## 4 Thermal and Structural Analysis and Design Improvements of the BC Region
### The First Update (v1) of the BC Region Design
#### 4.1.1 The FEM Model  
A 3D FEM model of the BC region, obtained by cutting the COB reference design mode, has been set up. The above-considered improvement has been taken into account by increasing the Cap plate thickness from 25 mm (that is the reference value to 40 mm. Then, the elementary cells have been equipped with the proper cooling systems. With regards to the DWTs, the \"v06b\" layout, consisting of 22 tubes, has been implemented in each cell. Instead, as to the cooling channels within the FW-SWs region, ten channels have been considered for the last cell, containing the BC plate, whereas six channels have been considered for the remaining two cells, as given in the reference layout [9], as reported in Figure 10.  
A spatial discretisation grid composed of \(\sim\)3.8 M nodes connected in \(\sim\)1.8 M tetrahedral and hexahedral elements, reproducing the BC region structure, DWTs, PbLi, DWTs' and cooling channels' water, has been set up. Temperature-dependent material properties have been considered, drawn from [10; 11; 13]. In order to assess the thermal performances of the BC region under the WCLL BB operational steady state scenario, the following set of loads and boundary conditions [12] has been considered:  
* Nonuniform heat flux on the Tungsten surface: the value of heat flux at the end of the flat-top for the WCLL COB segment, at the corresponding poloidal region, has been selected in order to take into account the heat flux due to particles and radiation from the plasma. A uniform value of 0.67 MW/m\({}^{2}\)[14] has been applied to the straight surface, whereas a cosine-dependent law has been assumed for the bend tungsten surfaces to consider a decreasing value from the uniform one to zero. * Nonuniform nuclear power density: In order to consider the heat power deposited by neutrons and gamma photons, a 3D nonuniform spatial distribution of volumetric heat power density has been applied to the entire model, properly considering the Eurofer, Tungsten, PbLi, and water contribution, drawn from [15] and reported in Figure 11.  
* Imposed temperature on the water manifolds: Because the water manifolds region is currently in a design phase and, in this configuration, does not allow the DWTs to be properly housed, a uniform temperature equal to 315 \({}^{\circ}\)C has been set directly derived from the thermal analysis of that poloidal COB region [9]. * Convective heat transfer between cooling water and cooling channels and DWTs: A forced convective heat transfer condition between coolant and internal surfaces of both FW-SWs cooling channels and DWTs has been imposed. In order to reproduce the coolant flow, the \"thermal fluids\" approach, available in the Ansys Steady-State Thermal module, has been adopted. The coolant flow direction has been properly modelled considering the counter-current flow of the cooling channels and the flow path, comprehensive of the recirculation system, of the DWTs water. Thanks to this approach, it is possible to model the fluid flowing within each channel and/or tube by means of a 1-D body, which is discretised and coupled to the nodes of the channel/tube surfaces by means of a convective boundary condition. Therefore, the fluid mass flow per unit area, the Heat Transfer Coefficient (HTC) and the bulk inlet temperature are assigned to each thermal fluid and the bulk temperature profile along the line is calculated and used for the convective boundary condition application. A first attempt value of mass flow rate, derived from [9], has been considered, and the corresponding HTC value has been calculated by means of Dittus & Boelter correlation, considering a water temperature difference (\(\Delta\)T) between inlet and outlet of 33 \({}^{\circ}\)C. The final HTC and mass flow rate values ensuring the imposed \(\Delta\)T have been calculated by means of an iterative approach.