Why do fuel rods continue heating after the reactor is shut down?

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I have a question about nuclear fission reactors. If the reaction is stopped, then why do the fuel rods continue to heat up after being exposed to air to the point where it could cause a meltdown.
Thank you
Jim
 
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residual radioactivity of short lived isotopes
 
I'd also like to know, Pengwuino.

There are about 160 posts on that thread to filter. The only thing I seem to know is that withdrawl of the moderating rods stops the thing from producing power--or reduces the power--so why is keeping the core submerged important?
 
See granpa answer. There is still a lot of short lived isotopes that produce heat, these can't be stopped, they just have to decay. That takes time and produces heat.

From what I understand first several days are critical, later heat production is low enough to be not that problematic, after all it goes down exponentially.
 
As Penguino pointed out, there's already a thread on this in the appropriate section.