Kidphysics said:
In case of a meltdown wouldn't large amounts of boron dust dumped over the core eat up all the free neutrons?
Boron (and specifically B-10) would not do much outside (on the periphery) of the molten core, if that molten core attains a critical state. The boron would have to be distributed in the core mass. One would have to determine if the molten core is porous such that water could infiltrate and provide moderation. Molten cores may be undermoderated.
As others indicated, the problem with damaged/molten cores is the decay heat, which comes from the decay of fission products and transuranics. Radionuclide decay is not affected by boron, or any other chemical element.
The idea of boron or other neutron absorber is to prevent a mass of fissile material or molten core from achieving criticality.
Otherwise, the objective, as others have stated, is to remove the decay heat in a closed loop. The decay heat is then dissipated to the environment. Loss of heat removal was the problem at TMI and Fukushima.
Two key design objectives in nuclear reactor design are reactivity control (ability to shutdown the fission reaction) and coolability (the ability to keep the core fuel and structures well below the temperature which would cause damage or severe failure of the fuel). The goal is to retain the fission products and prevent them from entering the environment.