Multi-objective constructal design of a printed circuit cooler for S-CO₂ cycle

A printed circuit cooler for S-CO₂ cycle is optimized by constructal design. First of all, a complex function composed of pumping power consumption and entropy generation rate is optimized. Volumes of cooler and heat transfer channel are fixed, which are used to achieve optimal heat transfer channel radius and minimal complex function. The optimized structural design of the cooler reduces overall pumping power consumption and complex function by 23.96% and 5.70%, respectively, and e entropy generation rate is increased by 12.55%. There is an optimal number of plate layers that can yield a bi-minimum complex function. Secondly, the NSGA-II is used for multi-objective optimization (MOO), dense distribution of optimal channel radius ( \(R_{{{\text{Rh}},{\text{opt}}}}\) $R_{\text{Rh},\text{opt}}$ ) is between 0.8 and 1.0 mm, whereas that of optimal plate layer number ( \(N_{{{\text{c}},{\text{opt}}}}\) $N_{\text{c},\text{opt}}$ ) is between 100 and 160. The smallest deviation index obtained by LINMAP or TOPSIS decision-making method is 0.088. In this case, \(R_{{{\text{Rh}},{\text{opt}}}}\) $R_{\text{Rh},\text{opt}}$ and \(N_{{{\text{c}},{\text{opt}}}}\) $N_{\text{c},\text{opt}}$ are \(1.0\;{\text{mm}}\) $1.0\text{mm}$ and 144, respectively. This result can be considered the best alternative for MOO design scheme of printed circuit cooler with the objectives of entropy generation rate and overall pumping power consumption. Theoretical guidance for structure designs of printed circuit coolers can be served from constructal optimization results obtained herein.