New constraints on the thermal conductivity of the upper mantle from numerical models of radiation transport

To address uncertainties in the values and mathematical form of the radiative thermal conductivity k_rad in the mantle, we developed new models for the transport, scattering, and absorption of thermal radiation in semitransparent multiphase polycrystalline assemblages. We show that the Rosseland diffusion equation correctly describes the diffusion of thermal radiation and infer the form of the effective spectral coefficients through numerical experimentation. We show that the scattering coefficient depends on the grain size and on interphase contact statistics in complicated ways, but that simplifications can be employed in practice. The effective opacity of a composite random material is a harmonically weighted mixture in the limit of infinitely large grain size and an arithmetically weighted mixture in the limit of infinitesimal grain size. Using existing absorption spectra for major upper mantle minerals, we estimate k_rad as a function of temperature, grain size, and petrology. In mantle assemblages, the scattering effect is important for small grain sizes (<1 mm), but the grain size effect on the effective opacity of a multiphase medium is important for grain sizes up to 10 cm. We calculate that upper mantle k_rad is about 2–3.5 W·m⁻¹·K⁻¹ for a representative mean grain size range of 0.01 to 1 cm. This translates to a total thermal conductivity of 5.5–7 W·m⁻¹·K⁻¹. Application of our model to the cooling of oceanic lithosphere shows that k_rad increases net cooling by about 25%.