Finite difference computations were used to follow boron migration in the melt and segregation in CZ Si crystal growth. With no applied magnetic field, transport near the growth interface was dominated by advection, resulting in a nearly uniform radial distribution of boron. Application of a 1 kG axial field calmed the melt motion enough that advection and diffusion appeared to play equal roles in transport near the crystal: the boron profile under the interface showed some characteristics of a diffusion boundary layer, but was quite shallow. Increasing to 2 kG further suppressed the melt motion until transport near the growth interface appeared to be strongly dominated by diffusion. Before equilibrium was reached, there was a fully developed diffusion boundary layer and a pronounced radial variation of boron concentration at the interface and in the Si crystal.