This work deals with the development of a numerical algorithm for the prediction of magnetic force lines inside a flowing solidifying melt with the ultimate purpose of simulating and controlling alignment of short nickel coated fibers during the curing process in composites. A complete mathematical model and an accompanying computer program have been developed for the computational simulation of a steady laminar flow of an incompressible fluid with strong heat transfer (involving solidification) and a strong superimposed magnetic field. An extended form of the Boussinesq approximation allowing for temperature-dependent physical properties of the fluid including latent heat of phase change was incorporated. This formulation simultaneously predicts detailed velocity, pressure and temperature fields for the moving fluid while capturing the forming solid phase by using a single computer code. The same code can simulate the reverse process of thawing or melting of the solid phase. The computed example configurations involve a two-dimensional closed container, a straight and a U-shaped channel, and a passage of an arbitrary shape. It was found that the presence of an external steady magnetic field: a) diminishes flow field vorticity, b) causes higher velocity gradients within the boundary layers, c) inhibits the solid phase accretion rate and the total amount of solid accrued, and d) is able to orient magnetized fibers along the lines of local magnetic forces.
