The general solution to the radiation exchange problem in the zone method is given in the system of surfaces in the presence of nonparticipating medium for the model of specular-diffuse reflection and direct and diffuse transmission. The reflection indicatrix for all surfaces of the considered system of bodies is assumed as a superposition of diffuse and specular components of reflection, and the transmitted radiation for transparent materials—as a superposition of direct and diffuse transmission. The cornerstone of the offered approach is in obtaining the exchange radiation factors by the semi-analytical method by solving a system of linear algebraic equations that include specular exchange factors or diffuse configuration factors of radiation. This allows one to combine exact computational methods of diffuse reflection and diffuse transmission through diffuse configuration factors with methods of direct ray tracing for accounting of specular reflection and direct transmission. Solutions for all possible particular models of reflection and transmission are provided. The solution for diffuse transmission by the semi-analytical method is obtained for the first time. Results of the numerical experiments confirming accuracy and efficiency of the offered approach are given.

中文翻译：

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镜面漫反射与直接漫反射模型中辐射换热的计算

区域方法中的辐射交换问题的一般解决方案是在存在非参与介质的表面系统中，建立镜面-漫反射模型以及直接和漫透射模型。所考虑的物体系统所有表面的反射指标假定为反射的漫反射和镜面反射分量的叠加，透明材料的透射辐射为直接和漫反射的叠加。所提供方法的基础是通过求解包括辐射的镜面交换因子或扩散配置因子的线性代数方程组，通过半解析方法获得交换辐射因子。这样一来，就可以将漫反射和通过漫反射配置因子的漫透射的精确计算方法与直接射线跟踪方法结合起来，以解决镜面反射和直接透射。提供了所有可能的反射和透射模型的解决方案。首次获得了通过半解析法进行漫透射的解决方案。数值实验的结果证实了所提供方法的准确性和效率。