Striations of impurities in Gallium Arsenide crystals grown by the liquid encapsulated Czochralski technique mainly occur due to temperature fluctuations arising from the flow oscillations in the melt. Because molten GaAs has a large electrical conductivity, the thermal convection in the melt can be suppressed by the application of a magnetic field. The flow and heat transfer in the melt and encapsulant, and the heat transfer in the crystal with and without the application of an axial magnetic field are obtained numerically for various combinations of crystal and crucible rotational rates for a 0.104 m diameter crystal growth. When no magnetic field is applied, the flow and temperature fields in the melt are strongly dependent on crystal and crucible rotational rates. The flow in the melt is progressively suppressed by the application of stronger axial magnetic fields but the convection in the melt is significant even for a field strength of 0.5 T. When a magnetic field strength of 0.25 T or more is applied, the isotherms near the crystal-melt interface become flatter and the meridional flow in the melt becomes less sensitive to the rotational rates.