# Design of Novel Cooling Systems Based on Metal Plates with Channels of Shapes Inspired by Nature
## 4 Results and Discussion
### Heat Transfer
#### 4.2.2 Steady State Heat Transfer  
Heat transfer was also evaluated for all configurations under steady state conditions, considering a total power input \(q_{\text{in}}\) uniformly distributed across the plate. The total heat rate input was varied from 0 to 200 W and the steady state temperature distribution for each shape of the channel was determined. The plate was assumed to be initially at ambient temperature, i.e., 25 \({}^{\circ}\)C, and the temperature of all points of the plates was calculated as time progressed until a steady state temperature distribution was reached. The temperature distribution of the plate for various thermal power inputs, from 25 to 200 W in intervals of 25 W, is depicted in Figure 8 for each configuration. Obviously, the temperature of the plate is proportional to the thermal power input for all configurations, as can be anticipated in view of Equation (1). However, both the temperature distributions and their values vary substantially among the different configurations of the channel considered. The square configuration shows a great zone of high temperature at the center of the plate, whereas the fork shape channel induces the appearance of the maximum temperature at the corner of the plate at the side where the inlet and outlet of the channel are located. Regarding the novel configurations, the crateriform configuration is characterized by the presence of small zones of high temperature at the center and the four corners of the plate, while the salverform configuration shows a maximum temperature zone at the center of the plate, similar, although smaller, in extension compared to the high temperature regions of the square configuration. In contrast to the rest of configurations, the cruciform shape shows a more homogeneous distribution of temperature across the plate, avoiding the presence of hot spots in the plate. The temperature distribution maps obtained for steady state cooling conditions resemble again the contour maps of distance to the channel reported in Figure 4. Thus, the geometrical analysis can be used as a first design tool to determine optimal configurations of channels for heat transfer applications. Figure 7: Time evolution of the reduction in maximum temperature attained by the novel configurations (nc) respect to the common configurations (cc). The evolution of the mean and maximum temperatures of the plate with the heat rate input can be observed in Figure 9. Both the average and the maximum temperature of the plate present a linear increase with the thermal power input for all configurations, as expected in view of Equation (1). The highest average temperature was obtained for the square shape channel due to the large zone of high temperature at the center of the plate. Figure 8: Evolution of the temperature distribution across the plate with the thermal power input under steady state conditions. Among the novel configurations proposed, the highest average temperature was obtained for the crateriform configuration, whereas the lowest values were attained for the cruciform configuration, in agreement with the results obtained from the geometrical analysis of the different channel shapes. In fact, the increase in the average temperature of the plate over the ambient temperature can be reduced by 6.5% using the cruciform configuration compared to the squared channel plate. Concerning the maximum temperature of the plate, even though the maximum distance to the channel was the same for the square and the fork shape configurations, the maximum temperature attained in the plate under steady state conditions was slightly higher for the square shape channel than for the fork configuration, confirming again the importance of the extension of the region of maximum distance to the channel.