Heat Transfer Through Cylindrical Nuclear Fuel Pin

[a1234]

Let's say we have a cylindrical fuel pin with fissile material in the middle, followed by a gas gap and cladding material. It is being cooled by water on the outside. The temperature drop through the fissile material should be parabolic due to heat generation, and the temperature drops through the gap and cladding material should both be linear as there is no heat generation within these regions.

How would the temperature profile through the pin change if all of the gas were moved to the center of the fuel pin, assuming that the radius of the fuel and cladding remain the same? Could we model the new gas gap as being adiabatic, since the only coolant is the water on the outside of the cladding?

 

[Astronuc]

How would the temperature profile through the pin change if all of the gas were moved to the center of the fuel pin, assuming that the radius of the fuel and cladding remain the same? Could we model the new gas gap as being adiabatic, since the only coolant is the water on the outside of the cladding?

Is one asking about annular fuel, where there is a central void in the fuel column (pellets)?

If one were to remove the gas from the pellet-cladding gap, then one changes the mode of heat transport to radiative instead of conductive. There is always some radiative heat transport, which is proportional to (T_h⁴-T_c⁴), but if gas is present, then the heat transfer by conduction is dominant.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html

Also, consider that the fuel column (pellets) will expand thermally until some equilibrium temperature profile is achieved, and to make it more complicated, the some of the pellets in the column will lean to contact the cladding, so there will be some direct conduction between the fuel pellet and cladding. In the gap, we refer to a so-called jump distance (related to surface roughness of pellet and cladding surfaces), which treats the 'thermal' gap as being apparently larger than the 'mechanical' gap.

If one were to reduce the heat transfer from the fuel, then the surface temperature would increase as would the temperatures across the fuel pellet, but then this would cause the fuel pellet to thermally expand and the pellet-cladding gap would decrease.

Helium is typically used as the fill gas since it has high conductivity. In PWR fuel, 20 atm (at room temperature) is a typical number, although some fuel designs might use about 7 atm if a ¹⁰B is used as a burnable absorber. The pressurization prevents collapse of the cladding early in life due to the much greater coolant pressure (~155 atm). In BWR fuel, with lower coolant pressure (~73 atm), the internal pressures are lower (5-10 atm).

There is some heating going on in the cladding from neutron collisions, beta radiation and gamma radiation, but it is on the order of 1% of the thermal energy from the fission reactions in the pellet. A similar amount of heat is directly deposited in the coolant. Together, the fraction of energy released in fission and directly deposited into the cladding, other structures (guide tubes in a PWR or Water Rods, Channels and Control Rods in a BWR) is about 2.3 to 3.5% depending on the fuel design (lattice geometry and component dimensions).