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研究生:林昇誼
研究生(外文):Lin, Sheng-Yih
論文名稱:以逆算法預測二維物體表面之熱行為
論文名稱(外文):Prediction of the Surface Behavior of a Two-Dimensional Body Using the Inverse Method
指導教授:陳寒濤陳寒濤引用關係
指導教授(外文):Han-Taw Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:55
中文關鍵詞:逆算法二維表面熱行為
外文關鍵詞:Inverse MethodTwo-DimensionalSurface Befavior
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本文提出一種混合拉氏轉換法(Laplace transform technique)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)來預測未知的邊界溫度。首先利用拉氏轉換法處
理系統之時間域而後再以有限差分法處理系統轉換後之空間域,最後再以
數值逆拉氏轉換法來求取系統之溫度值。拉氏轉換法的優點是可以求得在
某一特定時間的溫度值,而不需要由初始時間慢慢的求解。最小平方法的
應用在於使數值結果能較快地收斂。本文將探討熱電偶(Thermocouple)
的安置位置與數量對預測結果的影響。由本文之結果可知此數值方法能夠
精確地、有效地預測出未知的邊界溫度。再者量測誤差對預測值的影響也
將在文中加以討論。由數值結果顯示在考慮量測誤差時本文之數值方法仍
可以正確地預測出未知的表面溫度。因此本文之混合數值方法可成功地被
應用來解析本文之逆向熱傳導問題。
The present study introduces a numerical method to analyze
inverse heat conduction problem concerning the prediction of the
surface behavior. The numerical algorithm combines the Laplace
transform technique and the finite difference method in
conjunction with the least square scheme. Time-dependent terms
in the governing equation are removed by using the Laplace
transform technique, and then the resulting differential
equation are solved by using the finite difference method.
Temperature distributions in the domain are obtained by using
the numerical inversion of Laplace transform. Due to the
application of the Laplace transform technique, the temperature
can be calculated at a specific time without step-by-step
computation in the time domain. By using the least square
scheme, the convergence of iteration is fast and stable. In the
estimation of the unknown boundary temperature, various examples
are illustrated to show the applicability and efficiency of the
present numerical method. The influences of measurement time
intervals and thermocouple locations are investigated. It can be
seen from various illustrated examples that the present
numerical method can accurately and efficiently estimate the
unknown boundary temperature and the thermocouple can be located
far from the estimated surface. In addition, the effect of the
measurement error and noises on measurements will be
investigated. It is fount that the present numerical method can
also estimate the boundary surface well while the measurement
error and noises are considered. Thus, it can be concluded that
the present numerical method can successfully be to analyze
inverse heat conduction problem applied.
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