縱長型及環狀型散熱鰭片應用遞迴公式於變動之熱性質分析與散熱座之最佳化設計

Longitudinal and Annular Fin Analysis with Variable Thermal Properties by Recursive Formulation and Optimum Design of a Heat Sink

賴其淵(Chi-Yuan Lai)

指導教授 ： 李基禎 ； 郭鴻森

大同大學/工程學院/機械工程學系所/博士(2006年)

摘要

本文前兩個主題提供了一個新的方法來計算可變動熱性質的鰭片散熱效果。研究中可將單一縱長型以及環狀型鰭片分割成許多個分段區域來運算。在個別運算後，每一段可以用遞迴公式整合成為整個鰭片的散熱公式。一般鰭片的數學模型中常用的頂部散熱條件與頂部絕熱條件在本研究中使用遞迴運算方法將可以很快的得到結果。最後，對於不同熱傳導係數複合材料的鰭片以及鰭片在池沸騰的現象在本文也進行模擬印證。
稍後的兩個主題是從理論分析的角度探討散熱座的冷卻效果。結果顯示只要代入研究中推導出的Bi, H 和H*的數值，則縱長型鰭片散熱座，其散熱量最佳化的鰭片長度可以很快的求得。文中所使用的最佳化方程式只存在這三個參數。而本研究也導入熱阻的概念來衡量散熱座的散熱性能，並且應用在後來不同鰭片的散熱座的例子。至於環狀型鰭片散熱座的最佳化，研究中有探討不同鰭片參數對散熱座的性能影響，也找到其中重要的四個鰭片參數來計算鰭片的最佳尺寸或鰭片個數。

關鍵字

熱性質 ； 最佳化 ； 散熱座 ； 散熱鰭片

並列摘要

The first two topics in this study supply a new approach to calculate thermal performance of a singular longitudinal fin and annular fin with variable thermal properties. With discrete model, the singular fin can be divided into many sections. Then, each section can be combined together to obtain the whole solution of the fin by recursive numerical formulation. The recursive formulas for both conditions with and without heat transfer on fin tip are derived in the present study. Finally, several examples including composite and boiling mode of a fin have been simulated to demonstrate the validity of the present approach.
Later the theoretical analysis of the cooling effect of a heat sink is presented. With the input data of Biot number, Bi, heat transfer coefficient ratios, H and H*, the optimum heat transfer equation can be utilized to obtain the optimum length of fins in a longitudinal fin heat sink that affects the overall thermal effectiveness of a heat sink. This optimum equation is in transcendental form, which involves three dimensionless parameters. The thermal resistance of a heat sink is derived and examples are provided to illustrate the effect on the cooling performance of a heat sink under various design conditions. Subject to annular fin heat sink, the four parameters are found to provide the optimum equation in transcendental form. Heat sink performance with its various parameters is also discussed in this topic. This optimum equation can be utilized to find the optimum outer radius of annular fins and fin number on a heat sink that affects the overall thermal effectiveness of a heat sink. Finally, examples are offered to illustrate the cooling performance of a heat sink including annular fins.

並列關鍵字

fin ； heat sink ； optimum ； thermal properties

參考文獻

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