About the validity of analytical approximations for temperature and stress for actively cooled windows during thermal loading

The verification of analytical approximations for temperature and stresses during thermal loading is done for ceramic edge-cooled windows for the stellarator W7-X by comparison with more accurate numerical calculations. Numerical calculations show that a steady state temperature and stress approximations assuming edge-cooled circular plates can be applied only in the case when radiative cooling from a surface is neglected. The prediction for poor thermal conductivity ceramics under high heat flux load based on simple analytical equations can result in considerable mistakes in the temperature and, consequently, stress values. Even the prediction of the qualitative tendency of temperature and stress behaviour as a function of the window size can be wrong.