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This work relies on constructal design to perform the geometric optimization of the V-shaped pathways of highly conductive materials (inserts) that remove a constant heat generation rate from a body and deliver it to isothermal heat sinks. It is shown numerically that the global thermal resistance of the V-shaped pathway can be minimized by geometric optimization subject to total volume and V-shaped pathways material constraints. Constructal design and genetic algorithm (GA) optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly of pathways and optimal geometry features for the V-shaped pathway. Parametric study was performed to show the behavior of the minimized global thermal resistance as function of the volume fraction of the V-shaped pathways. First achieved results for ϕ = 0.3 indicated that when freedom is given to the geometry, the thermal performance is improved. Afterward, the employment of GA with constructal design allowed the achievement of the optimal shapes of V-shaped pathways for different volume fractions (0.2 ≤ ϕ ≤ 0.4). It was not realized the occurrence of one universal optimal shape for the several values of ϕ investigated, i.e., the optimal design was dependent on the degrees of freedom and the parameter ϕ and it is reached according to constructal principle of optimal distribution of imperfections.

Abstract The SA (Simulated Annealing) is a meta-heuristic to combinatorial and optimization problems. The main purpose here is to investigate several cooling schedules (main parameter of SA) combined with Constructal Design for geometric optimization of an isothermal Y-shaped cavity intruded into a solid conducting wall with internal heat generation. This shape was optimized with Exhaustive Search and Genetic Algorithm in previous studies of literature. The problem has four degrees of freedom ( H / L , L 1 / L 0 , t 1 / t 0 , α) and two constraints: the cavity and auxiliary fraction cavity areas (ϕ and ψ). Five different cooling schedules are evaluated: Fast, Exponential, Boltz, BoltzExp and ConstExp1. The first three methods are default, while the others are hybrid proposed here. Firstly, it is evaluated the percentage of simulations in which the global optimal point is achieved for the case with square solid wall. Algorithms hybrid and Fast lead to the highest and lowest reliabilities to find global optimal geometries. Posteriorly, a complete optimization of the Y-shaped cavity evaluating the effect of constraints ϕ and ψ over four times optimized Y-shaped cavity are performed. Results are compared with those previously obtained with GA (Genetic Algorithm). The combination of the best cooling schedules improves even more the achievement of the global optimal shapes.