In the present work the heat transfer form the corium molten pool to the external cooling water has been investigated in order to predict the heat fluxes distribution at the external surface of the lower head. Coupled thermal-hydraulic finite element simulations of the corium and vessel cooling transient, in presence of external cooling water, are presented. Natural convection, convective, diffusive and radiative heat transfer and phase change are considered. Configurations with uniformly spread homogeneous corium have been first considered. Then stratified corium configurations with a metallic layer covering an oxide layer, the latter dominated by uranium dioxide, have been analysed. Several thickness of the metallic layer and different repartition of the volumetric heat source between the two layer have also been considered.