ColJack said:
if the reaction has stopped, then why are the rods still heating up? they only get hot when the reaction is happening..
Unfortunately not.
Fission can be stopped instantly by dropping the control rods but it accounts for only 80% of a reactor's power. The remaining 20% comes from the radioactive decay of the fission products which are overloaded with neutrons and thus highly unstable. It's this decay that heats up the rods and it can't be turned off. You have to keep on taking the heat out until it runs down.
The spent fuel rods pose a similar problem. They're spent only in the sense that they contain insufficient fissionable material to be worth using but the fission products are still breaking down. That's why they have to sit in cooling ponds for a long time.
There are quite a few things wrong with the design of the Japanese reactors. Firstly, water is a terrible choice of coolant:
1) If you lose the pressure, it boils and you lose your cooling.
2) It limits the operating temperature of the turbines which is not good for efficiency. Fossil fuel power stations can superheat their steam up to 900°C. This would create impossibly high pressures inside a water cooled reactor so they have to run at a rather pathetic 300°C.
3) Water absorbs the neutrons that are needed to sustain a fission reaction so you have to put extra fissionable material in. This is, arguably, its biggest shortcoming. If you must use water, it should at least be heavy water but, as far as I know, only Canadian reactors do this.
Water cooling was originally developed for submarines where space was at a premium. Sadly, it's now the most common choice for land based reactors because it's cheap. Moreover, the boiling water reactor, which is what the Japanese ones are, is the cheapest and nastiest of the lot. There isn't even a secondary heat exchanger in there. Radioactive steam goes directly to the turbines!
And then there's the cooling ponds for spent fuel rods. It would appear that the Japanese ones are kept just above the reactors (but outside the primary radiation shielding), ideally placed to be damaged in any reactor explosion.
There's a lot of misconception about spent fuel. I remember a survey in which a substantial fraction of the general public wouldn't go anywhere near a new fuel rod but would happily pick up a spent one.
It's not just the decaying fission products you have to worry about. The greatest danger comes from long-lived heavy elements, including plutonium, which you get when you leave uranium stewing in a neutron soup. Plutonium isn't particularly radioactive but it is highly toxic, even in microgram quantities. You really don't want it being blown into the atmosphere.
So, to summarize:
1) Cheap, nasty reactor design.
2) Cooling plant not protected from tsunamis.
3) Spent fuel ponds not protected at all.
That's what you call an accident waiting to happen.
On a happier note, you might like to know that UK reactors are CO2 gas cooled. This allows for much higher operating temperatures (650°C) with no risk of boiling. Our only nuclear accident involved an air cooled reactor in which the graphite moderator caught fire, something that really should have been foreseen.