本文主要為使用循次方法解析逆向熱傳導問題（或稱熱傳導逆問題），在解析過程使用有限差分法將描述問題之微分方程式與已知條件離散化，進而推導循次運算式，隨後合併導入未來時間原理與線性最小平方誤差法以處理計算結果之穩定度與準確度問題。
本文方法在理想量測行為之無誤差情況，不需使用未來時間數據即可獲得與實際情形一致之測定結果；在考慮量測誤差之情況，則可藉由加入未來時間數據而獲得穩定良好之估算結果。在本文中亦發現在加入未來時間之運算過程中，亦會同時產生一種特定誤差－前置誤差（leading error）。此種特定誤差之效應在使用少量未來時間之情況下並不明顯，然隨著所使用未來時間數之增加，其效應亦逐漸擴大，致影響計算分析之準確度。有鑑於此，在本文中，亦針對此點做詳細探討，並提出一有效之修正方法－修正型循次算則。
在本文中所探討之問題型式包括一維桿件暫態熱傳導、具多項熱源同時作用之二維平板暫態熱傳導、建築物表面對流熱傳係數估算、三維輥輪在輥壓製程熱行為預測等問題，本文以循次算則在不同之限制條件下分別敘述與探討其解析模式，由估算結果顯示本文方法可有效應用於各種逆向熱傳問題之解析運算，甚至在具有顯著量測誤差之特定情況（例如3%、5% 或以上），使用修正型循次算則亦可提供較之其它方法更為穩定與準確之估算結果，並且同時擁有極佳之運算效率。
本文方法應用於解析逆向熱傳問題之優點不僅擁有極佳之計算效率，在計算過程不需疊代，亦不需預先設定待測函數型式，在考慮量測誤差時仍可獲得準確之估算，甚至在量測誤差顯著之情況，修正型循次算則亦可提供具有良好可靠度之估算結果。

An efficient sequential approach is proposed to determine the unknown conditions of the inverse heat conduction problem (IHCP). As a beginning, a sequential algorithm is derived based on the analysis of mathematical formulation, then combined with the concept of future time and linear least-squares error method in order to stabilize the computational results when the measurement noises are considered.
In the procedure of computation, adding the future time information is essential to obtain a stable estimation due to the ill-posed characteristic of inverse problem when the measurement error is considered. Furthermore, the stability of solution of the IHCP is improved progressively by increasing the number of future times. But such an operation would cause a systematic “leading error” that caused due to the use of future temperatures to compute the present parameter. The leading error is different from the error caused by measurement error. In contrast, the leading error also rises depending closely on the increase of number of future times. Nevertheless, when the measurement error is considered, more future times is often essential to obtain a stable estimation. Base on the reason, such an incompatible problem also discuss in this thesis, and then proposed a modified sequential function specification method (MSFSM) to provide the stable and accurate computational result.
In this thesis, there are several distinct kinds of problems including the determination of heat sources in one- and two-dimensional transient heat conduction problems, the determination of convection heat transfer coefficient in the surface of building, and the estimation of surface thermal behavior of the working roll in a rolling process, etc., in order to verify that the proposed method in this study can be applied to provide a good solution for the IHCP. Even when the larger measurement error is considered in some special cases, the proposed method can also yield a good estimation.

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