Radiative heat transport in the Mantle

The energy transfer of photons through a grey body (i.e. one in which absorption by photons is finite, non-zero and independent of wavelength) is given by (Stacey, 1969, p. 248) 

Here Kr is the effective radiative conductivity, n is the mean refractive index, T 

Radiative heat transport through olivine has been discussed extensively (e.g., Fukao et al., 1968 Shankland, 1970 Schatz and Simmons, 1972 Scharmeli, 1979 Shankland et al., 1979). The radiative thermal conductivity, Kt of forsteritic olivine increases with rising temperature and would contribute to heat flow in the Upper Mantle (Shankland et al., 1979). However, values of Kt for olivine are considered to be rather low to satisfactorily explain the dissipation of the Earth s internal heat by radiation and lattice conduction alone. Note, however, that Fe2 CF transitions in almandine, pyroxenes (M2 site) and, perhaps, silicate perovskites absorb strongly in the wavelength range 1,250 to 

200 nm (see figs 5.6 and 5.19 9.5.8), the region where the radiation energy flux for a black body is a maximum in the temperature range 1,000 to 1,500 °C. Thus, Fe2+ ions in pyroxene or garnet phases in the Upper Mantle and Transition Zone, and perhaps silicate perovskite in the Lower Mantle, would reduce radiative heat transfer in these regions of the Earth s interior. 

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