定迴流比 (R=1.5)、冪次指數 (omega=0.4)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	138
圖(5.3.18)  管末端出口實驗，固定格板位置(delta=0.5)、冪次指數(omega=0.4)及beta(beta=1.0)，上通道壁無因次溫度與通道位置之關係	139
圖(5.3.19)  管末端出口實驗，固定格板位置(delta=0.5)、冪次指數(omega=0.4)及迴流比(R=1.5)，上通道壁無因次溫度與通道位置之關係	140
圖(5.3.20)  管末端出口實驗，固定隔板位置(delta=0.5)、迴流比(R=1.5)及beta(beta=1.0)，中間壁無因次溫度與通道位置之關係	141
圖(5.3.21)  管末端出口實驗，固定隔板位置(delta=0.5)、冪次指數(omega=0.4)及beta(beta=1.0)，中間壁無因次溫度與通道位置之關係	142
圖(5.3.22)  出口迴流至入口實驗，固定beta(beta=1.0)、迴流比(R=1.5)及格拉茲數(Gz=10)，通道截面無因次溫度之關係	143
圖(5.3.23)  出口迴流至入口實驗，固定beta(beta=1.0)、迴流比(R=1.5)及冪次指數(omega=0.4)，流體無因次平均溫度與不同通道位置之關係	144
圖(5.3.24)  出口迴流至入口實驗，固定beta(beta=1.0)、隔板位置(delta=0.5)及冪次指數(omega=0.4)，流體無因次平均溫度與不同通道位置之關係	145
圖(A.1)  不同冪次指數於通道中之速度分佈	163

 
表目錄
表(4.3.1)  熱傳導係數與比熱量測結果	51
表(4.3.2)  物質標準狀況下比熱對照表	52
表(4.3.3)  二行程無迴流實驗參數表	58
表(5.0.1)  二型程無迴流型式，級數收斂情形當 95和100於delta=0.5、beta=0.5及omega=0.4	60
表(5.0.2)  出口迴流至入口型式，級數收斂情形當 125和130於delta=0.5、beta=0.5、R=5及omega=0.4	60
表(5.0.3)  管末端出口型式，級數收斂情形當 125和130於delta=0.5、beta=0.5、R=5及omega=0.4 	61
表(5.0.4)  二型程無迴流型式，特徵值收斂情形於delta=0.5、beta=0.5及omega=0.4 	61
表(5.0.5)  出口迴流至入口型式，特徵值收斂情形於delta=0.5、beta=0.5、R=5及omega=0.4 	62
表(5.0.6)  管末端出口型式，特徵值收斂情形於delta=0.5、beta=0.5、R=5及omega=0.4 	62
表(5.0.7)  二行程無迴流實驗值與理論值之平均誤差	64
表(5.0.8)  出口迴流至入口實驗值與理論值之平均誤差	65
表(B.1)  各項冪次指數之係數表	176

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