Thermal radiation and natural convection are of crucial importance as these two mechanisms determine the arrester resistance in continuous operation as well as its thermal
stability under voltage surges. External convection and radiation contributions are included in the simulation by applying appropriate boundary conditions. For the heat transfer in the
air gap, a nonlinear heat conduction model is proposed. The air gap is assumed to be filled with an equivalent material with thermal conductivity combining the effects of thermal conductivity, λair, natural convection, λconv, and radiation, λrad. The conductive and the convective contributions are combined into λcc. It is estimated separately for each arrester segment as λcc = Nuλair, where Nu is the mean Nusselt number of a closed vertical annular cylinder. This dimensionless number depends on the inner and outer wall temperature difference T . The geometric dimensions are the height of the segment h, the inner and outer radii r1,2, and the gap width δ. The temperature-dependent fluid and flow properties are described by the Grashof Gr(T ) and Prandtl number Pr