This article presents two very different models for the resolution of conduction-radiation coupling within grey Beerian and non-Beerian semi-transparent slabs enclosed between two black surfaces imposing their intensities and temperatures. The first model is deterministic, based on finite differences and discrete ordinates. The second one is fully stochastic, using Monte Carlo ray tracing for the modeling of the radiative transfer and a Brownian walkers method for the modeling of conduction. These two models allow the evaluation of the temperature, surface flux, and radiative volume power fields in Beerian and fictitious non-Beerian semi-transparent media. They provide the very first resolution of the coupled Generalized Radiative Transfer Equation and energy equation. The results of these two models are compared and show excellent agreement. The results obtained on fictitious non-Beerian media show significant differences with the classical Beerian cases.

中文翻译：

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非比尔半透明介质内传导辐射耦合建模的确定性和随机方法


本文提出了两种截然不同的模型，用于解决封闭在两个黑色表面之间的灰色比尔半透明板和非比尔半透明板内的传导辐射耦合，并施加强度和温度。第一个模型是确定性的，基于有限差分和离散坐标。第二个是完全随机的，使用蒙特卡罗射线追踪来模拟辐射传输，并使用布朗步行者方法来模拟传导。这两个模型允许评估比尔和虚构的非比尔半透明介质中的温度、表面通量和辐射体积功率场。它们提供了耦合广义辐射传输方程和能量方程的第一个分辨率。对这两个模型的结果进行比较并显示出极好的一致性。在虚构的非比尔媒体上获得的结果与经典比尔案例有显着差异。