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Why can't we use fissions products for electricity production ?

As far has I know fissions products from current nuclear power plants create enough 'waste' heat to boil water; and temperature decreases too slowly for an human life. So why can't we design a reactor to use this energy.

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    $\begingroup$ I assume that You mean spent fuel, right? Because actually the main role of fission products (or rather the energy emitted during fission) is to heat water and produce electricity. $\endgroup$ – Wojciech Mar 15 '14 at 21:55
  • $\begingroup$ I assume you already looked up the thermal output of the reactor waste (typically expressed in units of W/Kg) and decided that it was economically viable, right? $\endgroup$ – DumpsterDoofus Mar 15 '14 at 21:56
  • $\begingroup$ Yes. The wastes we are trying to put in the deep of the earth for long time. $\endgroup$ – Galigator Mar 15 '14 at 21:58
  • $\begingroup$ @DumpsterDoofus economically viable is a point of view, because waste already exists and we spend a lot of money to manage them. $\endgroup$ – Galigator Mar 15 '14 at 22:00
  • $\begingroup$ Actual spent fuel form only couple % of the fuel rod. Many countries reprocess spent fuel rods to retrieve uranium which didn't burn out and use it again as a fuel. I can guarantee that this is much more economic. $\endgroup$ – Wojciech Mar 15 '14 at 22:06
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Here are some "order-of-magnitude" arguments:

Quoting https://en.wikipedia.org/wiki/Decay_heat#Spent_fuel :

After one year, typical spent nuclear fuel generates about 10 kW of decay heat per tonne, decreasing to about 1 kW/t after ten years

Now since this is heat, you can't convert it to electricity with 100% efficiency, the maximum possible efficiency is given by the Carnot efficiency $\eta$:

$$ \eta \le 1 - \dfrac{T_\mathrm{cold}}{T_\mathrm{hot}} $$

where $T_\mathrm{hot}$ would be the temperature of the spent fuel rods (in Kelvin) and $T_\mathrm{cold}$ would be the temperature of a cold reservoir against which a generator would work. One would have to do another calculation what a reasonable temperature of the fuel rods would be (in practice they currently seem to be kept at 50 degrees C).

With 'primary' fuel typically 55 Gigawatt days per tonne can be produced, i.e. a 1 Gigawatt powerplant would use 365.25 / 55 = 6.6 tonnes per year.

Even assuming you would be able to convert this to electricity with 100% efficiency and assuming an average 5 kilowatts per tonne over 10 years, this would yield about 18'000 Kilowatt days or 0.018 Gigawatt days, about 0.03% of the primary energy production.

You'll also see from the Carnot efficiency above that higher temperatures imply a higher possible efficiency, i.e. if one can spend some energy to extract the still fissionable material to be used in a reactor again, that is likely to be more efficient in terms of electricity generation.

It's true on the other hand that radioisotope thermoelectric generators (radioactive sources combined with thermocouples) have been used on satellite missions.

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    $\begingroup$ So the production per tonne could be about the same as a medium wind turbine. I have heard that radio-isotope thermoelectric generators are'nt popular because of security reason. End of life device need specials cares. $\endgroup$ – Galigator Oct 5 '14 at 7:55

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