Constructal Design of Conductive Asymmetric Tri-Forked Pathways

This work relies on the constructal design method associated with exhaustive search and genetic algorithms to perform geometric optimization of an asymmetric tri-forked pathway of highly conductive materials (inserts) that remove a constant heat flux from a body and deliver it to three isothermal heat sinks. It is shown numerically that the global thermal resistance, represented by the maximum excess of temperature, can be minimized by means of geometric evaluation subject to two constraints, the total rectangular area where the forked pathway is circumscribed and the tri-forked pathway area, and seven degrees of freedom. A parametric study is performed to show the influence of the degrees of freedom over the global thermal resistance. The optimal geometry was obtained for a 40% area fraction, leading to a maximum excess temperature seven-times minimized with a thermal performance 627% better than a once optimized architecture, showing the importance of the design for thermal performance. For higher values of aspect ratio, height/length, the optimal configuration is highly asymmetrical, while for lower ratios the bifurcated branches has low influence over the thermal performance of the system. The optimal tri-forked pathway presented a 307% lower thermal global resistance compared to a V-shaped pathway on the same conditions.