Impact of Non-Uniform Surface Temperature on the Apparent Radiative Properties of Cavity Receivers

Radiative surface properties play a critical role in the design, analysis and optimization of solar–thermal systems. Cavity receivers increase the efficiency of solar–thermal energy systems through the cavity effect. The cavity effect refers to increased absorption of radiation due to multiple reflections within a cavity. Apparent radiative surface properties of a cavity characterize the effective interactions of radiation passing through an imaginary surface covering the cavity aperture. In this study, we investigate the extent to which the apparent emissivity of a cavity with a non-uniform surface temperature profile may be estimated using an isothermal enclosure model. A cylindrical cavity was assumed to have a linearly increasing, linearly decreasing or parabolic temperature profile. The cavity's apparent emissivity and absorptivity were calculated for various length-to-diameter ratios $(L/D)$ and intrinsic emissivity $(ε)$⁠. This work shows that a spatially varying surface temperature can significantly affect the apparent emissivity and absorptivity, especially for shallow cavities with low intrinsic emissivity. Moreover, under non-isothermal conditions, changes in the cavity's geometry result in larger changes in the apparent radiative properties than observed for isothermal cases. For a cavity with an intrinsic emissivity of 0.3, the percent difference between non-isothermal and isothermal conditions reaches ∼25% for $L/D$ ratios of 4 and 8 for cavities with linearly increasing or parabolic temperature profiles. Similarly, for $ε=0.9$ and $ΔTw/T0=0.1$⁠, this difference is <1% across all three wall temperature cases when $L/D=4$⁠.