逆向熱傳導問題(IHCP)在一維及二維分析已有相當多數的研究，但三維分析的文獻並不多。由於邊界條件難以設定，且計算過程繁複，故一般在求解過程上有所困難。本文使用特徵函數展開法(Eigen function expansion)來求解逆向熱傳導問題之多維度分析。藉由特徵函數展開法的使用，可將逆向三維熱傳導問題在分析上簡化為用一維分析處理，將壁面溫度分佈轉換為一系列特徵函數，搭配有限差分法(Finite difference method)配合拉式轉換法(Method of Laplace transform)、最小平方法(Least-squares scheme)及量測溫度數據來求解特徵函數之值，進一步來預估垂直平板兩側之壁面溫度分佈、熱傳量及熱傳係數。研究的範圍包括下列重點：(1)簡化逆向熱傳導問題之多維度分析的複雜性。(2)垂直平板表面溫度之模擬及分析。 (3)平板兩側的熱傳量分析。(4)平板兩側的自然對流熱傳係數之暫態分析。本文之實驗系統主要由一在水平放置通道中之垂直平板作為測試工件，以燈光水平加熱，促使自然對流效應在壁面上生成。結果顯示，本文預測平板壁面溫度分佈可以得到良好的結果，且溫度量測點不需置於靠近未知邊界的表面處。藉由特稱函數展開法的使用，可簡化複雜的計算過程，且縮短運算的時間。

The inverse heat transfer conduction problem (IHCP) has been studied in one-dimensional and two-dimensional analysis in many researches, but rarely analyzed in three-dimension because of the difficulties in assuming unknown boundary conditions and solving process. The eigenfunction expansion method was applied to analyze the three-dimensional inverse heat conduction problem. Using the eigenfunction expansion method, the three-dimensional heat conduction differential equation is replaced by a system of one- dimensional partial differential equation with coefficients in the eigenfunction expansion, which are then solved efficiently in conjunction with the Laplace transform, finite-difference and least-squares method. Furthermore, the prediction of temperature distribution, heat flux and heat transfer coefficient on both sides of the vertical flat plate can be achieved. The present investigation includes: (1)To reduce the complexity in analyzing multi-dimensional inverse conduction problem. (2)The simulation and analysis of the temperature distribution on the vertical flat plate surface. (3)The prediction of the heat transfer rate on both sides of the vertical flat plate. (4)The transient analysis of heat transfer coefficient on both sides of the vertical flat plate. The experimental system is mainly composed of a vertical flat plate in the channel where natural convection heat flow is generated on the surface. The vertical flat plate was heated directly by a lamp. The results showed that good estimations of the surface temperature could be obtained from the knowledge of the transient temperature recording only at a few selected locations. Furthermore, the complexity of solving problem is reduced and the computational cost would be decreased, effectively.

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