Perspective Projection of an Ellipse and an Ellipsoid for Analytical View Factor Evaluation

Abstract

Radiative view factors are fundamental quantities for evaluating radiative heat transfer between different surfaces. While analytical expressions of view factors have been evaluated for various types of basic geometries, including circular disks and spheres, extending these solutions to more complex geometries, such as ellipses and ellipsoids has remained challenging due to mathematical complexity. This study evaluates the analytical view factor expressions of an ellipse and a triaxial ellipsoid from a plate element in an arbitrary position and orientation. The proposed analytical methods generalize the existing analytical solutions for disk and sphere related geometries, and extend their applicability to more complex geometrical configurations. For both cases, the perspective projection of the target geometry is analyzed, and the original view factor is transformed into an equivalent ellipse view factor, which has known analytical solutions from the previous study. Finally, the derived view factor expressions are validated by comparison with the numerical results.