本文乃以有限差分法（Finite difference method）配合最小平方法（Least-squares scheme）及實驗溫度數據來預測於風速下對應之不同鰭片高度及鰭片間距之環狀鰭管式熱交換器之垂直環狀圓鰭片上的平均熱傳係數（Average heat transfer coefficient）、熱傳量(Heat transfer rate)及鰭片效率（Fin efficiency）。本文鰭片上之總熱傳係數事先假設為非均勻分佈。為了欲求得所須之平均總熱傳係數、熱傳量及鰭片效率，因此將整個環狀圓鰭片分割成數個小鰭片區域，並假設每個小區域上的總熱傳係數為未知的常數。結果顯示，於自然對流條件下，平均熱傳係數與鰭片效率會隨著鰭片高度增加而減少，但會隨著鰭片間距的增加而增加，並會趨近於單一環狀圓鰭片之值。鰭片上之熱傳量也會隨著鰭片間距的增加而有增加的趨勢。於自然對流之情況下，頗吻合課本的經驗公式所得之值，此乃由於輻射熱傳係數可能需要考慮所致。於強制對流之情況下，平均熱傳係數與鰭片效率會隨著鰭片高度增加而減少。為了驗證本文反算法之準確性與可靠性，本文所預測之結果將與其他相關文獻之結果相比較

The finite difference method in conjunction with the least-squares scheme and experimental temperature data is proposed to predict the average overall heat transfer coefficient, heat transfer rate on a vertical annular circular fin of annular-finned tube heat exchangers for two kinds fins and various fin spacings. The overall heat transfer coefficient on this annular circular 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 overall heat transfer coefficient. heat transfer rate from the knowledge of the measured experimental temperatures. 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 the fin efficiency decrease with increasing the fin height and increase with increasing the fin spacing. The average heat transfer coefficient and fin efficiency can approach their corresponding asymptotical value obtained from fin for the fin spacing above a certain value. The heat transfer rate also increases with increasing the fin spacing. The average heat transfer coefficient increases with the air speed for various fin spacing in force convection. The average heat transfer coefficient increases with the fin spacing and it can approach its corresponding asymptotical value obtained from a single annular circular fin for various air speed above a certain value. The present estimates of the heat transfer coefficient under the isothermal condition in natural and force convection agrees with those were obtained from textbooks. In order to evidence the accuracy and reliability of the present inverse scheme, A comparison between the present results estimated and previous results will be made.

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