An analytical model for optimal directional solidification using liquid metal cooling

In what follows, a model is developed that describes the optimal processing parameters for directional solidification using liquid metal cooling (LMC). The model considers a sample with a flat geometry and, as a first approximation, can be used to treat the flat sections of a turbine blade. The model predicts (1) the optimal withdrawal rate of the casting from the hot zone, (2) the temperature gradient in the liquid at the solidification interface, and (3) the temperature profile along the length of the casting. The model is then used to perform a sensitivity analysis of the LMC process. Cooling bath temperature, baffle thickness, shell thickness, and shell thermal conductivity are shown to have a strong influence on system performance.