Thermal Conductivity of the Mushy Zone and the Completely Solidified Region During the Solidification of a Binary Alloy

During solidification of a binary solution a two-phase region or “mushy zone” develops, and the study of the transport of momentum, heat, and species requires the understanding of its morphology. The traditional procedure to evaluate the thermal conductivity in the mush has been to average it over each of the two phases, neglecting anisotropy and the morphology of the mushy zone. The present work proposes a model for the thermal conductivity which takes into account the morphology of the dendrites and anisotropic effects. The characteristic lengths needed to model the thermal conductivity are discussed, and comparisons of the proposed model with the current models are made. It was found that the model proposed in this research can be more appropriate to evaluate the effective thermal conductivity of the mushy zone. Also, in alloys with components of similar thermal conductivity in the solid phase, the effective thermal conductivity of the completely solidified region can be evaluated using the traditional approach (resistances in parallel).