Modelling of ‘thermal shocks’ in composite materials using a meshfree FEM

This work discusses an application of a meshfree, semidiscrete finite element method to solving the ‘thermal shock’ problem for a thin, cylindrical plate made of functionally graded ceramics. The unsteady heat conduction equation is discretized in space with the partition of unity FEM. The temporal discretization is realized by using an explicit finite difference method. The computations are performed on two model samples: the homogenous one, made of the pure Al 2 O 3 material, and the composite plate, made of the alumina/zirconium layers with variable weight content of ZrO 2 . The heat transfer coefficient on the surface subjected to the ‘thermal shock’, as well as thermal conductivity and thermal diffusivity of the material, are modelled with the theoretical distribution function based on the experimental findings. The discrete solution is first checked for accuracy against the analytical solution to an exemplary test problem, yielding very advantageous results. Finally, it is verified in comparison with the jet-impingement-cooling experimental data, showing good accordance.