發光二極體(LED)為近代節能計畫光源的代表，具有省電與壽命長等優點，但事實上LED 卻是一種高熱的發光元件，無法有效的將LED所產之熱能散出，將導致發光效率嚴重下降，因此LED之散熱已成為其使用效率之重要條件。LED燈具最根本散熱系統為鰭片散熱，鰭片結構不僅易製作、穩定且經濟。本文乃以有限差分法(Finite difference method)並配合最小平方法(Least-squares scheme)及溫度量測值來研究LED燈具上鰭片之平均熱傳係數(Average heat transfer coefficient)、總熱傳量(Total heat transfer rate)和鰭片效率(Fin efficiency)。鰭片上的熱傳係數是不均勻的，為了利用鰭片上的溫度量測值來預測鰭片上之熱傳係數，因此將鰭片分割成數個小區域，並假設每個區域上的熱傳係數為常數。結果顯示，於自然對流(Free convection)之條件下，平均熱傳係數會隨著鰭片間距增加而提高，卻隨鰭片高度增加而減小。而在強制對流(Forced convection) 與相同風速之條件下，平均熱傳係數會隨著鰭片間距增加而減小並趨近於單一鰭片之值。本文所估算之平均熱傳係數與相關文獻之經驗公式相比較，已驗證本文逆算法之準確性及經驗公式之合理性。

LED, the illuminating light source in energy saving, can save more power and have longer life cycle comparing to traditional light source. In fact, LED is a lighting component with high heat. That high heat of LED can’t be transferred effectively will seriously result in lower illuminating efficiency. Thus, heat transfer function of LED has played an important role in its working efficiency. A fin is a basic heat transfer system of the LED lamp, which is not only easy to produce, but also stable and economical.
The present study applies the finite-difference method in conjunction with the least-squares scheme and measured temperatures to estimate the average convection heat transfer coefficient, total heat transfer rate, and fin efficiency on a vertical rectangular fin. The heat transfer coefficient on this rectangular fin is non-uniform. Thus the whole plate fin is divided into several sub-fin regions in order to predict the average heat transfer coefficient. The heat transfer coefficient on those sub-fin regions is assumed to be constant. The results show that the average heat transfer coefficient increases with increasing the fin spacing and decreases with increasing the fin height in free convection. The average heat transfer coefficient decreases with increasing the fin spacing for a fixed air speed in forced convection.. However, this value approaches its corresponding asymptotical value obtained from a single fin as S → ∞ . In order to evidence the accuracy of the present inverse scheme and the reliability of some experimental formulas, a comparison of the average heat transfer coefficient between the present predicated results and those obtained from correlation recommended by current textbook is made.

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