## 3 Numerical Model of the Data Center  
The geometric model was developed taking into account the characteristics of the computational processing in order to avoid complications during the developed simulations. Thus, the three-dimensional geometry was simplified to avoid that the mesh generated by the software being very refined. To achieve this, the server racks are represented as parallelepipeds, and the cables, rails, access doors and fixtures have been concealed to facilitate the construction of the mesh. In the case of lamps, these were concealed not only by the complexity they would generate in the developed mesh, but also because they were disconnected during the operation of the ICT room, generating no heat production. Figure 1 shows the three-dimensional geometry developed for the present study. The computational mesh is composed of control volumes so that the equations of continuity, momentum and energy, presented in Section 2, could be solved. A mesh that has high quality is very important for the accomplishment of the simulations proposed in this paper, because this is fundamental for the numerical solution to converge and so that the achieved results are consistent and trustworthy. The resulting mesh consists of tetrahedral (cold corridors) and hexahedral (hot corridors and server racks) elements. This solution was adopted because the mesh would have a high number of control volumes if a mesh composed of only one type of elements were used. Additionally, as the air flow changes from horizontal direction when crossing the racks to vertical direction when going through the air outlet vent areas, the use of tetrahedral elements is required to reduce false mathematical diffusion and thus improve the accuracy of the numerical predictions. Figure 2 shows the mesh resulting from the study in an isometric perspective. Table 1 presents the characteristics of the computational mesh. The mesh density is an important metric and it is utilized for controlling accuracy and a high-density mesh delivers results with high accuracy. The meshes creation was an iterative process as its quality plays a significant role in the accuracy and stability of the numerical computation. The attributes associated with mesh quality are node point distribution, smoothness, and skewness. The quality of the mesh elements was assessed during the meshes creation in order to balance the results accuracy with the computational cost and simulation time. Three key parameters were analyzed to measure the mesh quality: aspect ratio, skewness and orthogonal quality. The aspect ratio is a measure of the stretching of a cell. It is computed as the ratio of the largest and smallest dimensions of the edges of the faces of the control volume. A good aspect ratio has a value close to one. Skewness is defined as the difference between the shape of the cell and the shape of an equilateral cell of equivalent volume. \begin{table}
\begin{tabular}{c c} \hline \hline
**Constants** & **Values** \\ \hline Nodes & 1,183,613 \\ Number of Control Volumes & 2,341,172 \\ Aspect Ratio & 1.645 \\ Skewness & 0.177 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the generated computational mesh. Figure 1: The representation of three-dimensional geometry developed for the present study. Figure 2: The representation computational mesh in an isometric perspective. The mesh quality improves as skewness value approaches the null value. The orthogonal quality for cells is computed using the face normal vector, the vector from the cell centroid to the centroid of each of the adjacent cells, and the vector from the cell centroid to each of the faces. The orthogonal quality for a cell is computed as the minimum of these quantities. The mesh quality increases as the value of orthogonal quality is towards unity. Several computational meshes were created until the size of mesh elements provided a good aspect ratio, a small skewness and a good orthogonal quality, ensuring a good relation between the computational cost and the accuracy of the results.