Radiation Energy Density and Radiation Heat Flux in Small Rectangular Cavities

Abstract

The present paper investigates the impact of one or more small cavity dimensions on the radiation energy density and radiation heat flux in rectangular metallic cavities. The emphasis of the present analysis is the exact treatment of the modal structure of the electromagnetic field in a small cavity in determining the properties of the thermal radiation field in the cavity. The excitation spectrum of the modes is assumed to be given by the Planck distribution function. The Poynting theorem is invoked in order to determine the radiative heat flux absorbed by the walls from the radiation in the cavity. Variation of the dimensions of the rectangular cavity allows the effects of cavity size and shape on the radiant energy density and radiant heat transfer to be assessed, particularly in several interesting limiting cases. It is found that significant deviations from the classical theory occur whenever any of the cavity dimensions satisfy the inequality lT ≤ 1 cm-deg K. It is further found that, when two or more of the cavity dimensions satisfy the above inequality, the radiant energy density and radiant heat transfer are significantly reduced in comparison to the results of classical theory. However, when only one dimension is limited, as in the case of a closely spaced parallel-surface geometry, the radiant energy density and radiant heat transfer are significantly increased compared to the classical theory.