本文之逆算法乃以有限差分法(Finite difference method)並配合最小平方法(Least squares scheme)及實驗溫度量測數據來估算自然對流(Free convection)環境下，不同間距、不同高度之矩形鰭片(Rectangular fin)垂直放置在垂直加熱平板上的平均熱傳係數(Average heat transfer coefficient)、總熱傳量(Total heat transfer)以及鰭片熱傳效率(Fin efficiency)。為了欲求得較正確的估算值，將垂直矩形鰭片分割成數個小區域在進行逆算分析。本文擬以小型風洞來量測於自然對流環境下矩形鰭片上溫度並與課本經驗公式及相關研究結果做比較。結果顯示，於自然對流之條件下，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。平均熱傳係數值會隨著鰭片間距增加而減小並趨近於單一鰭片。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。

This present study applied an inverse method involving the finite difference method in conjunction with the least-squares scheme and experimental temperature measurements to estimate the unknown heat transfer coefficient and heat transfer rate on a vertical rectangular fin with various fin spacing and fin height in natural convection. To estimate a more accurate estimation, thus the whole plate fin was divided into several analysis sub-fin regions before performing the inverse calculation. The small wind tunnel of our own device would be applied to measure the temperature of the test rectangular fin at several measurement locations in natural convection. Based on these experimental temperature measurements, the unknown heat transfer rate and heat-transfer coefficient on the vertical rectangular fin could be predicted. To validate the accuracy and reliability of the present inverse method, the predicted results of this present study would compare with those obtained from the correlation recommended by current textbooks or previous results. The results showed that the average heat transfer coefficient increases with increasing the fin spacing and decreases with increasing the fin height in free convection. However, this value approached its corresponding asymptotical value obtained from a single fin as . In order to evidence the accuracy of the presented 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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