Investigation on the Association of Differential Evolution and Constructal Design for Geometric Optimization of Double Y-Shaped Cooling Cavities Inserted into Walls with Heat Generation

Featured Application A new complex geometry cavity is optimized by associating the constructal design (CD) method with the differential evolution (DE) algorithm. Statistical analyses are performed to indicate the best parameters of the meta-heuristic to be applied during the optimization process. Kruskal-Wallis and Dunn's statistical tests were applied to investigate the DE algorithm and its parameters to reproduce the effects of design on the thermal performance of a cooling cavity inserted into a wall with heat generation. Results demonstrated the best parameters of the metaheuristic that improve the algorithm's performance in the geometric optimization process. In the constructal design method, the comprehension of the effect of design on the system performance is crucial to understanding the contributions of the degrees of freedom or constraints in the system evolution in direction of optimal configurations. However, problems with many degrees of freedom are prohibitive of optimization with exhaustive search, requiring meta-heuristic strategies. Therefore, the investigation of the optimization algorithms is essential. This work investigates the canonical differential evolution algorithm associated with the constructal design for the geometric optimization of an isothermal double Y-shaped cooling cavity inserted into a wall with internal heat generation. The effect of four degrees of freedom over the thermal performance of the system is investigated using sixteen different combinations of differential evolution algorithms: four variations of mutation parameter, two values of amplification factor (F) and two values of crossover rate (CR). The non-parametric statistical methods of Kruskal-Wallis and Dunn test were used to identify the parameters that improve the meta-heuristic efficiency. Results indicated that the proposed methodology selected the proper combination of DE algorithm parameters (CR, F, and mutation) that led to the best effect of degrees of freedom over the thermal performance in all optimization levels investigated.