Since the reactors were shut down when the earthquake hit, the generation of heat through the fission of Uranium has basically stopped. Fission creates by products which continue to break down and generate heat. Nominal rule of thumb for most commercial reactors is it takes about 8-10 days for this to drop to a level where external cooling is no longer critical to maintaining core integrity.

Core integrity will basically start to fail about 45 minutes after loss of cooling water (air isn't a good enough conductor). Note this means exposing the rods to air, not loss of pumps. This initial failure will be the casing for the fuel rods which will start to melt around 2,000 degrees. If the temperature continues to climb the ceramic fuel pellets will be compromised around 3,000 degrees. As the temperatures reach these levels parts of the core will melt and may drop to the bottom of the reactor vessel, typically several inches of steel. If hot core parts hit unpressurized water on their way to the bottom they will create a lot of steam and some nuclear material can be carried along with the steam. If pressure is vented to maintain the reactor integrity, some radiation can escape with the steam. Mostly this will be very short lived particles. The makeup of the radiation is a big clue to the state of the core.

Sea water could be used in two ways within these BWRs. Most likely is they are pumping sea water directly into the reactor vessel. As long as this is possible it is the best way to minimize the release of radioactive materials since it will keep the rods immersed in a good conductor (water). They could also be circulating seawater around the outside of the reactor vessel to help manage the temperature inside the vessel and to keep the steel from melting even if a significant portion of the core were to slag at the bottom of reactor vessel.

Even worst case - complete loss of reactor vessel cooling water would be unlikely to result in the core material escaping through the bottom of the building. The final containment structure is very very thick and designed to disperse the core material to both contain and cool it. Of course with earthquakes and tsunamis this final measure may also be compromised so the game plan seems to be keep the cores as cool as possible within the primary containment system (the reactor vessels).

Here is a reference with a lot more information: Link

- Eric