Thermodynamic and optical thickness corrections to diffusive radiative transfer formulations with application to planetary interiors

Radiative transfer of high-frequency light under diffusive conditions is key to planetary heat flow and is important in astronomy and engineering. In geophysics, the effective radiative conductivity (k_rad) has been overestimated by threefold due to modeling refraction across planar interfaces as conical emanations of a point source. This assumption violates the second law of thermodynamics because heat can only flow down the thermal gradient. In addition to an extraneous factor of the index of refraction squared, calculations of k_rad need to address low absorbance in the near-infrared which cannot be quantified using small samples as required for diamond anvil cell experiments. We provide a new derivation and approximate k_rad in the Earth's mantle as 1.9×10^-10T³ in Wm^-1K^-1, which is larger than previous estimates by a factor of up to 10, and will affect geodynamic models. It is also important in geodynamic models to incorporate the fast speed of the carriers, which cause this phenomenon to dominate transient events, and the relative flux of photons and phonons. Key Points A factor of 3 error in radiative transfer formulae is revealed and corrected Radiative thermal conductivity in Earth's mantle is ~2×10-10T3 in Wm-1K-1 Fast photon speeds and flux need to be incorporated in geodynamic models