The local effective emissivity for a point on the interior surface of a diffusely reflecting blackbody cone obeys an integral equation. A new analytic approximate solution of the integral equation is presented. This approximation is very good for interior portions of narrow cones where the effective emissivity is very close to unity. Another approximation of Kelley is better near the mouth of a narrow cone. Either approximation works for wide angle cones. The new approximation is modified to give a quantitative estimate of the effects of a temperature gradient along the side of the cone.
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Shirley et al. (1979) studied this question.
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