# Design of Novel Cooling Systems Based on Metal Plates with Channels of Shapes Inspired by Nature
## 4 Results and Discussion
### Heat Transfer
#### 4.2.1 Transient Heat Transfer
Higher variations between different configurations were observed for the evolution of the maximum temperature of the plate, as predicted by the geometrical analysis of the configurations. The evolution of the maximum temperature for square and fork shape channel almost collapse, obtaining the highest values among all configurations. This is also in accordance with the geometrical analysis, in which both configurations presented the same maximum distance to the channel, which is higher compared to that of the novel configurations proposed, as reported in Table 1. Lower values for the maximum temperature of the plate were obtained for the crateriform and salverform channels compared to the standard configurations with square and fork shape channels. Even though the maximum distance to the channel was higher for the crateriform than for the salverform configuration, the time evolution of the maximum temperature obtained for crateriform and salverform channels is very similar. This may be attributed to the larger extension of the zone with large distance to the channel at the center of the salverform configuration, from which the dissipation of heat to the channel could be slower than from the smaller regions of high distance to the channel of the crateriform configuration located at the center and corners of the plate. The lowest maximum temperature of the plate was found for the cruciform channel, which is the best configuration among those studied in this work, as previously concluded from the geometrical analysis. Considering the time evolution of the maximum temperature of the plate during the cooling process shown in Figure 6, the novel configurations proposed, i.e., crateriform, salverform, and cruciform channels, improves the performance of the standard configurations, i.e., square and fork shape channels, during transient heat transfer. To quantify the speed of the cooling process, the time required to attain the mean temperature between the initial and final temperature of the plate, i.e., a temperature of 40 \({}^{\circ}\)C, was determined. A similar value was required for the square and fork configurations, with values of 21.8 and 21.5 s, respectively. The time required to reduce the maximum temperature of the plate to 40 \({}^{\circ}\)C was decreased to 19.3 and 19.0 s when using the salverform and crateriform configurations, respectively. Among all the configurations studied, the fastest reduction in the maximum temperature of the plate was found for the cruciform configuration, requiring a time of only 16.3 s. Thus, a maximum reduction in the time required to reduce the maximum temperature of the plate from 55 \({}^{\circ}\)C to 40 \({}^{\circ}\)C of 25.4% was attained using the cruciform configuration. Figure 6: Time evolution of the (**a**) average and (**b**) maximum temperature of the plate for all configurations. The maximum temperature of the plate can also be reduced using the novel configurations proposed compared to the standard configurations. This reduction in the maximum temperature was quantified by calculating the reduction in maximum temperature attained from each of the novel configurations with respect to the average of the usual configurations. Figure 7 shows the time evolution of the maximum temperature reduction attained by the novel configurations. The maximum temperature obtained during transient cooling of the plates can be reduced up to 2 \({}^{\circ}\)C by the crateriform and salverform configurations and up to 4.5 \({}^{\circ}\)C by the cruciform configuration. This temperature reductions are remarkable considering that the plate is initially heated up to only 55 \({}^{\circ}\)C, that is, only 30 \({}^{\circ}\)C above ambient temperature. Therefore, the maximum temperature reduction reached by the crateriform and salverform channels is around 6.6%, while for the cruciform channel it is approximately 15%. It should be noticed that this reduction is attributed only to the difference in shape of the channel since the length and diameter of the channel is the same for all configurations.