The experimental determination of the thermal con­ductivity of LM is very difficult because of the pro­blems related to convection and to wetting, therefore large discrepancies exist between different sets of data. The high thermal conductivity of LM is mainly due to free electrons. A simple theoretical relation exists for pure metals between electrical and thermal conductivities, known as the Wiedemann-Franz — Lorenz (WFL) law:

le = L0TI r [21]

where 1e is the electronic thermal conductivity, r is the electrical resistivity, and L0 = 2.45 x 10-8W O K-2 is the Lorenz number.

With reasonable uncertainties, this law has been confirmed for many LM, taking into account the fact that the contribution of phonons to the thermal conductivity of the metals of interest is small. There­fore, the approximate prediction of the thermal

Figure 13 Electric resistivity of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

conductivity of LM and several alloys is possible by combining WFL law and the existing, reliable values of the electrical resistivity.

Valuable recommendations for the thermal conductivity of Na, Pb, and Pb-Bi(e) based on the available at this time experimental data were pub­lished by Touloukian et a/.86 in 1970 and for Na by Cook and Fritsch87 in 1985. Later, Mills et a/.88 took the first publication as the starting point and reestimated recommendations for the thermal con­ductivity of many LM. Fink and Leibowitz22 exam­ined the recommendations from various assessments for the thermal conductivity of liquid Na and con­cluded that significant differences (up to ±15%) exist over the range of experimental data (371­1500 K). Available data on the thermal conductivity of liquid Pb and Pb-Bi(e) were also analyzed by Sobolev et a/.23,24 in the temperature range from TM,0 to 1300 K. It was found that all data on the Pb thermal conductivity were in good agreement close to the melting temperature; however, they differed in the temperature dependence and some of them were in serious contradiction with WFL law. These anomalies were explained by the effects of impurities, oxidation and by not relevant experi­mental conditions and techniques. In an effort to find a physically reasonable compromise between the available data and taking into account the WFL law, the linear correlation was recommended for the thermal conductivity of a pure liquid, which allows to describe the most reliable data with the maximum difference of ±15% in the temperature range of TM0-1300K. At present, few experimental
data are available on the thermal conductivity of liquid Pb-Bi(e). A nonnegligible difference exists between different recommendations at lower tem­peratures. The parabolic function can describe the temperature dependence of the Pb-Bi(e) ther­mal conductivity up to 1100 K with an uncertainty of 10-15%. The WFL law can be used for an estimate of the Pb-Bi(e) thermal conductivity with the same precision. In the report,34 the following correlation was used to describe the temperature dependence of the thermal conductivities of liquid Na, Pb, and Pb-Bi(e) at normal atmospheric pressure:

1(T;p0) = 1M,0 + Al,0(t- tm,0)±b2,q(t- TM,0)2 [22]

The parameters of this correlation are presented in Table 13. In Figure 14, the recommended values of the thermal conductivity of liquid Na, Pb, and Pb-Bi(e) are presented as a function of temperature.

In nonstationary thermal calculations, the thermal diffusivity is often used, which is defined as follows:

1(T, p)Ma
p(T, p)Cp (T, p)

Temperature (K)

Figure 14 Thermal conductivity of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

The thermal diffusivities of the considered LM cal­culated at normal atmospheric pressure with the recommended correlations presented earlier are pre­sented in Figure 15.

2.14.6 Conclusions

For liquid Na, Pb, and Pb-Bi(e), the experimental data and correlations for the prediction of their ther­mophysical parameters of interest are available in the temperature region of the normal operation of nuclear installations. In spite of the fact that most of the properties were mainly measured at atmospheric
pressure and some of them have not yet been deter­mined with the needed accuracy, the proposed recom­mended correlations can be used for the predesign calculations of Gen IV nuclear installations with these coolants.

The simplified EOS can be applied for the pre­diction of the effect of pressure far away from the critical point in the pressure and temperature range typical for normal and abnormal operation of new generation power nuclear reactors with LM cool­ants. However, for the prediction of the properties of the Pb and Pb-Bi(e) coolants at higher tem­peratures and pressures, which can be potentially reached under accidental conditions, the existing

EOS can be used with utmost care. In order to improve the precision of EOS, the critical para­meters of Pb and Pb-Bi(e) should be determined with lower uncertainty.

Acknowledgments

This work was supported by funds of the SCKCEN project MYRRHA and by the EURATOM FP6 pro­jects ELSY and IP EUROTRANS.