本文乃以混合拉氏轉換法(Laplace transform method)和有限差分法(Finite-difference method)的數值方法，並配合最小平方法(Least-squares scheme)、二次仿樣曲線(Square spline)及溫度量測值來預測圓柱於各種不同傾斜角度之熱傳係數。本文之圓柱上的熱傳係數假設為非均勻，因此將圓柱劃分為數個小空間域，而後以數個連續之位置二次多項式函數與時間線性函數來計算未知圓柱表面條件隨位置與時間的變化情形。

實驗結果顯示，於自然對流下，圓柱表面上之平均熱傳係數會隨傾斜角度的增加而減少。為了驗證本文逆算法之可靠性及準確性，本文之平均熱傳係數的預測值將與相關文獻相比較。

The study applies the Laplace transform method and the finite-difference method in conjunction with the least-squares scheme, the square spline and temperature measurements to estimate the heat transfer coefficient on the cylindrical surface at different inclined angle. The study assumed the heat transfer coefficient on this cylinder is non-uniform. Thus the whole cylinder is divided into several sub-intervals. Later, a series of continuous square polynomial function in space and a linear function in time are introduced to estimate the distribution of the unknown cylindrical surface condition.

The results of experiment show that average heat transfer coefficient on cylindrical surface decreases with inclined angle in natural convection. A comparison of the average heat transfer coefficient between the present estimates and previous results is made in order to evidence the dependability and accuracy of the present inverse scheme.

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