Emissivities of diffuse cavities 4: Isothermal and nonisothermal cylindro-inner-cones

A precise calculation is presented of the local hemispherical effective emissivities of isothermal and nonisothermal diffuse cylindro-inner-cone cavities. For those cases where shadowing occurs, it is shown how to obtain exact analytical expressions for the angle factors involving incomplete circular bands and conical frustums by application of the Stokes theorem and contour integration. The effective emissivities of the cone and adjacent part of the cylinder are lower than predicted by previously published approximate calculations by from 1 to 5 × 10−4, amounts significant in metrological applications. The effective emissivities of nonisothermal cavities change with wavelength and depend on the details of the temperature distribution.