本文主要探討脈衝雷射加工的熱傳現象，在熱對流的邊界條件下，利用有限差分法來離散暫態熱傳方程式及搭配殘差修正法，進而求得相對於物體溫度場分佈之正確解的近似上下限。所解得之近似上下限，不但在其平均值上有良好的精度，更可分析其數值解與解析解的最大可能誤差範圍。整體來說，殘差修正法為一種便利、效率高且具備高精確度的數值方法。
在數值分析方面，首先以兩個一維暫態熱傳範例，來驗證殘差修正法於脈衝雷射加工上之正確性及熱傳分佈情形。其次，將該問題延伸至二維圓柱座標系統模擬探討脈衝雷射加工之熱傳分佈。最後，探討脈衝雷射應用於皮膚治療之表面及內部熱傳分佈，且藉由調整脈衝雷射強度參數及熱對流係數使其更符合真實治療的情況，以供臨床治療之參考。

This study focused on the heating process of a pulse laser. Under boundary conditions of convection, the transient heat transfer equation is discretized using the finite difference method. Then, the approximate solution of the workpiece temperature field distribution can be obtained by residual correction. Using the residual correction method, the precise average value of upper and lower approximate solutions is achieved and the error range between the analytical solution and the numerical solution can be analyzed. As a result, the residual correction method is an effective numerical method with high accuracy.
In this dissertation, one dimensional transient heat transfer cases are firstly used to verify the accuracy of pulse laser heating process using residual correction method. The heating process of pulse laser on a two dimensional cylindrical system is considered. An application of tissue treatment using pulse laser is also simulated and the heat transfer distributions of tissue surface and interior are demonstrated. By adjusting parameters of pulse laser intensity and heat transfer coefficients, the heat transfer distributions are in agreement with literature results. Therefore, the proposed heat transfer distribution can be used as a prior simulation of clinical treatment.

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