A Formulation of Radiation View Factors from Conical Surfaces
A closed form solution for the radiative shape factor from a differential element to a cone with an arbitrary angle is derived. The limiting solution for which the plane of the element is perpendicular to the axis of the cone reduces to the mathematical expression obtained by Minning (1977). Based on the derived formula, a general formulation is developed for a view factor from a cone to a coaxial axisymmetric body. Numerical results for view factors from cone or truncated cone to cone, paraboloid, and ellipsoid are obtained through a single numerical integration instead of conventional quadruple integration. The only restriction on this scheme is that the axisymmetric body under consideration cannot block any radiation incident to itself.
Chung, Benjamin T.F.; Kermani, M. M.; and Naraghi, Mohammad, "A Formulation of Radiation View Factors from Conical Surfaces" (1984). Mechanical Engineering Faculty Research. 1056.