A view factor is a fundamental parameter for evaluating radiative heat transfer between two surfaces. View factors for various geometries have been investigated in the past studies. However, the view factors of a spheroid and an ellipse are known only for limited configurations. In this study, the analytical view factor expressions of an ellipse and a spheroid from a plate element are derived. The spheroid view factor solution applies to a plate element with any position and orientation, and the ellipse solution is valid when the plate element is on the perpendicular axis through the ellipse center. The derived analytical solutions are validated against the numerical results for various configurations, showing deviations of less than 0.0001 for all cases.

中文翻译：

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板单元的椭球体和椭圆体的视角系数


视角系数是评估两个表面之间的辐射传热的基本参数。在过去的研究中已经调查了各种几何形状的视角因素。然而，已知椭球体和椭圆体的视角因子仅适用于有限的配置。在本研究中，推导了板单元的椭圆和椭球体的分析视图因子表达式。椭球体视角因子解适用于任何位置和方向的板单元，椭圆解当板单元位于通过椭圆中心的垂直轴上时有效。导出的解析解根据各种配置的数值结果进行验证，显示所有情况下的偏差均小于 0.0001。