Heat transfer through the fuel-sheath gap is governed by three primary mechanisms (Lee et al., 1995). These mechanisms are 1) conduction through the gas, 2) conduction due to fuel — sheath contacts, and 3) radiation. Furthermore, there are several models for the calculation of heat transfer rate through the fuel-sheath gap. These models include the offset gap conductance model, relocated gap conductance model, Ross and Stoute model, and modified Ross and Stoute model.

In the present study, the modified Ross and Stoute model has been used in order to determine the gap conductance effects on the fuel centerline temperature. In this model, the total heat transfer through the gap is calculated as the sum of the three aforementioned terms as represented in Eq. (21):

htotal — hg + hc + hr (21)

The heat transfer through the gas in the fuel-sheath gap is by conduction because the gap width is very small. This small gap width does not allow for the development of natural convection though the gap. The heat transfer rate through the gas is calculated using Eq. (22).

Where, hg is the conductance through the gas in the gap, kg is the thermal conductivity of the gas, R1 and R2 are the surface roughnesses of the fuel and the sheath, and tg is the circumferentially average fuel-sheath gap width.

The fuel-sheath gap is very small, in the range between 0 and 125 y. m (Lassmann and Hohlefeld, 1987). CANDU reactors use collapsible sheath, which leads to small fuel-sheath gaps approximately 20 ^m (Lewis et al., 2008). Moreover, Hu and Wilson (2010) have reported a fuel-sheath gap width of 36 ^m for a proposed PV SCWR. In the present study, the fuel centerline temperature has been calculated for both 20-um and 36-um gaps. In Eq. (22), g is the temperature jump distance, which is calculated using Eq. (23) (Lee et al., 1995).

(23)

Where, g is the temperature jump distance, yi is the mole fraction of the ith component of gas, go/i is the temperature jump distance of the ith component of gas at standard temperature and pressure, Tg is the gas temperature in the fuel-sheath gap, Pg is the gas pressure in the fuel-sheath gap, and s is an exponent dependent on gas type.

In reality, the fuel pellets become in contact with sheath creating contact points. These contact points are formed due to thermal expansion and volumetric swelling of fuel pellets. As a result, heat is transferred through these contact points. The conductive heat transfer rate at the contact points are calculated using Eq. (24) (Ainscough, 1982). In Eq. (24), A is a constant, Pa is the apparent interfacial pressure, H is the Mayer hardness of the softer material. A and n are equal to 10 and 0.5.

hc = A——————

(kf + ksheath )

The last term in Eq. (21) is the radiative heat transfer coefficient through the gap, which is calculated using Eq. (25) (Ainscough, 1982). It should be noted that the contribution of this heat transfer mode is negligible under normal operating conditions. However, the radiative heat transfer is significant in accident scenarios. Nevertheless, the radiative heat transfer through the fuel-sheath gap has been taken into account in this study. In Eq. (25), ef and £sheath are surface emissivities of the fuel and the sheath respectively; and temperatures are in degrees Kelvin.

/t4 _t4

if/o isheath, ij

ef + esheath _ ef esheath ff _ Tsheath/i /