There are many publications numbering over hundreds dealing with thermal conductivity of UO2. Washington [116], Brandt and Neuer [117], and Fink et al. [50] made appraisals of the conductivity data found in the open literature. Brandt and Neur [117] presented a mean correlation curve of thermal conductivity versus temperature for UO2 by using data from number of sources. Their equation had three terms: the first two terms are for phonon and electronic conductions, respectively. The third term stood for the decrease in thermal conductivity resulting from dislocations created at higher temperatures. Fink et al. [50] used a different model to fit the voluminous data on UO2. They showed the evidence of a phase transition for UO2 at 2,670 K from the enthalpy measurements and sug­gested a similar transition with temperature for thermal conductivity. Fink et al. [50] suggested a relation conforming with the enthalpy and heat capacity equa­tions. Their relation is given below:

kU02 (W. m — 1.K — 1)= (A + BT + CT2) 1 + DTe-£/kT, (298 < T < 2670 K)

where A = 6.8337 x 10-2 m-K-W-1, B = 1.6693 x 10-4 m-W-1, C =

3.1886 x 10-8 m-W-1K-1, D = 1.2783 x Ш-1 W-m-1 K-2, E = 1.1608 eV, and k is the Boltzmann constant.

For 2,670 K < T < 3,120 K,

ku02 (W — m-1 — K-1) = 4.1486 — 2.2673 x 10-4 T (53)

Equations (52) and (53) fit the thermal conductivity data within an error margin of 6.2 %. The two terms in Eq. (52) represent contributions from phonons and electrons, respectively. The inclusion of a dislocation term as recommended originally by Weilbacher [112] to fit his high temperature data was not justified.

In 2006, IAEA [40] made a detailed survey on thermal conductivity data and recommended equation for the thermal conductivity of 95 % dense solid UO2 which consists of lattice term and a term suggested by Ronchi et al. [118] to represent the small-polaron ambipolar contribution to the thermal conductivity. The lattice term was determined by a least squares fit to the lattice contributions to the thermal conductivity obtained by Ronchi et al. [118], Hobson et al. [119], Bates [120], Conway et al. [121] and Godfrey et al. [122]. The recommended equation for thermal conductivity of solid 95 % dense UO2 is:

kuo2 = [100/(7.5408 + 17.692t + 3.6142t2)] + (6400/t25) exp(-16.35/t)

(54)

where, t is T/1,000, T is in K, and k is the thermal conductivity in W-m-1 K — . Thermal conductivity values for 100 % dense UO2 or for a different density may be calculated using the porosity relation derived by Brandt and Neurer [117], which is:

k0 = kp/(1 — op), (55)

where, o = 2.6-0.5t. Here, t is T/1,000 where T is in K, p is the porosity fraction, kp is the thermal conductivity of UO2 with porosity p, and k0 is the thermal conductivity of fully dense UO2.

Uncertainties in thermal conductivity values for 298-2,000 K are 10 %. From 2,000 to 3,120 K, the uncertainty increased to 20 % because of the large dis­crepancies between measurements by different investigators [40]. Typical thermal conductivity of 95 % dense UO2 as a function of temperature is given in Fig. 15.

The lattice term has traditionally been determined by fitting the low tempera­ture thermal conductivity data because the lattice contribution dominates the thermal conductivity at low temperatures. Figure 16 shows the total thermal conductivity, the lattice contribution, and the ambipolar contribution as a function of temperature that have been calculated from the equation of Ronchi et al. [118], which is given below:

kuo2 = [100/(6.548 + 23.533t)] + (6,400/t25) exp(-16.35/t), (56)

ЮО 400 MO 900 1000 I?00 1*00 I COO WOO 7000 7900 7400 7000 7000 9000 3700

Temperature, К

Temperature, K

where t is 7/1,000, T is in K, and k is the thermal conductivity for 95 % dense UO2 in W m-1K-1. Below 1,300 K, the ambipolar term is insignificant and the total thermal conductivity equals the lattice contribution. Although the ambipolar term begins to have a significant contribution to the total thermal conductivity above
1,300 K, it is not larger than the lattice contribution determined by Ronchi et al. until 2,800 K. Even at 3,120 K, the lattice contribution is still significant.

No data is available on thermal conductivity of liquid ThO2. Based on an initial review of the limited data [12, 40] on the thermal conductivity and thermal diffusivity of liquid UO2, the liquid thermal conductivity is in the range of 2.5-3.6 W-m-1 K-1. Liquid thermal diffusivities range from 6 x 10-7 to 11 x 10-7 m2 s-1. The uncertainty in the thermal conductivity and thermal dif — fusivity of liquid UO2 is approximately 40 % [40].