# Design of Novel Cooling Systems Based on Metal Plates with Channels of Shapes Inspired by Nature
###### Abstract  
The effect of the channel shape of aluminum plates on cooling capacity was evaluated by studying different configurations. Common shapes of the channel, such as square and fork shapes, were compared with novel configurations inspired by shapes found in nature, specifically the shape of the outline of flowers, inspired these new configurations, consisting of channels with crateriform, salverform, and cruciform shapes. The aim of the study is to evaluate the effect of the channel shape on the cooling capacity of the metal plate. To that end, all the configurations were analyzed from a geometrical point of view, determining the minimum distance of each point across the plate to the channel. A finite difference method was implemented to study both transient and steady state heat dissipation across the plates for each configuration. Even though the effect of the channel shape on the average temperature of the plate is slight, the maximum temperature, the size and location of hot spots, and the temperature homogeneity of the plate are strongly affected by the shape of the channel through which the cooling fluid is circulated. A reduction in the maximum temperature of the plate during transient cooling of around 2 \({}^{\circ}\)C for the crateriform and salverform channels and approximately 4.5 \({}^{\circ}\)C for the cruciform channel can be attained, compared to the standard configurations. The steady state heat dissipation analysis concluded that the crateriform and salverform configurations reduced the maximum variation in temperature of the common configurations by roughly 15%, whereas a reduction of approximately 28% could be reached by the cruciform configuration. Regarding the homogeneity of temperature across the plate, a reduction up to 34.5% of the index of uniform temperature can be attained using the novel configurations during the steady state refrigeration of the plate. The cruciform channel is the optimal configuration for both transient and steady state cooling processes, reducing the size and temperature of hot spots and improving the temperature homogeneity of the plate, a result already anticipated by the geometrical analysis. In fact, the main conclusions attained from the cooling study are in good agreement with the results of the geometrical analysis. Therefore, the geometrical analysis was found to be a simple and reliable method to design the shape of channels of a cooling system. champel shape; cooling system; finite difference method; geometrical analysis; heat transfer; metal plates; temperature distribution +
Footnote †: journal: Applied  
Accepted: 22 March 2022  
device to the heat sink occurs by conduction and is transferred to the environment by natural, mixed or forced convection by means of extended surfaces or fins with various geometrical designs. The tendency to minimize the size of electronic devices implies a greater difficulty for the fluid to circulate between the fins of the heat sink. Thus, this configuration may be inefficient for dissipating all the necessary heat, which in many cases can cause irreparable damage to the devices generating heat during operation or an efficiency reduction of these elements that may not accomplish the requirements of miniaturization of electronic components [3]. As an alternative, cooling systems based on forced convection by circulation of a cooling liquid through a channel are widely used due to an improved heat dissipation capacity. Depending on the size of the conduits through which the cooling fluid circulates, the channels of the cooling systems are categorized as microchannels, minichannels, or simply channels. For the former, the hydraulic diameter of the channels ranges between 10 and 200 \(\upmu\)m [4], the second accounts for channels with hydraulic diameters of 200-3000 \(\upmu\)m [5], whereas the latter presents hydraulic diameters above 3 mm.