本研究的目的主要在探討壁面具可變折射係數塗層的一維平行板圍場的多模式熱傳遞現象。平板為半透明塗層與不透明基底結合而成，其中半透明塗層有輻射與傳導熱傳，而不透明基底僅具熱傳導，塗層在圍場內的邊界為Fresnel反射邊界，且具對流熱傳，塗層與基底間的邊界為散漫(diffuse)反射邊界，基底在圍場外的邊界具表面輻射與對流熱傳。經由離散方向法解輻射傳遞方程式與有限差分法解能量方程式求得平板的溫度分佈與熱通量。文中折射係數變化的斜率愈大的塗層，其溫度分佈比折射係數為平均值的塗層的溫度分佈有愈大的差異。折射係數的平均值愈大，其溫度變化有較和緩的現象。在塗層靠近塗層與圍場內空氣之間的邊界處，折射係數1.5至2的塗層的溫度曲線比塗層的折射係數為2的溫度曲線有較和緩的溫度變化。光學厚度愈大，塗層的溫度分佈曲線的斜率愈大，塗層兩端溫度的變化也較小。傳導輻射比愈小，不同折射係數變化的塗層的溫度分佈差異愈明顯。在折射係數變化的情況下，
散射比愈大，塗層溫度曲線較平緩的區域會減少，塗層兩端溫度變化的區域比較大且
變化較和緩。

The purpose of this work is to investigate the heat exchange in a parallel-plate enclosure with graded-index coatings on its walls. The multi-mode heat transfer of the enclosure walls including opaque substrates and semi-transparent coating is considered. There are thermal radiation and heat conduction in the coatings, and conduction only in the substrate. The internal surfaces of the coatings are Fresnel and convective, and the interface between coating and substrate is diffuse. There are radiation and convection at the external surface of the enclosure. Temperature distribution and heat flux are calculated from radiative transfer equation and energy equation by using discrete ordinates method and finite difference method. The variation of temperature over the depth of the coating decreases as the average of refractive index is increased. Around the internal surface, the temperature distributions of the coatings with refractive index from 1.5 to 2 are more gradual than those of the coatings with refractive index of 2. The optical thickness is larger, the temperature distribution in the coatings is steeper, and more gradual temperature variation near the surfaces of coatings can be found. When the conduction-radiation parameters is smaller, the difference of temperature distributions for various refractive indices is larger. For various refractive index distributions, when the albedo increases, the gradual-variation region of temperature distribution in the coatings shrinks, and more
gradual temperature variation appears around the surfaces of the coatings.

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