本研究的目的在探討鑽石薄膜的熱傳，採用兩種聲子輻射傳輸方程式(EPRT)的解法。首先，將EPRT轉為積分方程式，並利用積分格點法求解，由比較離散方向法與積分格點法所得的結果，可以發現積分格點法可以在聲學厚度小時，以較少的空間與角度格點數得到較離散方向法準確的結果，但在聲學厚度大時，其需要較多數值計算時間。然後，運用積分格點法求解受脈衝加熱的鑽石薄膜，並討論其熱通量隨時間的變化。接著以Schuster-Schwarzschild近似來推導雙曲線模式的修正邊界條件，並以 近似來修正雙曲線熱傳方程式的熱波速率，使其與EPRT一樣。修正邊界條件與修正方程式所得結果顯示：在靠近波前與邊界附近，本方法較其他雙曲線模式更為接近積分格點法所得的結果。

The purpose of this work is to investigate heat trasnsfer in a diamond thin film. Two methods based on the equation of phonon radiative transport (EPRT) are considered. First, we transform the EPRT into an integral equation, and then solve the equation by the quadrature method (QM). The results obtained by the QM and by the discrete ordinate method are compared. The results obtained by the QM with less position and direction grids agree well with those obtained by the discrete ordinate method. The former is more accurate than the latter in acoustically thin media, but the former takes more computational time in acoustically thick media. Then, the temporal profile of heat flux profiles of diamond thin films exposed to thermal pulses are discussed. Next, the Schuster-Schwarzschild approximation is used to develop modified boundary conditions of a hyperbolic model in which the hyperbolic heat conduction equation is modified by using the approximation to make heat wave speed to be the same as the EPRT. The results obtained by the modified hyperbolic equation with modified boundary conditions show batter agreement with those obtained by the QM around the boundaries and the wave front.

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