Using a phase field model, which fully couples the thermal and solute concentration field, we present simulation results in three dimensions of the rapid dendritic solidification of a class of dilute alloys at the meso scale. The key results are the prediction of steady state tip velocity and radius at varying undercooling and thermal diffusivities. Less computationally demanding 2-dimensional results are directly compared with the corresponding 3-dimensional results, where significant quantitative differences emerge. The simulations provide quantitative predictions for the range of thermal and solutal diffusivities considered and show the effectiveness and potential of the computational techniques employed. These results thus provide benchmark 3-dimensional computations, allow direct comparison with underlying analytical theory, and pave the way for further quantitative results.
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