## 4 Description of the Modeled Case Studies  
In this section, we present the parametric studies performed by changing different parameters that allowed the analysis of a good operation of an ICT room. For this analysis, the temperatures of the server racks and the hot aisles were studied, as well as the airflow in the ICT room. The investigated parametric studies differed among them, due to the variation of the thermal load of the server racks. Four case studies with different thermal loads were studied.  
Cases 1 and 2 represent a usual thermal load distribution in the data center, especially Case 2. This objective was to have a study that closely resembles the reality of the operation of the server racks located in the data center. Meanwhile, Cases 3 and 4 represent a more academic approach. The thermal is not usually constant throughout the row since the servers do not usually operate at the same level of thermal load. However, the values of the thermal load in Cases 3 and 4 are close to the reality since these servers do not usually operate at maximum performance.  
Each thermal load was simulated with the maximum and minimum air flow velocity. The dimensionless values are identified with a subscript \"adm\". Figure 3 shows the upper plan view of the TI room, where the numbering corresponds to the server rack number, ranging from 1 to 208. In this figure, it is also possible to observe the hot aisle/cold aisle configuration of the data center. The smaller extraction aisle, mentioned in Table 3 and seen in Figure 3, is the one of the ranging racks from 181 until 208.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Magnitude** & **Relaxation Factor** \\ \hline Density & 0.3 \\ Pressure & 1 \\ Body Forces & 1 \\ Amount of movement & 0.7 \\ Turbulent kinetic energy & 0.8 \\ Turbulent dissipation rate & 0.8 \\ Turbulent Viscosity & 1 \\ Energy & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The relaxation factors applied to the numerical methods.  
In all four case studies addressed in this study, a dimensionless thermal load was used, \(q_{ahn}\). In Case 1, different thermal loads imposed at the boundary conditions of the heat flow were applied symmetrically to every row of all server racks, as shown in Figure 4a. The thermal load is as follows: at the end of the rows of the server racks, 90% of the maximum thermal load was applied, while 70% of the maximum thermal load and 50% of the central racks were imposed on the intermediate server racks. For each case, the maximum and minimum air flow velocity was applied, simulated and studied. The purpose was to observe the behavior of the temperature and air flow in the room. To better understand how the loads were applied along the rows, a single row of server racks is shown in Figure 4 for each of the four case studies, where each color represents a value of the thermal load.  
Figure 4: The thermal load of the racks according to every case study.  
Figure 3: The representation of upper plan view of the data center room.  
Case 2 is similar to Case 1. However, in this case study, the thermal load applied on the end of the server racks is exchanged with the one of the central server racks, that is, the central server racks had a maximum heat load of 90% and the end server racks dissipated 50% of the maximum heat load. For Case 3, the thermal load applied was 75% of the maximum thermal load in the heat flow frontier condition, \(q\). It was applied equally in every server rack, for the maximum and minimum velocity of the air flow. Finally, Case 4 is similar to Case 3, the difference being only the applied thermal load, which in this case was equal to the measured and nominal load value of the data center room.