本文以有限差分法(Finite difference method)及實驗溫度數據配合最小平方法(Least-squares scheme)來預測於各種不同風速與鰭片間距下，橢圓鰭管式熱交換器之垂直橢圓鰭片上的平均熱傳係數及鰭片熱傳效率。本文之橢圓鰭片上的熱傳係數預先假設為非均勻。為了欲求得鰭片上之平均熱傳係數，因此將鰭片劃分成數個小區域，並假設每個小區域的未知熱傳係數為常數。結果顯示，在自然對流下，鰭片上之平均熱傳係數與等溫平均熱傳係數會隨著鰭片間距增大而增加，並會趨近於單一鰭片之值。但鰭片熱傳效率會隨著鰭片間距之增大而減少，並且也會趨於單一鰭片之值。於強制對流條件與各種鰭片間距下，平均熱傳係數會隨著風速增加而增加，而鰭片熱傳效率會隨著風速增加而減少。於相同風速下，等溫平均熱傳係數會隨著鰭片間距的增大而增加並趨於單一鰭片之值，但鰭片熱傳效率受鰭片間距的影響較不明顯。本文的預測結果吻合其他文獻之趨勢，此意味著本文之逆算法是可靠的。

The finite difference method in conjunction with the experimental temperature data and least-squares scheme is proposed to predict the average heat transfer coefficient and fin efficiency on a vertical elliptic fin of elliptic-finned tube heat exchangers for various air speeds and fin spacing. The heat transfer coefficient on this elliptic fin is assumed to be non-uniform. Thus the whole plate fin is divided into several sub-fin regions in order to predict the average heat transfer coefficient on the fin. The unknown heat transfer coefficient on each sub-fin region can be assumed to be constant. The results show that the average heat transfer coefficient and isothermal average heat transfer coefficient increase with increasing the fin spacing, and the fin efficiency decreases with increasing the fin spacing in natural convection. The average heat transfer coefficient and fin efficiency can approach their corresponding asymptotical value obtained from a single elliptic fin for the fin spacing above a certain value. The average heat transfer coefficient increases with increasing the air speed, and the fin efficiency decreases with increasing the air speed for various fin spacing in forced convection. The isothermal average heat transfer coefficient increases with increasing the fin spacing for a fixed air speed. It can also approach its corresponding asymptotical value obtained from a single elliptic fin for the fin spacing above a certain value. However, the effect of the fin spacing on the fin efficiency is very small. In order to evidence the reliability of the present inverse scheme, the present estimated results of the average heat transfer coefficient agree with the direction of the experiment results. Thus the reliability of the present inverse scheme is expected.

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