Extension of Planck's law to steady heat flux across nanoscale gaps

Recent experiments report that the radiative heat conductance through a narrow vacuum gap between two flat surfaces increases as the inverse square of the width of the gap. Such a significant increase of thermal conductivity has attracted much interest because of numerous promising applications in nanoscale heat transfer and because of the lack of its theoretical explanation. It is shown here that the radiative heat transport across narrow layers can be described in terms of conventional theory adjusted to non-equilibrium structures with a steady heat flux.