## 3 Thermal Analysis of the WCLL COB Segment
### Thermal Analysis of the Equatorial Radial-Toroidal Cell of Each of the 7 COB Poloidal Regions
#### 3.1.2 Loads and Boundary Conditions  
In order to perform the thermal analysis, a set of loads and boundary conditions, pertinent to the Normal Operation steady state loading scenario, was considered for each model taken into account. The temperature-dependent properties of materials were taken into account. In particular, for Eurofer, Pb-15.7 Li and Tungsten, the physical properties were drawn from [9; 10; 11]. A non-uniform value of heat flux (\(\Phi\)), due to particles and radiation arising from plasma, for each of the COB poloidal regions was imposed on the straight and bent FW plasma facing surface. The selected heat flux values [8], assumed at the end of flat-top, are reported in Table 1. In particular, the values reported in Table 1 were applied to the straight FW surface. In contrast, for the bent FW surfaces, a decreasing value according to a cosine-dependent law was assumed, considering the values reported in Table 1 as maximum ones:  
\[\Phi_{\text{FWbend}}=\Phi_{\text{FW}}\cdot\cos\alpha \tag{1}\]  
where \(\Phi_{\text{FWbend}}\) is the value imposed to the bend FW surface, \(\Phi_{\text{FW}}\) the values reported in Table 1 as maximum ones and \(\alpha\) varies between 0, corresponding to the start of the bent region, and \(\pi/2\), to the SW. Moreover, a spatial distribution of volumetric density of nuclear-deposited heat power, derived from neutron transport analysis [3], was imposed upon each FEM model to simulate the distributed power deposition as a result of the neutrons, gamma photons and nuclei interactions. Moreover, differently from the previous thermal analysis carried out, the contribution of the decay heat, caused by the activated materials, was also taken into account [12]. In particular, the decay heat power spatial distribution calculated at the shut-down was assumed for the normal operation scenario, as it contributes to heating the structure. Since the spatial distributions of nuclear power and decay heat were calculated only for the O4 region, the analogous spatial distributions for the other six poloidal regions were obtained using the ratio between the Neutron Wall Loadings (NWLs) in the i-th region and that in the O4 region as a scaling factor. The adopted NWLs average values for each COB region [3] are reported in Table 1.  
Moreover, in order to simulate the thermal contact of the PbLi with the SB and DWTs breeder-wetted surfaces, a pure diffusive heat transfer contact with a conservative value of thermal conductance equal to 100 [\(\text{kW}/\text{m}^{2}\cdot^{\circ}\text{C}\)] was assumed. The breeder, since it flows very slowly, due to the action of buoyancy and magneto-hydrodynamics forces, can in fact be considered as stagnant. Then, the DWTs and the SB structure are considered as a continuum concerning the thermomechanical behaviour. Finally, a forced convective heat transfer between coolant and water-wetted surfaces adopting a proper thermal contact was considered. In particular, a countercurrent flow path was imposed for the FW-SW cooling water. Concerning the DWTs cooling water, the path shown in Figure 3 was simulated and the recirculation system was properly modelled. To reproduce the DWTs water path, the tubes were divided into two groups: the first, in which the water enters at 295 \({}^{\circ}\)C, including 14 tubes; and the second, where the recirculation takes place, including 8 tubes. In order to correctly simulate the recirculation system, the average water outlet temperature, namely mixing temperature, of the first group was calculated and set as the water inlet temperature of the second group of tubes, by means of a proper Abaqus procedure. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **O1** & **O2** & **O3** & **O4** & **O5** & **O6** & **O7** \\ \hline Maximum Heat Flux [MW/m\({}^{2}\)] & 0.24 & 0.27 & 0.26 & 0.27 & 0.27 & 0.67 & 0.67 \\ Average NWL [MW/m\({}^{2}\)] & 0.9834 & 1.1592 & 1.2802 & 1.3335 & 1.3287 & 1.1844 & 0.7539 \\ \hline \end{tabular}
\end{table} 
Table 1: Total Heat Flux and average NWL poloidal distribution.