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各種不同鰭片間距及風速下之環狀圓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 rate)及鰭片效率（Fin efficiency）。本文之環狀圓鰭片上的平均熱傳係數事先假設為非均勻。為了欲求得所須之平均熱傳係數，因此將整個環狀圓鰭片分割成數個小鰭片區域，並假設每個小區域之熱傳係數為未知的常數。結果顯示，於自然對流條件下，環狀圓鰭片上之平均熱傳係數及鰭片效率會隨著鰭片間距的增大而分別增加及減少，並會趨近於單一環狀圓鰭片之值。熱傳量也會隨著鰭片間距的增大而有增加的趨勢。本文於等溫條件下之平均熱傳係數的預測值會略高於課本內之經驗公式的值，此乃由於自然對流與輻射熱傳係數於本文須同時考慮。於強制對流條件下，平均熱傳係數會隨著風速增加而增加，而鰭片效率會隨著風速增加而減少。於相同風速下，平均熱傳係數會隨著鰭片間距的增大而增加並趨近於單一環狀圓鰭片之值，但鰭片效率受鰭片間距的影響有限。當鰭片間距固定時，熱傳量會隨著風速增加而增加。然而，當風速固定時，鰭片間距雖增大，鰭片之熱傳量僅是微幅增加。本文之強制對流平均熱傳係數的預測結果也頗吻合其他研究之實驗值，此意味著本文之反算法是可靠的。

　　The finite difference method in conjunction with the least-squares scheme and experimental temperature data is proposed to predict the average heat transfer coefficient, heat rate, and fin efficiency on a vertical annular circular fin of annular-finned tube heat exchangers for various fin spacings and air speeds. The 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 heat transfer coefficient and fin efficiency from the knowledge of the measured 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 increases 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 annular circular fin for the fin spacing above a certain value. The heat rate seems to increase with increasing the fin spacing. The present estimates of the average heat transfer coefficient under the condition of the isothermal situation are slightly higher than those obtained from the correlation recommended by current textbooks for various fin spacing. This phenomenon can result from the simultaneous consideration of the convection and radiation heat transfer coefficients in the present study. 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 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 annular circular fin for the fin spacing above a certain value. However, the effect of the fin spacing on the fin efficiency is very small. The heat rate increases with the air speed for a fixed fin spacing. However, the effect of the fin spacing on the heat rate is small for a fixed air speed. In order to evidence the reliability of the present inverse scheme, the present estimated results of the average heat transfer coefficient in forced convection agree with the experiment results. Thus the reliability of the present inverse scheme is expected.

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