Prediction of the effective thermal conductivity of three-dimensional dendritic regions by the finite element method

The finite element method has been used to predict the variation in effective thermal conductivity, keff, in evolving three-dimensional dendritic mushy zones. The model demonstrates the influence of a dendrite-like geometry and volume fraction of solid on keff assuming that the conductivities of the solid and liquid phases remain constant and uniform as the structure evolves. The three-dimensional dendrite-like shapes have been generated by a cellular automaton-finite difference model. Numerical solutions are presented for both columnar and equiaxed dendritic zones.