Heat Transport by Radiation in Solids

An expression for the effective thermal conductivity λ_eff solids is derived, taking into account conduction by phonons and radiation, which displays the fact that λ_eff depends, generally in an involved manner, on temperature, temperature gradient, and the geometry of the experimental device. Explicit results are obtained in the limit of small temperature gradients, yielding a correction to the well-known radiation term proportional to T³, which is frequently employed to explain the observed rise of the thermal conductivity of certain semiconductors and insulators at elevated temperatures.