本研究中，修改離散方向法來解具可變折射係數平板的暫態輻射熱傳。介質考慮吸收及散射輻射，平板的一邊突然曝露於散漫入射，另一邊則為散漫反射。本模擬採用四種方法，包括以donor-cell內差的離散方向法，以van Leer內差的離散方向法，以donor-cell內差的修正的離散方向法，以van Leer內差的修正的離散方向法，其計算結果將與蒙地卡羅法所得到的結果作比較。這些方法的結果比較顯示，在暫態輻射熱傳的起始階段，以van Leer內差的離散方向法的結果比以donor-cell內差的離散方向法的結果較少數值擴散，而兩個修正的離散方向法則是優於普通的離散方向法。接著，求各種光學厚度、散射比和基底反射率的線性可變折射係數平板的時間分解半球反射率( R )與半球穿透率( T )。這些結果顯示：(1) R曲線和T曲線在折射係數的平均值較大時，需要更多的時間到達穩態，而在 時，在穩態的R值隨著折射係數梯度的增加而減少。相對的，在穩態的T值則隨著折射係數梯度的增加而增加。 (2)穩態的R值隨著基底反射率增加而增加，然而穩態的T值則隨著 的減少而增加。 (3) 穩態的R值隨著散射比的增加而增加，R曲線則在散射比較大時，需要更多的時間到達穩態。

In this work, the discrete ordinates method has been adapted to solve transient radiative transfer in a graded index slab suddenly exposed to a diffuse strong irradiation at one of its boundaries. The medium is absorbing, scattering, and the other boundary is diffusely reflecting. The simulation is based on four methods, including the discrete ordinates method ( DOM ) with donor-cell interpolation, the DOM with van Leer interpolation, the modified DOM with donor-cell interpolation and the modified DOM with van Leer interpolation. The computational results are compared with those obtained by the Monte Carlo method. The comparison of the results by these methods shows that the results obtained by the DOM with van Leer interpolation has less numerical diffusion than the DOM with donor-cell interpolation at the early stage of the transient radiative transfer. The two modified DOM’s are superior to the two ordinary DOM’s. The time-resolved hemispherical reflectance ( R ) and transmittance ( T ) of the slabs with linearly varying refractive index are obtained for various optical thicknesses, scattering albedos and substrate reflectances. Effects of these parameters on transient radiative transfer in the planer media are investigated. The results show that (і) Both the R curve and the T curve for the case with a larger average of refractive index take more time to reach the plateau. For the case with the value of R on the plateau decreases with the increase of refractive index gradient. By contrast, the value of T on the plateau increases with the increase of refractive index gradient. (іі) The value of R on the plateau increase with the increases of substrate reflectance, while the value of T on the plateau increases with the decrease of . (ііі) The value of R on the plateau increases with the increase of albedo and the R curve for the case with a larger albedo takes more time to reach the plateau.

中文摘要.............................................................................................................i
英文摘要.............................................................................................................ii
誌謝.....................................................................................................................iv
目錄.....................................................................................................................v
表目錄.................................................................................................................vii
圖目錄.................................................................................................................viii
符號說明.............................................................................................................xii

第一章 緒論........................................................................................................1
1.1 研究動機、背景與文獻回顧....................................................................1
1.2 研究目的與方法簡介................................................................................2
1.3 本文架構....................................................................................................2
第二章 理論分析
2.1 物理模型和基本假設................................................................................4
2.2 數學模式....................................................................................................5
2.2.1 暫態輻射熱傳遞方程式.......................................................................5
2.2.2 將熱輻射強度分成兩部分應用在暫態輻射熱傳遞方程式...............6
2.2.3 熱輻射參數的表示式...........................................................................12
第三章 數值方法................................................................................................15
3.1 離散方向法................................................................................................15
3.2 修正的離散方向法....................................................................................23
第四章 結果與討論............................................................................................33
4.1 數值方法的比較........................................................................................33
4.2 參數之影響討論........................................................................................38
第五章 結論........................................................................................................42
參考文獻.............................................................................................................44

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