In a cylindrically symmetrical fuel element, the temperature Tfs of the surface of the fuel is related to the temperature of the surrounding coolant Tc by

(2.1)

where q is the linear heat rating in the fuel element, h is the heat transfer coefficient between cladding and coolant, Ks is the thermal conductivity of the cladding, and hf is the heat transfer coefficient between the fuel and the inside surface of the cladding. Rs is the outer radius of the cladding and Rf is its inner radius, which we can also take to be the outer radius of the fuel because, as we shall see, at times the fuel is in close contact with the cladding, and even when it is not the gap between them is small.

In a fast reactor there is usually no significant flux depression in the fuel element and the fission rate can be taken to be approximately uniform over its cross-section. The temperature distribution within the fuel itself however is complicated by the fact that over the wide temperature range in question the variation of the fuel conductivity Kf has to be taken into account. If the fuel temperature at a distance r from the axis is Tf (r), and if the fuel is solid and heat is generated uniformly throughout it, then

CKf(T)dT=4П 1 — R2 ■

and the maximum fuel temperature Tfm is given by

Under some circumstances, however, there is a cylindrical hole in the centre of the fuel. If this has a radius Rh and heat is generated uniformly throughout the annular fuel region the temperature at r is given by

where a = R2h/R2f. The maximum temperature is given by

Comparison of equations 2.3 and 2.5 shows that for constant q the presence of a central hole reduces the maximum temperature.