# Influence of Micro-Textures on Cutting Insert Heat Dissipation
## 2 System Design and Implementation
### Numeric Study
The thermal conductance final values between the top chamber (5), and the cutting insert (3) of 67,467 W/m\({}^{2}\).K, between the heat sources (6) and the cutting insert (3) of 6325 W/m\({}^{2}\).K, and 20,240 W/m\({}^{2}\).K between the cutting insert (3) and the support seat (2). The remaining values were kept unchanged. The polyhedron mesh of 2,448,604 elements is shown in Figure 2. This was initially generated in Ansys Workbench as tetrahedron mesh and later converted using Fluent tools. A convergence study was carried out to define the proper mesh size. Five inflation layers were specified to properly describe the thermal and flow boundary condition effects. Numerical simulations were conducted for a steady regime by considering the previously described mesh and values of convection coefficients and thermal conductance, and the mass density and thermal properties values of the materials presented in Table 1. A constant mass flow rate of 15.6 g/s of water was considered for all the simulations. Figure 3 presents the temperature distribution of the cross-section and internal fluid flow lines, for the steady-state condition. In the cross-section is observed that the temperature of the cutting insert is lower than the heat sources, which is justified by the contact resistance and heat transfer to the fluid. The flow lines analysis also reveals a uniform path distribution over the top surface of the insert, as well as an increase in the fluid temperature from inlet to outlet. Figure 2: The model with polyhedron mesh, use in numerical simulations. The quantification of the heat transfer rate from the insert top surface to the fluid can be determined by measuring the fluid temperature differences between the inlet and outlet channels. However, the fluid temperature is not the same along the channels and, thus, the accuracy of the results strongly depends on the locations of the measurements. The position selection is not straightforward, since the stabilization of the fluid temperature tends to occur far from the cutting insert, see Figure 1, where the influence of heat transfer from the top chamber to fluid is more prevalent. Therefore, the selection of the best locations will result from the balance between the minimum distance to the cutting insert and the region where is achieved a reasonable fluid temperature stabilization. These were found by analyzing the fluid temperatures in the numerical model, being the most suitable locations for measuring the inlet (T1) and outlet (T2) temperatures identify in Figure 4.  
Figure 4: The best locations for measuring the fluid inlet and outlet temperatures. Figure 3: Temperature representation for steady-state condition: (**a**) model cross-section; (**b**) fluid flow lines. Assuming a constant heat input power, a steady-state mass flow rate, a negligent kinetic and potential energies, and the work interaction, the heat transfer rate \(\dot{Q}\) can be given by [40],  
\[\dot{Q}=\dot{m}.c_{p}.\Delta T\ \ \ \ \ [W] \tag{1}\]  
where \(\dot{m}\) is the mass flow rate in [kg/s], \(c_{p}\) is the specific heat at constant pressure in [J/kg.K], and \(\Delta T\) is the temperature gradient, between the inlet T1 and outlet T2 express in [K]. The water mass density and thermal properties defined for numerical simulations were the following: mass density of 998.2 kg/m\({}^{3}\), specific heat of 4187 J/kg.K, thermal conductivity of 0.6 W/m.K, and dynamic viscosity of 0.001 kg/m.s. From the numerical simulations and by considering four input power levels, the heat transfer rate was determined. This involves the measurement of the inlet and outlet fluid temperatures at locations identified in Figure 4 and the application of Equation (1). The measured temperatures, the mass flow rate, and the correspondent heat transfer rate for the input power of 100, 200, 300, and 400 W are presented in Table 2.  
The values in Table 2 show a linear trend between heat transfer rate and the input power.