A model has been developed to predict the thermal hydraulics in the uncovered part of a pressurized water reactor core. The core is considered to be a heterogeneous porous medium with different permeabilities and effective thermal conductivities in the radial and axial directions. The flow in the core is modeled by the Brinkman-Forchheimer extended Darcy equations. The dependence of the thermophysical properties of the coolant (steam-hydrogen mixture) and the fuel rods with temperature is accounted for. Oxidation of the Zircaloy is also modeled, and transport of the generated hydrogen in the uncovered portion of the reactor core is considered. The effects of the thermal boundary condition at the outlet of the core (i.e., at the upper tie plate) are studied and reported. Partial blockage of the core due to the mechanical failure and/or melting of some of the fuel rods is also modeled, and its effects on the thermal hydraulics of the core are studied and discussed. Numerical simulations are reported for the Three Mile Island Unit 2 reactor conditions. The results show that the flow field in the core is affected by exothermic heat release as well as by a decrease of the coolant density due to the Zircaloy cladding oxidation. In addition, the results show that there is entrapment of the coolant from the upper plenum into the core. The partial blockage of the core was found to have a profound influence on the heatup of the core.