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

Abstract

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, 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.

New Constraints on the Thermal Conductivity of the Upper Mantle From Numerical Models of Radiation Transport

“…Our mantle k rad estimates are generally similar to previous estimates for olivine polycrystals, although our values are significantly higher at ambient mantle temperature and large grain size (Figure ). On the other hand, our values are much higher at all temperatures than more recent models (e.g., Hofmeister, , , ). Therefore, it may be necessary to reappraise the character of heat transport in a number of important geodynamic settings.…”

“…Including all effects together in multiphase polycrystalline media results in a complicated problem for which a general effective medium theory is so far unavailable. Moreover, Hofmeister () has suggested that the usual inclusion of n 2 in the source function n 2 I νb (equation ) is fundamentally erroneous, although we dispute this (supporting information section S1).…”

Experimental study of thermal conductivity at high pressures: Implications for the deep Earth’s interior

“…47 Knowledge of the depth-dependent thermal conductivity of the Earth's mantle would 48 complement recent advances in mantle convection modeling, where a range of possible 49 dynamic structures are predicted using estimated values for the thermal conductivity of 50 the region (Dubuffet et al, 1999;Naliboff and Kellogg, 2006;Tosi et al, 2010). Current 51 estimates of the thermal conductivity of mantle and core materials often rely on 52 extrapolations of experimentally determined values at relatively low pressures and/or 53 temperatures (P-T) (Hofmeister, 1999;Hofmeister, 2010;Hofmeister, 2014) Goncharov et al, 2010). 61…”

“…We note that this 284 formulation is based on Planck's theory of heat radiation (Planck, 1914), which 285 essentially includes the refractive index of the material (cf. Hofmeister, 2014…”

Terrestrial planets fractionated synchronously with accretion, but Earth progressed through subsequent internally dynamic stages whereas Venus and Mars have been inert for more than 4 billion years

“…The following summaries of these chains of conjectures, and of objections to them, are in part abridged from Hamilton (2011Hamilton ( , 2013. Among those who have long raised similar, and other, objections to popular speculations regarding Earth are Anderson (2013), Foulger (2010), Hofmeister (2010Hofmeister ( , 2014, and Hofmeister and Criss (2005, 2012.…”