**4. Results**

The results for different temperatures of the aluminium sample selected in the experiment are described below, which were at 50 ◦C and one at 175 ◦C and the behaviour at an HST of 600 ◦C. It is because the heater that was acquired reaches a maximum operating temperature value of 600 ◦C. Only the points where the thermocouples are located were compared, both in copper and aluminium bars. The tables include material properties and initial conditions applied to the model of the finite element method. Also, this work shows a comparison of the results obtained in the simulation using ANSYS and the data acquired experimentally [13,14].

#### *4.1. 2d and 3d Analysis at a Temperature of* 150 ◦*C*

In Table 1 appears the boundary conditions applied for the 150 ◦C test. Also, in that table the material properties were introduced in the simulation the values, like 214.4 W/mK for aluminium, 386 W/mK for copper and 0.044 W/mK for fibreglass. The values for temperature loads used in the model in ANSYS were 279.5 ◦C for the hot source and 20 ◦C for the cold source.


**Table 1.** Boundary conditions applied for *TBAR* = 150 ◦C.

Figure 5 shows the results obtained for the 150 ◦C test in the 2D model. In the distribution of temperature, it can be seen where the hot source, in red colour, and the cold source, in blue colour, are, in Figure 5a, the path begins with the origin and 289.6 ◦C on the coordinate axis, which corresponds to the point located in the hot source. The graphic represents the vertical line, where the model presents symmetry [15]. The graph in Figure 5b points out three slope changes, indicating the two types of materials since their thermal conductivities are different. Then the first slope from left to right is equal as the third slope since they are the same material and therefore have the same thermal conductivity value.

**Figure 5.** Results for 2D analysis at a test temperature of 150 ◦C. (**a**) temperature distribution in ◦C. (**b**) graphic of temperatures of the symmetry line.

The results of using a 3D model with azimuthal symmetry are illustrated in Figure 6; the differences are notorious compared with the temperature distribution image concerning the 2D model. In the graph, the changes are smoother; however, changes in the slopes are more defined. Also, we can see the point where contact exists in each metallic bar [16].

**Figure 6.** Results for 3D analysis at a test temperature of 150 ◦C. (**a**) Temperature distribution in ◦C. (**b**) Graphic of temperatures of the symmetry line.

In Figure 6b it can be observing a better definition of slope change between each bar. Even with that inflection point in the graphs, it can be obtained the temperature reached the junction of each bar. The transition between the boundary of each material is due to in analysis 2D, the interface is a line, but in 3D analysis, there are two surfaces, so in this case, ANSYS take in account radial heat transfer through surfaces.

However, Figure 7 shows the graph where the results are compared between 2D, 3D models, and the points that represent the thermocouples where experimentally are located in the metallic bars. The deviations are more significant near the borders, where the cold and hot sources are located. From the 2D and 3D simulations performed, the temperature values were extracted at the points where the thermocouples are experimentally located. The differences between these values were calculated to obtain the maximum and the minimum deviation between the results obtained from the simulation and the experiment. Therefore, the most substantial variance was around 20 ◦C, and the lowest was 1.6 ◦C.

**Figure 7.** Comparison of results for 2D, 3D and experimental analysis at a test temperature of 150 ◦C in thermocouple positions.

#### *4.2. 2d and 3d Analysis at a Temperature of* 175 ◦*C*

The boundary conditions applied for the 175 ◦C test are shown in Table 2.


**Table 2.** Boundary conditions applied for *TBAR*= 175 ◦C.

Figure 8 indicates the results obtained for the 175 ◦C test in the 2D model. In the temperature distribution, it is possible to observe where the hot source, in red, and the cold source, in blue, whose gradients are very similar to the test temperature at 150 ◦C. Figure 8b shows a graph where begins with the origin and 339 ◦C on the ordinates axis, which corresponds to the point where the hot source is, which represents a maximum temperature reached by the hot source. The graph describes the vertical line where the model presents symmetry. The graph represents the nodes that are on the vertical line of symmetry of the model. As in the previous case, it points out three slopes because there are two section changes, in this case, the slopes are of higher value because the operating temperature for the heater was higher than in the previous case.

**Figure 8.** Results for 2D analysis at a test temperature of 175 ◦C. (**a**) temperature distribution in ◦C. (**b**) graphic of temperatures of the symmetry line.

Figure 9 indicates the results of using a 3D model with azimuthal symmetry. The differences are notoriously comparing the temperature distribution image concerning the 2D model. In the graph, the changes are smoother, showing the variation of the section between the copper reference bar and the aluminium test. The changes are due to the temperature gradient and the different values of the thermal conductivity of each bar [17,18]. In this case and the previous one, the deviations concerning the experimental results are more significant near the cold source, and, in both comparisons for the case of the hot source, the finite element method predicts and for the cold source sub predicts the actual values according to those obtained in the experiment, which means that heat leaks are present.

**Figure 9.** Results for 3D analysis at a test temperature of 175 ◦C. (**a**) Temperature distribution in ◦C. (**b**) Graphic of temperatures of the symmetry line.

However, Figure 10 shows a result comparison between 2D, 3D models, and the experiment. Where the deviations are more significant near the borders, where the cold and hot source are located. Because in that zones exists the most more significant gradients with the surroundings, because temperature laboratory is 22 ◦C. The most significant deviation for this case was around 37 ◦C and less than 7 ◦C.

**Figure 10.** Comparison of results for 2D, 3D and experimental analysis at a test temperature of 175 ◦C in thermocouple positions.

#### *4.3. 2D and 3D Analysis at a Temperature of 310* ◦*C*

Because a new heater was purchased, which operates at a maximum temperature of 600 ◦C, it is essential to know the temperature that the aluminium bar reaches, and by consequently evaluate if the conditions of the equipment are adequate to this new working temperature [19]. In Table 3 appears the boundary conditions applied for the 310 ◦C test, where it is observed that the maximum temperature reached by the new heater at 600 ◦C.

**Table 3.** Boundary conditions applied for *TBAR* = 310 ◦C.


Figure 11 indicates the results obtained for the 310 ◦C test in the 2D model. In the distribution of temperature, it is possible to observe the hot source, in red, and the cold source, in blue, whose gradients are equal to the test temperature at 150 ◦C. However, the values of temperature in each zone are higher than the last case. In Figure 11b, the graph begins with the origin and 600 ◦C on the ordinate axis, which corresponds to the point located in the hot source as we can see slopes are greater than the last case because the temperature is higher. The graph represents the vertical line where the model presents symmetry.

**Figure 11.** Results for 2D analysis at a test temperature of 310 ◦C. (**a**) Temperature distribution in ◦C. (**b**) Graphic of temperatures of the symmetry line.

Figure 12 indicates the results from the 3D model with azimuthal symmetry. The differences are notorious by comparing the temperature distribution image concerning the 2D model. The graph points out the temperature reached by the sample aluminium bar is 310 ◦C. Ideally, the temperature of the sample bar reached with the new heater.

**Figure 12.** Results for 3D analysis at a test temperature of 310 ◦C. (**a**) Temperature distribution in ◦C. (**b**) Graphic of temperatures of the symmetry line.

However, the Figure 13 shows the comparison between 2D and 3D models. It was found the maximum difference is 40 ◦C, and the minimum is 0.6 ◦C in the two analyses. In this case, there is no experimental evaluation, because with the information obtained in this work, it is possible to evaluate if it is necessary to make modifications to the existing bar system to implement the new heater, due to the temperature reached in the system that includes the bars and the insulator [20,21].

**Figure 13.** Comparison of results for 2D and 3D at a test temperature of 310 ◦C in thermocouple positions.

### **5. Discussion and Conclusions**
