8th. World Congress on Computational Mechanics (WCCM8) 5th European Congress on Computational Methods in Applied Sciences and Engineeering (ECCOMAS 2008) June 30 –July 5, 2008 Venice, Italy Effects of Magnetic Fields on Crystal Growth * Andrew Kao 1 , Koulis A. Pericleous 2 and Vaughan Voller 3 1 University of Greenwich London, SE10 9LS a.kao@gre.ac.uk 2 University of Greenwich London, SE10 9LS k.pericleous@gre.ac.uk 3 University of Minnesota Minneapolis, 55455-0116 volle001@umn.edu Key Words: Dendritic Growth, Magnetohydrodynamics, Multiphyics Problems, Modelling. ABSTRACT The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidifica- tion were investigated using an enthalpy based numerical model. It was found that the resulting Lorentz force generates a complex flow influencing the solidification pattern. Experimental work of material processing under high magnetic field conditions has shown that the microstructure can be significantly altered. There is evidence that these effects can be atrtributed to the Lorentz force created through the thermoelectric magentohydrodynamic interactions.[1,2] However the mechanism of how this occurs is not very well understood. In this paper, our aim is to investigate the flow field created from the Lorentz force and how this influences the morphology of dendritic growth for both pure materials and binary alloys. The enthalpy based method is a front tracking method using a coarse mesh compared to other phase field methods. Finite difference approximations are used to calculate the curvature, interface speed, interface orientation and thermoelectric currents. Navier-Stokes equation provides a velocity field in the liquid fraction which is used to calculate the transport of the temperature and solute fields. This leads to two-way-coupling of the flow and the liquid fraction. Using a sub-stepping technique the full transport equation is not solved everytime step reducing the simulation time, while minimising the inheritted errors. The current density J is derived from the electric potential, requires a boundary condition to be placed at the solid/liquid interface. A submeshing technique is implemented on cells close to the interface to give a better approximation of the electric potential. The system begins in a meta stable state with a non-dimensional temperature of -0.65 and the domain size is 1000x1000. At t =0 a solid seed is placed in the domain and solidification proceeds. Using a finite difference enthalpy based method the subsequent growth is calculated. The first case looks at a stagnant liquid with no magnetic field. The crystal shows clear 4-fold symmetry and the tip velocity converges to a constant in line with microscopic solvability theory.[3] The thermoelectric current is derived by resolving the electric potential field. The current emanates from the tip and crosses the interface at the root of a fully developed dendrite. In the presence of a constant external convection (fig 1) the transport of the temperature and solute fields causes the interfacial temperature and solute gradients to change the growth potential. In this case the