# Design of Novel Cooling Systems Based on Metal Plates with Channels of Shapes Inspired by Nature
## 4 Results and Discussion
### Geometrical Analysis  
All configurations were analyzed from a purely geometrical point of view by calculating the minimum distance of each point of the plate to the channel considering a 2D domain. A grid of 338 \(\times\) 338 points was built on the 2D domain of the plate and the minimum distance from each point to the cooling channel was computed. Contour plots of the distance from each point across the plate to the channel are depicted in Figure 4 for all the configurations studied. The square shape configuration presents the maximum distance to the channel for points located at the center of the plate, whereas for the fork  
Figure 3: Top view of a section of half plate for the novel configurations for cooling systems based on flower outlines: crateriform (**left**), salverform (**center**), and cruciform (**right**) shapes of channels. Figure 2: Top view of a section of half plate for the common configuration for cooling systems: square (**left**) and fork (**right**) shapes of channels. shape configuration the maximum distances are found at the corners placed at the side where the inlet and outlet of the channel are situated. The maximum distance obtained for both standard configurations is similar; however, using fork shape channels results in a more homogeneous distribution of the distance across the plate compared to a square shape configuration. All the novel configurations proposed, based on the outline of flowers, result in lower maximum distances to the channel. The crateriform configuration shows maximum distances to the channel at the four corners and the center of the plate, while the maximum distances appear at the center of the plate for the salverform channel. Among all configurations, the cruciform channel minimizes the distances for all points of the plate to the channel, reducing the maximum value and inducing a more homogeneous distance to the channel across the whole plate compared to the rest of configurations considered. The main characteristic parameters of the distribution of distances from all points across the plate to the channel for each configuration, including the maximum distance \(r_{\text{max}}\), the average distance \(r_{\text{m}}\), and the standard deviation of the distance \(\sigma_{r}\), are reported in Table 1. The maximum distance of the common configurations, i.e., square and fork shape channels, coincides, obtaining a significant reduction of this parameter for all the novel configurations proposed. This substantial reduction in the maximum distance to the channel is very relevant for a heat transfer application since the maximum temperature of the plate will be proportional to this distance due to the proportionality of the heat rate by conduction through the solid with the distance. Regarding the average distance of all points of the plate to the channel, the highest value was obtained for the square configuration, whereas in the case of the fork shape channel, the average distance is lower. Thus, even though the maximum distances of the square and fork configurations are similar, the average distance is higher for the square shape channel due to the larger region of points with high distance to the channel close to the center of the plate in this case. The average distance for the crateriform configuration is even larger than that of the fork shape channel, although the maximum distance is lower for the former configuration. The salverform channel leads to a similar value of the average distance to the fork shape configuration, whereas this value is lower for the cruciform channel. The homogeneity of the distribution of distances to the channel across the whole plate can be analyzed based on the standard deviation of the distance \(\sigma_{r}\). The less uniform distribution of distances to the channel corresponds to the square configuration, for which the standard deviation of the distance is  
Figure 4: Distribution of minimum distance to the channel for all configurations. maximum.