A novel spectral emissivity model for rough surfaces applicable beyond geometrical optics region

Abstract

The accurate prediction of emissivity for rough surfaces is critical in fields such as solar thermal energy and radiation thermometry. For practical rough surfaces, directly solving electromagnetic equations is computationally intensive and often lacks analytical solutions. Geometrical optics approximation offers computational efficiency and, in some cases, explicit formulas. However, their applicability is inherently limited, particularly for surfaces with steep slopes or small σ/λ ratios. This paper introduces a formula for calculating a roughness factor based on Gaussian random rough surfaces and presents a concise, wide-range emissivity model that integrates the Finite-Difference Time-Domain (FDTD) method. Results demonstrate that the predicted roughness factor deviates by less than 5 % compared to measurements of sandblasted surfaces, while the derived emissivity values exhibit a maximum relative deviation of less than 3 % from experimental results. In regions where geometrical optics approximation is invalid, emissivity is governed by two dimensionless parameters: σ/τ and σ/λ, within specific ranges. By incorporating an effective roughness factor related to σ/λ into the geometrical optics model, the proposed approach significantly extends the model's applicability. The new model reduces the maximum absolute error compared to FDTD results from 0.43 (using conventional geometrical optics models) to 0.09. This study addresses the limitations of existing emissivity models for rough surfaces where geometrical optics approximation fails, while advancing the understanding of how surface morphology influences emissivity.