View factor of a spheroid and an ellipse from a plate element

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.