本論文的主旨為使用拉凡格氏法(Levenberg-Marquardt Method)搭配套裝軟體 CFD-ACE+，探討在自然對流情況時三維的Y型散熱器之鰭片偏移及等體積最佳尺寸設計之研究。
　　本研究以Y型散熱器作為為參考模型，並以此外型之等體積材料作為限制條件，探討在自然對流下以鰭片主幹高度h0、分支長度h1、開口角度α及鰭片偏移距離d作為設計變量進行最佳化設計，目的為降低鰭片底板溫度，進而提高散熱性能，其中並考慮鰭片和空氣之間的輻射熱傳效應，以求得最佳化之鰭片外形及偏移距離。
　　由最佳化結果可得，Y型鰭片的主幹高度變低、分支長度變長與分支開口角度變大時，可使散熱器底板溫度降低；若新增鰭片偏移距離作為一設計變量進行最佳化計算，則當鰭片上上上偏移排列設計之Design B1與鰭片上下上交錯排列設計之Design B2最佳化結果可更有效的降低底板溫度，增加散熱效果，其原因為煙囪效應使得浮揚煙流更加劇烈。此外，因為鰭片上上上偏移排列的模型設計還可產生一對縱向渦流，所以表現出更佳的散熱性能。
　　最後將初始設計及Design B1進行實驗驗較數值模擬與實際實驗的差異，由實驗結果比對後可得，數值模擬結果與實際量測之溫度最大誤差小於0.8%，而進行計算熱阻做比較，其最大誤差低於0.4 %，即驗證本論文數值模擬之準確性。
　　結果顯示Design B1在底板垂直、鰭片垂直( vBvF )情況下熱阻最低，比初始設計的熱阻值小2.6%，即證明該設計經過最佳化之有效性；但在底板水平、鰭片垂直( hBvF )情況下Design B1之熱阻比初始設計高8.3%，符合數值模擬預期之結果，並經實驗驗證後，數值模擬結果與實際情況十分吻合。

An optimum design problem for a three-dimensional natural convection Y-shape-shifted heat sink is investigated numerically and experimentally in the present study. The software package CFD-ACE+ and the Levenberg-Marquardt method (LMM) are utilized as the numerical solution solver and design tool, respectively. The objective of this work is to design the optimal fin stem height, fin branch length, branching angle, and shift distance of the Y-shaped fin under fixed Y-shaped fin volume conditions to minimize the base plate temperature and enhance the heat dissipation performance of the heat sink. The thermal radiation effect between the air and Y-shaped fin is considered in this work to improve the accuracy of the numerical solution of temperatures. The result indicates that in the optimized Y-shaped heat sink, the stem height and branching angle become shorter and larger, respectively, than those of the original design. When the shift distance is considered as a design variable, i.e., the optimized Y-shape-shifted heat sink with an up-up-up fin displacement arrangement, the chimney-flow effect due to the buoyant plume is much more pronounced than that of the original design, and a pair of longitudinal vortices also occur; therefore, better heat dissipation performance can be achieved. Experiments were performed on manufactured heat sinks to verify the accuracy of the design results. The results indicated that the measured temperatures of the heat sinks are very close to the computed data since the maximum error between the computed and measured base temperatures is less than 0.81%. In addition, design B1 (a vertical heat sink) has the smallest thermal resistance among all designs at 2.6% smaller than that of the original vertical heat sink, which confirms the validity of the present work in determining the optimal design of the Y-shape-shifted heat sink.

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