臺灣博碩士論文加值系統

本論文是利用逆向熱傳導問題裡的共軛梯度法設計冷凍空調系統內部附著蒸發器圓柱熱交換裸管上之最佳化環形鰭片與計算其最佳效率，同時也考慮熱傳係數為固定常數或溫度函數兩種情況給定期望鰭片體積與鰭片效率來運算。隨著大氣中存在水蒸氣的多寡對於鰭片外型設計影響甚大，此時需將空氣濕度分別納入包含乾式、全濕式、半濕式鰭片表面之最佳外型環形鰭片設計。本研究也搭配了有限插分法求解乾式、全濕式、半濕式三種狀態下裸管及鰭片表面的溫度分佈，利用鰭片與外界空氣的溫度差算出熱通量同時也算出鰭片效率。
本研究分為六個章節，其中第一章為前一段所敘述，在第二章分別秀出鰭片表面為乾式、全濕式、半濕式三種條件下利用共軛梯度法來反算的求解過程，其中清楚的表示出直接解問題、靈敏性問題、伴隨問題、梯度方程、目標函數的定義以及鰭片體積與效率的計算公式。在上述的數值運算過程中，熱傳導係數及比爾特數都假設為常數形式。而第三張則藉由假設熱傳導係數及比爾特數為溫度的函數情況利用共軛梯度法分別設計出乾式、全濕式、半濕式之非線性環形鰭片最佳外型。
在第四章說明了乾式、全濕式與半濕式三種線性環形鰭片最佳外型設計之數值結果，並針對不同比爾特數、鰭片體積大小、熱傳導性比率及外界相對濕度與給定希望體積與希望效率條件下設計最佳鰭片外型與效率，並將其與一般常見五種鰭片進行比較，可清楚得知設計出來的鰭片具有最大化鰭片效率。環形鰭管式熱交換器已經廣泛的使用於冷氣機與冰箱系統，除此之外，許多工程問題的熱流係數也都表示溫度的函數，所以在第五章節討論藉由共軛梯度法於給定的希望鰭片效率及希望鰭片體積範圍去設計非線性最佳環形鰭片，在數值運算中秀出同樣設計條件下最佳化鰭片具備的鰭片效率確實比五種常見環形鰭片效率還高。當外界空氣的比爾特數改變時設計出來環形鰭片之最佳外型也有顯著的差易。然而，當裸管內部的比爾特數及裸管與鰭片的熱傳導係數發生變化時 設計出來的鰭片外形幾乎相同。這也說明了裸管內部的比爾特數及裸管與鰭片的熱傳導係數對於最佳鰭片的外型設計影響甚小。
在上述的研究中可說明使用共軛梯度法隨著疊代運算過程已經成功應用在熱係數為常數及溫度函數兩方面並設計出最佳環形鰭片之幾何外形。

This dissertation is intended to find an optimum shape and fin efficiency of annular fin adhere to the bare tube of evaporator for the air conditioner when considering the thermal properties of fin are either constant or temperature-dependent. It uses the conjugate gradient method (CGM) of inverse heat conduction problem to design an optimum annular fin based on the desired fin efficiency and fin volume. The amount of vapor in the ambient air influences fin shape a lot, as a result, it needs to consider the specific humidity when the optimum annular fin shape is designed. There are three types of annular fin surfaces including dry, fully wet and partially wet, respectively. In order to find the temperature distribution on bare tube and the fin, the finite difference method is utilized. Based on the temperature difference between the fin and the surrounding air, the heat flux and the efficiency of annular fin can be calculated in the dry, fully wet and partially wet conditions.
This dissertation consists six chapters. Chapter 1 is the preface as stated above. Chapter 2 shows the computational procedure of the inverse problem in determining the linear optimal annular fin shapes by using the conjugate gradient method under dry, fully wet and partially wet conditions. It clearly illustrates the direct problem, sensitivity problem, adjoint problem and gradient equation and leads to an objection function and fin efficiency equation. On the above process of numerical computation, the thermal conductivities kf and kw and Biot numbers Bii, Bio and Bia are considered constants. Chapter 3 introduces the computation procedure to estimate nonlinear dry, fully wet and partially wet optimum annular fin shapes by assuming the thermal conductivities kf and kw, Biot numbers Bii and Bia are temperature-dependent. The CGM is utilized to solve the present nonlinear inverse design problem.
Chapter 4 illustrates the numerical results for the optimal shapes and fin efficiency for linear annular fin under the dry, fully wet and partially wet conditions based on the desired fin volume and fin efficiency by using different Biot numbers Bii and Bia, fin volume V, conductivity ratio G and relative humidity. The technique of optimal fin design problem can indeed obtain the maximum fin efficiency when compared with five common annular fins.
Annular finned-tube heat exchangers are widely used in applications of air-conditioning and refrigeration systems. Besides, the thermal parameters of the fin are also function of temperatures in many practical engineering applications. Based on the above stated two conditions a nonlinear optimum annular fin design problem is considered in Chapter 5. The conjugate gradient method (CGM) is utilized as the optimization algorithm based on the desired fin efficiency and fin volume. The numerical experiments show that the optimum annular fin has the highest fin efficiency among six annular fins with the same operating fin conditions. When the Biot numbers for ambient air (Bia) varied, the optimum fin efficiency and optimum fin shape of the nonlinear annular fin also changed. However, when the Biot numbers for the inner tube (Bii), the thermal conductivities of the bare tube (kw) and the annular fin (kf) varied, the optimum fin shape remained almost the same. This implies that Bii, kw and kf have a limited influence on the optimum annular fin shape.
Based on the above studies it can be concluded that the conjugate gradient method (CGM) with iterative regularization process is applied successfully to the fin design problem to estimate the optimum shape of annular fins with constant and temperature-dependent thermal parameters.

Contents
Abstract(Chinese)..I
Abstract..III
Acknowledge..V
Contents..VI
Figure Captions..IX
Table Captions..XVIII
List of Major Symbols..XIX
Chapter 1 Introduction..1
1-1 Research Background and Motivation..1
1-2 Literature Review..3
Chapter 2 Theory of Linear Annular Fin Design..7
2-1 Dry Annular Fin with Constant Thermal Properties..7
2-1-1 The Direct Problem of Dry Annular Fin..7
2-1-2 The Dry Annular Fin Design Problem..10
2-1-3 The Conjugate Gradient Method (CGM) for Minimization..12
2-1-4 The Sensitivity Problem of Dry Annular Fin and Search Step Size..13
2-1-5 The Adjoint Problem of Dry Annular fin and The Gradient Equation..14
2-1-6 The Computational Procedure of Dry Annular Fin..16
2-2 Fully Wet Annular Fin with Constant Thermal Properties..17
2-2-1 The Direct Problem of Fully Wet Annular Fin..17
2-2-2 The Fully Wet Annular Fin Design Problem..20
2-2-3 The Conjugate Gradient Method (CGM) for Minimization..21
2-2-4 The Sensitivity Problem of Fully Wet Annular Fin and Search Step Size..22
2-2-5 The Adjoint Problem of Fully Wet Annular fin and The Gradient Equation..24
2-2-6 The Computational Procedure of Fully Wet Annular Fin..26
2-3 Partially Wet Annular Fin with Constant Thermal Properties..27
2-3-1 The Direct Problem of Partially Wet Annular Fin..27
2-3-2 The Partially Wet Annular Fin Design Problem..31
2-3-3 The Conjugate Gradient Method (CGM) for Minimization.. 32
2-3-4 The Sensitivity Problem of Partially Wet Annular Fin and Search Step Size..33
2-3-5The Adjoint Problem of Partially Wet Annular fin and The Gradient Equation..35
2-3-6 The Computational Procedure of Partially Wet Annular Fin..38
Chapter 3 Theory of Nonlinear Annular Fin Design..39
3-1 Dry Annular Fin with Temperature-Dependent Thermal Properties..39
3-1-1 The Direct Problem of Dry Annular Fin..39
3-1-2 The Dry Annular Fin Design Problem..41
3-1-3 The Conjugate Gradient Method (CGM) for Minimization..43
3-1-4 The Sensitivity Problem of Dry Annular Fin and Search Step Size..44
3-1-5 The Adjoint Problem of Dry Annular fin and The Gradient Equation..46
3-2 Fully Wet Annular Fin with Temperature-Dependent Thermal Properties..48
3-2-1 The Direct Problem of Fully Wet Annular Fin..48
3-2-2 The Fully Wet Annular Fin Design Problem..51
3-2-3 The Conjugate Gradient Method (CGM) for Minimization..52
3-2-4 The Sensitivity Problem of Fully Wet Annular Fin and Search Step Size..53
3-2-5 The Adjoint Problem of Fully Wet Annular fin and The Gradient Equation..55
3-3 Partially Wet Annular Fin with Temperature-Dependent Thermal Properties..58
3-3-1 The Direct Problem of Partially Wet Annular Fin..58
3-3-2 The Partially Wet Annular Fin Design Problem..62
3-3-3 The Conjugate Gradient Method (CGM) for Minimization..64
3-3-4 The Sensitivity Problem of Partially Wet Annular Fin and Search Step Size..64
3-3-5 The Adjoint Problem of Partially Wet Annular fin and The Gradient Equation..67
Chapter 4 Result and Discussion of Linear Annular Fins..71
4-1 Dry Annular Fin..71
4-2 Fully Wet Annular Fin..87
4-3 Partially Wet Annular Fin..103
Chapter 5 Result and Discussion of Nonlinear Annular Fins..120
5-1 Dry Annular Fin..120
5-2 Fully Wet Annular Fin..133
5-3 Partially Wet Annular Fin..146
Chapter 6 Conclusions..161
References...164

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