本論文使用電腦程式語言Fortan來計算太陽能式蒸餾器一日之中的淡水資源產量，並配合拉凡格式法(Levenberg-Marquardt Method)，以提高一日之中淡水產量為目的，來算出太陽能式蒸餾器最佳化之內部尺寸與外部反射鏡與蒸餾器之間的夾角。本論文考慮在兩個不同的環境條件下進行設計，研究主題可分為以下三個部分:
在本文第二章中，採用日本福岡縣久留米市(Kurume, Fukuoka, Japan)冬季的環境條件，包含日照量、太陽高度角、太陽方位角、環境溫度等，為了改善太陽能蒸餾器的生產效率，吾人使用四個不同的方法來假設外部反射鏡與蒸餾器之間的夾角函數。Case 1為假設太陽能蒸餾器的夾角是常數來求得最佳化結果，Case 2為夾角每小時變化的太陽能蒸餾器之最佳化結果。Case 3假設太陽能式蒸餾器與外部反射鏡而夾角為餘弦(Cosine)函數的最佳化結果。Case 4假設太陽能式蒸餾器與外部反射鏡而夾角為雲形線(B-Spline)函數時的最佳化結果。以上四種方式皆以獲得太陽能式蒸餾器的最佳日產量為目標來求得太陽能式蒸餾器與其外部反射鏡在不同時間的最佳夾角。
在本文第三章中，採用埃及謝赫村省(Kafrelsheikh, Egypt)夏季的環境條件，包含日照量及環境溫度。此外並考慮以冷卻水膜厚度、冷卻水體積流率和玻璃上蓋長度三個係數為設計參數，在一定的範圍之內，找出最佳的參數組合，並計算出裝置冷卻水膜的階梯式太陽能蒸餾器的最佳化日產量結果。
在本文第四章中，吾人根據第二章與第三章的結果將兩部分最佳化的結果結合，亦即設計成裝置冷卻水膜且外部與內部均有反射器的階梯式太陽能蒸餾器，並採用第三章的最佳尺寸設計來求出裝置冷卻水膜的階梯式太陽能蒸餾器與其外部反射鏡在不同時間的最佳夾角，以獲得裝置冷卻水膜且外部與內部均有反射器的階梯式太陽能蒸餾器的最佳日產量為目標。

SUMMARY
An inverse design problem is examined in this thesis using the Levenberg-Marquardt Method (LMM) to estimate the optimal reflector angle and sizes of the internal solar still with different design variables. The objective of this thesis is to maximize the freshwater productivity in the solar still.
In chapter two, the purpose is to estimate the optimal design when the external reflector angle is simulated with different functional forms. The winter environmental conditions are based on Kurume, Fukuoka, Japan.
In chapter three, the aim is to estimate the optimal design when three key dimensions of the internal solar still sizes are considered. The summer environmental conditions are based on Kafrelsheikh, Egypt.
In chapter four, the mathematical formulations in the previous two chapters are combined to estimate the optimal design when the external reflector angle is assumed using different functional forms. The summer environmental conditions are again based on Kafrelsheikh, Egypt.
Results indicated that using the present design algorithm the optimal design of the solar still for obtaining maximum distillate can always be obtained.

Keywords : Solar still ; Reflectors ; Film cooling ;Optimization design

INTRODUCTION
Ocean and earth are closely related, and up to 70 percent of the Earth is covered by oceans, with up to 1.4 billion cubic kilometers of water on Earth. Theoretically, it is adequate for every person on the Earth who can receive the water resources, but most of the water contains salt, bacteria and impurities and thus it cannot be used for drinking purpose or irrigation of crops. Only 3% of the Earth's water is fresh water, and slightly over two thirds of this is frozen in glaciers and polar icebergs. According to statistic, human can only access fresh water by merely 0.36 percent among all water resource. In order to meet demands of water, saline desalination is widely used because of 97 % of the water on the Earth is salt water.
There are several ways of desalination, while most of them are driven by fossil fuel. Solar energy base distillation system should be an ideal method in terms of conservation energy and reduction of environmental pollution among distillation ways.

MATERIAL AND METHODS
A solar still with internal and external reflectors is considered as the test model in the present thesis. This test model will be utilized to illustrate the methodology for developing expressions used in the design of optimal angle for external reflector of solar still to maximize the freshwater productivity in this design problem by using the LMM.
A solar still with internal and external reflectors is considered in the present thesis. The angle between the external reflector and solar still is denoted as . Here i represents number of four different designs with i = 1 to 1 or 9 or 2 or 4, respectively.
In the first design problem, the angle between the external reflector and solar still is assumed as a constant, i.e. the angle between the external reflector and solar still, can be assumed in the following expression: θm(B1).
In the second design problem, the angle between the external reflector and solar still will be changed hourly, i.e. it remains as a constant within an hour. Therefore the design variables in this design problem become: θm (B1, B2, B3, B4, B5, B6, B7, B8, B9).
In the third design problem, the angle between the external reflector and solar still is assumed as a Cosine function that is dominated by two constants. The design variables in this design problem become: θm (B1, B2).
In the fourth design problem, the angle between the external reflector and solar still is assumed as B-Spline function that is controlled by four control points, i.e. the design variables in this design problem become: θm (B1, B2, B3, B4).

RESULTS AND DISCUSSION
In the first case of chapter two, the optimal solar still obtained 5.24 kg fresh water per day and there is a 138 % increase in mre from the solar still without reflectors and 63 % increase from the solar still with only internal reflector and 27 % increase from the solar still with internal and external reflectors but the angle between external reflector and still equals zero.
In the second case of chapter two, the optimal solar still obtained 5.33 kg fresh water per day, it implies that there is a 142 % increase in mre from the solar still without reflectors and 66 % increase from the solar still with only internal reflector and 30 % increase from the solar still with internal and external reflectors but the angle between external reflector and still equals zero. Besides, there is a 1.7% increase from the case 1. The third and fourth cases in the chapter two have exactly same result as was obtained in case 2.
In chapter three, the optimal solar still can obtain 5.62 kg fresh water per day, and there is a 1.8 % increase in mre from the original design problem reported by A [15].
In chapter four, the optimal solar still can obtain 5.93 kg fresh water per day in the first case. In the second case, 5.98 kg fresh water per day can be obtained by the optimal solar still, it implies that there is a 8.3 % increase in mre from the result obtained in chapter three and 0.8% increase in mre from the case 1 in the same chapter. In case 3, the obtained fresh water per day by optimal solar still is almost that same as that obtained in case 1.

CONCLUSION
A solar still design problem using the Levenberg-Marquardt Method is successfully examined in this thesis to obtain the optimal angle for external reflector of solar still is (LMM). The optimization design process is performed by maximizing the freshwater productivity. The numerical design results show that the optimal designs always obtain higher freshwater productivity than any initial designs considered in this thesis. The produced freshwater can be increased up to 142% when compared with the solar still without internal and external reflectors.
Based on the results obtained in different cases considered here, they illustrated that the productivity rate of freshwater can be increased with the installation of the external reflector, however, during the summer season the effect of external reflector becomes nonsignificant.

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