A major uncertainty in predicting the fuel temperature is the value of the conductance across the interface or gap between the fuel and the cladding. This is hf in equation 2.1.

If the fuel is manufactured in the form of pellets they are inser­ted into the cladding tubes with a radial clearance of some 50 цm or more when cold. This is reduced by the differential thermal expansion when the reactor is at power. The thermal expansion coefficient of the cladding (about 18 x 10-6 K-1) is greater than that of the fuel (about 13 x 10-6 K-1), but as the increase in the fuel temperature is greater the gap is reduced. The extent of the reduction is hard to predict, how­ever, as the expansion of the fuel is irregular because it cracks (see section 2.4.2).

To increase hf the fuel elements are usually filled with helium when they are manufactured because it has a high thermal con­ductivity of about 0.3 Wm-1 K-1 at 600 °C. If a helium-filled radial gap is 20 gm wide and symmetrical when at power, hf is about 15 kWm-2 K-1.

As irradiation proceeds the fuel swells and the gap becomes nar­rower until the fuel and the cladding are in contact, but because the surfaces are rough this does not mean that the effective width of the gap is zero. When two solid bodies touch each other contact is made only at a few places where extreme points on the two rough surfaces touch. The fraction of the apparent interface over which there is actual contact may be of the order of 1% and increases if there is a normal stress pushing the surfaces together. The effective thickness of the gas layer when the surfaces are in contact depends on their roughness and may be 0.5 gm if they are smooth, but cracks in the fuel increase it to an extent that is uncertain. Also the estimation of the area of solid-to-solid contact is uncertain.

A further large uncertainty is introduced by the changes in the composition of the gas in the gap. As irradiation proceeds inert fission- product gases, mainly xenon with some krypton, are released from the fuel (see section 2.3.5). Because of their high atomic weights they have much lower thermal conductivities than helium (.026 Wm-1 K-1 for krypton and.016 Wm-1 K-1 for xenon at 600 °C), and as they are released from the fuel they reduce the conductivity of the helium substantially by diluting it, introducing another uncertainty in the conductance.

In principle it is possible to estimate hf experimentally, either by examining fuel after irradiation and deducing the temperature distri­bution from the observed changes in the structure, or by measuring the fuel temperature during operation by inserting thermocouples into it. Either method involves large uncertainties however, mainly because the conductivity of the fuel itself is not known accurately as explained earlier.

As a result it is usually best to assume an approximate value of hf of about 5 or 8 kWm-2 K-1, and to recognise that it is very uncertain and that the actual value may differ by a factor of two either way. For Rf = 3 mm and q = 50 kWm-1, hf = 6 kWm-2 K-1 gives an interfacial temperature difference between fuel and cladding of 440 K, but the actual value may be anywhere between 200 and 800 K.