本文的研究在於提出一種新的數值方法，來分析逆解熱傳導問題(Inverse Heat Conduction Problem)。將此數值方法應用於研磨加工時，如何藉由量測工件的溫度場，進而逆求工件表面的熱量分佈。因此我們可以不用以假設工件表面的熱量分佈去求得工件的溫度場。此外本數值方法還可以逆求工件表面的熱對流係數。如此我們可以分析研磨加工過程之工件的溫度分佈以及能量分佈，進而防止由於研磨加工所產生的高溫對工件造成的熱破壞(Thermal damage)。
本數值方法可廣泛的運用於一維、二維、甚至三維的穩態或暫態之逆解熱傳導問題，例如可分析散熱片表面的熱對流係數，刀具刃口的熱傳導現象。本文亦成功的將此數值方法應用於研磨加工過程的逆向熱傳分析，此模擬研磨加工過程的精髓在於邊界為移動熱源的情形下，我們依然可以準確求得熱源的數值。比起其它逆問題的數值方法，分析上較為簡單化，在計算上更為簡潔，運算過程快速而準確。 其中數值方法的步驟是先重新安排逆解熱傳導問題的矩陣方程式，使得待求的未知條件能被明確的表示出來，再將此矩陣方程式運用線性最小均方根誤差法(Linear least-squares error method)，解出待求的未知條件。其中待求的未知條件可為邊界條件、初始條件、材料的熱傳導係數或熱對流係數、邊界的熱源…等等。

This paper presents a new approach to analyze inverse heat conduction problems, which estimates the initial and boundary conditions (i.e. heat source, heat convection coefficient or the property of material) using measurement data. Based on the finite difference method, the result can be obtained by minimizing the least-square error between the measured and estimated data. The finite difference methods are employed to discretize the problem domain and to construct a linear inverse model. For unknown condition estimation. The linear least-squares error method is adopted for the linear model, such that the number of iterations is limited to one and the unique solution can be identified easily.
　The proposed numerical method is applied to analyze the steady or transient inverse heat conduction problems. For example, The analysis of heat convection coefficient on the surface of fin and the problem of inverse heat conduction problem for insert tools. In this paper, we applied this numerical method to the Inverse heat transfer analysis of grinding process. We can accurately solve heat source when the boundary of workpiece is movingsource for the grinding process. And we can using the solved heat source to estimate the transient temperature field of workpiece but not using assumed data. The result show that the proposed methods can solve the inverse heat conduction problems efficiently and effectively.