本論文主旨在於應用拉凡格氏法(Levenberg-Marquardt Method)搭配套裝軟體 CFD-ACE+，探討在自然對流情況下的柱狀鰭片最佳尺寸及傾斜角之研究。
本研究以PFHS及SHFHS為測試模型，並以SHFHS外形之體積作為限制條件，探討在自然對流下，以鰭片高度及直徑與鰭片放置傾斜角作為設計參數，在固定柱狀鰭片體積的條件下提高鰭片散熱性能為目標，並考慮鰭片和空氣之間的輻射熱傳效應，求得最佳化之鰭片外形及傾斜角。
由最佳化結果可得，去除內部鰭片僅對外部鰭片做設計，可以獲得較佳的鰭片散熱性能。並以錐狀外形之鰭片為設計參數，建立一錐狀外形鰭片之方程式將其用於最佳化設計，由Design D之結果可得，在傾斜角下的錐狀外形鰭片有最佳之散熱效果，其熱阻較同體積之PFHS*降低了19.3%。
最後吾人將PFHS、PFHS*、Design B*、Design C及Design D進行實驗驗證，利用紅外線熱像儀實際實驗量測散熱鰭片表面溫度分佈，以比較數值模擬與實際實驗的差異。由實驗結果可得，模擬結果與實際量測之溫度最大誤差小於3.68%，進而驗證本論文之準確性以及最佳化設計之有效性。此外，將計算模擬結果與實際量測之熱阻做比較，其最大誤差低於1.79%。
柱狀散熱鰭片外形經過最佳化設計後熱阻確實能夠降低，經實驗驗證後，也證實數值模擬結果與實際情況十分吻合。

A three-dimensional optimum pin fin heat sink (PFHS) design problem is investigated numerically, using Levenberg-Marquardt Method (LMM) and a commercial package CFD-ACE+, and experimentally under natural convection condition and fixed fin material constraint. The purpose is to design the optimal shapes and orientation angle of the PFHS and to enhance the heat dissipation performance. The design process is to obtain the optimal pin heights, pin diameters and orientation angle of the heat sink and then minimize the thermal resistance of the system. The effect of radiation heat transfer between heat sink and air is also included. Numerical results indicate that when considers only the perimeter pin fins and neglects the interior pin fins, the best heat sink performance can be obtained. A functional form of tapered pin is established and its design variables are also estimated. It is found that the tapered pin heat sink (design D) with 66o orientation angle has the lowest thermal resistance among all designs and its thermal resistance is 19.3% smaller than that of PFHS*. Finally, experimental verifications are performed on the fabricated PFHS, PFHS*, designs B*, C and D heat sinks, the measured temperatures by thermal camera are found in a good agreement with the numerical temperatures on those heat sink.

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