# Design of Novel Cooling Systems Based on Metal Plates with Channels of Shapes Inspired by Nature
## 5 Conclusions  
The performance of a cooling system consisting of an aluminum plate with an interior channel through which cold water flows was numerically evaluated. Various shapes of the channel were tested, comparing commonly used shapes such as square or fork-alike channels with novel configurations inspired by nature, specifically by the outline of flowers: crateriform, salverform, and cruciform channels. The inlet and outlet location, diameter, and length of the channel were the same for all configurations, so that the effect of the channel shape from a thermal point of view could be quantified by direct comparison of the results obtained for each case. A geometrical analysis of the configurations, based on calculating the minimum distance of all points across the plate to the channel, was carried out. The geometrical analysis concluded that the maximum distance to the channel of the standard configurations, i.e., square and fork channels, coincided and was substantially reduced for the novel configurations. Among all configurations tested, the cruciform channel constitutes the optimum configuration in terms of the minimum distance of the points of the plate to the channel. The cooling capacity of each configuration was quantified based on a finite differences approach that solves the diffusion equation in the plate, considered as a 2D domain. Transient cooling was studied, assuming a high initial temperature of the plate and heat was dissipated to both ambient air at the external surfaces of the plate and flowing cold water at the surface of the channel. The time evolution of the maximum temperature of the plate showed that the cooling capacity was improved by the proposed novel configurations with regard to the standard shapes of the channel. Even though the time evolution of the average plate temperature was only slightly affected by the channel shape, the maximum temperature 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 during transient cooling. This maximum temperature reduction reached by the crateriform and salverform channels corresponds to roughly 6.6%, while for the cruciform channel a reduction of around 15% was attained. In addition, the sizes of the hot spots located across the plate during transient refrigeration were substantially reduced when using novel configurations with channel shapes based on the outline of flowers, especially for the cruciform configuration. Therefore, the novel configurations tested showed a significant effect on the hot spots and the homogeneity of temperature across the cooling plate. Steady state heat dissipation was also analyzed, considering a uniform thermal input across the plates. In this case, both the maximum temperature attained by each configuration and the extension of the high temperature regions were considered by an index of uniform temperature. Again, the effect of the channel shape on the average temperature of the plate during steady state refrigeration was slight. However, the plate temperature homogeneity and the presence of hot spots is strongly affected by the shape of the channels through which the cooling fluid is circulated. These effects were quantified by calculating the average dimensionless temperature and the index of uniform temperature, obtaining  
Figure 10: (**a**) Maximum variation in temperature and (**b**) Index of Uniform Temperature (IUT) for each configuration as a function of the thermal power input. reductions in the average dimensionless temperature of 9.8, 11.3, and 21.1% using the salverform, crateriform, and cruciform channels compared to the common configurations, respectively. Regarding the index of uniform temperature, a maximum reduction of 34.5% can be attained by the cruciform configuration compared to the square channel plate, confirming the increased homogeneity of the plate temperature for this novel configuration.