Dwight G. Moore

A Test of Analytical Expressions for the Thermal Emissivity of Shallow Cylindrical Cavities

Analytical expressions for the directional thermal emissivity of a shallow cylindrical cavity were tested by means of room temperature reflectance measurements. The measurements were made by placing a paper-lined brass cavity of adjustable depth over the specimen opening of a recording spectrophotometer. Reflectance curves were obtained from 0.4 μ to 0.75 μ with the plunger positioned to give cavity depth-to-radius ratios of 0, 0.5, 1.0, 1.5, and 2.0. The resulting reflectances were then converted to emissivities through use of the relation that, for an opaque material, the emissivity is equal to one minus the reflectance. Two theoretical expressions predicted the emissivity of a cavity with a diffusely reflecting wall to within 0.01. A closed-form expression of Gouffe, which forms the basis of a shallow-hole method for measuring the emissivity of nonmetals at high temperatures, was in as good agreement with the experimental measurements as a more rigorous expression derived by a different approach. Sizable departures of the cavity walls from good diffusers had a negligible effect on the emissivity of the cavity at a depth-to-radius ratio of 0.5, but the effect of specular components became progressively greater as the cavity depth was increased.