*4.2. Mass Transfer Study*

The mass transfer behavior of iron was investigated by integrating with the turbulent flow of LBE. A much finer mesh in the near-wall region is required to study the mass diffusion behavior from the wall to the bulk flow than for the hydrodynamic study, because it is necessary to place the first node in the diffusion boundary layer. In the mass transfer study, the first node of the prism layer is placed about 0.34 μm from the wall, corresponding to approximately *y*+ = 0.1, the recommended value for mass transfer studies [27]. Fifty layers of prism cells are placed beside the wall. The cell size is 0.75 mm.

As described in Section 2.2, for a long term non-isothermal closed loop, the concentration of iron in the bulk fluid cannot exceed its saturation concentration at the lowest temperature, or it will deposit on the coldest part of the wall. On the other hand, the concentration of iron increases as operation continues. Therefore, it is reasonable to assume that the iron concentration in the bulk fluid equals its saturation point at the lowest temperature [22,23]. The iron concentration at the wall in the hottest part depends on the situation. If the oxygen concentration is high enough that an *Fe*3*O*4-based protective film forms on the metal surface, the film can be reduced by the lead in the fluid. As a result, the equilibrium concentration of iron on the wall surface is controlled by this chemical reaction. However, if the oxygen concentration is sufficiently low that no oxide film forms, the equilibrium concentration of iron on the wall equals its saturation concentration [29]. Therefore, the concentrations of iron at the solid/liquid interface and in the bulk fluid are about 8.978 × <sup>10</sup>−<sup>5</sup> wt % and 9.576 × <sup>10</sup>−<sup>6</sup> wt %, respectively [39]. The molecular diffusion coefficient of iron in LBE is only known at certain temperatures, and has a large degree of scatter, and there is no diffusion coefficient of iron in LBE at 450 ◦C [38]. In this study, the iron diffusion coefficient in LBE is approximated to that of pure lead, as the diffusion coefficients of the two are considered to be similar [40,41]. Therefore, it is extrapolated from Robertson's law that the molecular diffusion coefficient of iron in LBE at 450 ◦C is approximately 3.16 × <sup>10</sup>−<sup>10</sup> <sup>m</sup>2/s [38,41].
