An exact, closed-form expression is derived for the apparent local emissivity of a point at the vertex of a diffuse conical or V-groove cavity. This expression is obtained by a substitution into an approximate equation for the apparent local emissivity of a point within a cavity of any shape. The exact expression depends only on the emissivity of the cavity wall material and the angle factor between the point at the cavity vertex and the cavity opening. The values predicted by this expression agree well with those obtained from a numerical solution of the integral equation characteristic of a diffuse conical cavity.
Francis J. Kelly, "An Equation for the Local Thermal Emissivity at the Vertex of a Diffuse Conical or V-Groove Cavity," Appl. Opt. 5, 925-927 (1966)