V-groove, cavity effect, variable emissivity surface, angular surfaces, specular reflection


Multiple reflections in a cavity geometry augment the emission and absorption of the cavity opening relative to a flat surface in a phenomenon known as the cavity effect. The extent of the cavity effect is quantified using apparent absorptivity and apparent emissivity. Analysis of complicated thermal systems is simplified through application of apparent radiative properities to cavity geometries. The apparent radiative properties of a specularly-reflecting, gray, isothermal V-groove have been derived analytically, but these results have not been validated experimentally or numerically. Additionally, the model for apparent absorptivity of an infinite V-groove subjected to partial illumination in the presence of collimated irradiation is not available. In this work, the following existing models for a specularly-reflecting V-groove are collected into a single source: (1) the apparent absorptivity of a diffusely irradiated V-groove, (2) the apparent emissivity of an isothermal V-groove and (3) the apparent absorptivity of a V-groove subject to collimated irradiation with full-illumination. Further, a new analytical model is developed to predict the apparent absorptivity of an infinite V-groove subject to collimated irradiation with partial-illumination. A custom, Monte Carlo ray tracing solver is used to predict the apparent radiative properties for all cases as a means of numerical verification by comparing the ray tracing data with the results from the new model in this work and the previously existing models. For diffuse irradiation, the analytical model and ray tracing data show excellent agreement with an average discrepancy of 4.4 x 10-4, verifying the diffuse-irradiation analytical model. Similar agreement is found for collimated irradiation, where the full and partial illumination models indicate average discrepancies of 4.9 x 10-4 and 4.6 x 10-4 when compared with ray tracing data.

Original Publication Citation

Mulford, R. B., Collins, N. S., Farnsworth, M. S., Jones, M. R., and Iverson, B. D., 2018, "Total hemispherical apparent radiative properties of the infinite V-groove with specular reflection," International Journal of Heat and Mass Transfer, Vol. 124, pp. 168-176.

Document Type

Peer-Reviewed Article

Publication Date







Ira A. Fulton College of Engineering and Technology


Mechanical Engineering

University Standing at Time of Publication

Associate Professor

Available for download on Tuesday, March 26, 2019