This is due to the fact that as the fuel expands on heating, the core of the pellet expands more than the rim. Because of the thermal stress thus formed the fuel cracks, the cracks tend to go from the center to the edge in a star shaped pattern. A PhD thesis on the subject has been published by a student at the Royal Institute of Technology in Stockholm (Sweden).
The cracking of the fuel has an effect on the release of radioactivity from fuel both under accident conditions and also when the spent fuel is used as the final disposal form. The cracking increases the surface area of the fuel which increases the rate at which fission products can leave the fuel.
The temperature of the fuel varies as a function of the distance from the center to the rim. At distance x from the center the temperature (T) is described by the equation where ρ is the power density (W m) and K is the thermal conductivity.
T = T + ρ (r² – x²) (4 K)
To explain this for a series of fuel pellets being used with a rim temperature of 200 °C (typical for a BWR) with different diameters and power densities of 250 Wm have been modeled using the above equation. These fuel pellets are rather large; it is normal to use oxide pellets which are about 10 mm in diameter.
To show the effects of different power densities on the centerline temperatures two graphs for 20 mm pellets at different power levels are shown below. It is clear that for all pellets (and most true of uranium dioxide) that for a given sized pellet that a limit must be set on the power density. It is likely that the maths used for these calculations would be used to explain how electrical fuses function and also it could be used to predict the centerline temperature in any system where heat is released throughout a cylinder shaped object.