Distributed temperature estimation in Czochralski crystal growth process

In this work, the conduction-convection PDE model of heat transfer over the time-varying crystal domain is considered. The conduction-convection PDE model of heat transfer is coupled with crystal growth dynamics in the representative example of Czochralski crystal growth process. The infinite-dimensional representation of the heat conduction process is explored within the slow time-varying process effects. The computational framework of the Galerkin´s method is used for parabolic PDE model order reduction over the time-varying domain and the effect of moving boundaries are investigated. An observer is synthesized for temperature distribution reconstruction over the entire crystal domain. The developed observer is applied on the large scale moving mesh finite element model of the process and it is demonstrated that despite parametric and geometric uncertainties in the observer design, the temperature distribution is reconstructed with high accuracy.