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

• Published in: Materials science & engineering. A, Structural materials : properties, microstructure and processing Vol. 269; no. 1; pp. 90 - 97
• Main Authors: Ravindran, K., Brown, S.G.R., Spittle, J.A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 30-08-1999; Elsevier
• Subjects: Cross-disciplinary physics: materials science; rheology; Dendrite growth; Exact sciences and technology; Materials science; Numerical modelling; Phase diagrams and microstructures developed by solidification and solid-solid phase transformations; Physics; Solidification; Thermal conductivity; Thermal conductivity; Numerical modelling; Dendrite growth; Solidification; Finite element method; Theoretical study; Equiaxed structure; Boundary conditions; Numerical method; Cellular automata; Dendritic structure; Finite difference method
• ISSN: 0921-5093; 1873-4936
• DOI: 10.1016/S0921-5093(99)00160-4

The finite element method has been used to predict the variation in effective thermal conductivity,
k
eff, in evolving three-dimensional dendritic mushy zones. The model demonstrates the influence of a dendrite-like geometry and volume fraction of solid on
k
eff 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.