On the basis of two models，namely，the developed coupled model of two-dimensional transient heat transfer and multiphase flow and the model of three-dimensional transient heat transfer of single-roller crystallizers， the fluid flow and heat transfer behaviors during the puddle forming precess of the planar flow casting ( PFC) of Fe78 Si9B13 as well as the heat transfer characteristics of rollers are investigated according to the production data． The results show that ( 1) under a given casting condition，the upstream and downstream meniscuses of the formed puddle are respectively in a crescent shape and in a slope shape with ripple; ( 2) the time for the crystallizer to reach a quasi-thermal equilibrium state is 20 s; ( 3) the impact of high temperature melts on the crystallizer causes an melt impact region of a depth of 0. 0004 m to form，where the maximum temperature in the center of crystallizer surface is about 513. 5K; and ( 4) in comparison with the radial thermal expansion，the circumferential thermal expansion of crystallizer plays a more important role in the actual total expansion，which accounts for 96% ．