Thermoelectric effect in the surface layer of a metal exposed to a high-power heat flux

The one-dimensional electron temperature distribution problem in the surface layer of a metal simultaneously exposed to thermionic emission and a high-power heat flux, taking into account second-order thermoelectric effects is considered. Analytic solutions are obtained for the problem in particular cases. Conditions are indicated under which a decrease in the heat flux in the metal and a corresponding increase in thermionic emission from its surface is possible.