本文探討二維平板具時變性邊界條件之熱傳導問題。使用疊加原理與廣義傅立葉係數求解方式，將二維情況簡化為兩個單一維度問題，並使用移位函數法，將非齊次邊界的問題轉換成求解具齊次邊界的轉移函數，最後利用特徵函數展開法求解轉移函數。針對具時變性及空間分佈的線性狄氏邊界條件，發展出一個能簡單求解的解析解流程，無須任何積分變換。解析解的形式為乘積與級數。舉案例與現有文獻比較，說明方法的正確性。最後使用本文發展的方法探討一般的狄氏邊界條件熱傳導問題。

This thesis discusses the analytical solution for heat conduction of the two-dimensional plate with time dependent boundary conditions. Reducing the two-dimensional problem into two one-dimensional subsystems by means of the principle of superposition and generalized Fourier coefficient. With help of shifting function method, the non-homogeneous boundary conditions problem can be converted into the transformed function associated with homogeneous boundary conditions. Eventually, the transformed function can be determined by the method of eigenfunction expansion. For Dirichlet boundary conditions, this thesis has developed the solution method which does not require any integral transformation and is easy to solve. The analytical solution is expressed in product and summation form. To illustrate the accuracy, examples are given to compared to the existing literature. Finally, some Dirichlet boundary conditions are studied by the proposed solution method.

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