The Nusselt number is defined a priori based on the measured steady-state temperature distribution within each arrester segment separately. This is necessary because of the
large temperature difference of the segments leading to quite different natural convection conditions within the respective air gap. Similarly to the convective heat transfer, one aims for the definition of an equivalent conductivity λrad for the radiative heat transfer in the arrester gap. The Stefan–Boltzmann law relates the emissive power and the surface temperatures The radiation exchange factor C12 for the annular cylinder is given in [13], and the inner surface of the annular cylinder is A1. A temperature-dependent equivalent thermal conductivity
is introduced.
Note that the heat flow rate provided by this model is identical
with the one given by the Stefan–Boltzmann law for radiative
heat transfer in the air gap assuming solely radial steady-state
heat transfer. The validity of this approach for the circular
annulus case can easily be verified