Constructal design of underground heat sources or sinks for the annual cycle

Here we show that the heat transfer between a pipe assembly and the soil during the annual temperature cycle of a heat pump depends on the configuration of the flow system. We rely on constructal design to find the flow architecture (spacings, shapes) such that the heat transfer between the assembly and the ground is increased. The flow configuration changes freely, and its design is evolutionary. The better shapes change gradually from slender to square as the volume fraction occupied by the flow assembly increases. The heat transfer performance increases as the depth of the structure decreases, but the depth has a negligible effect on the shape of the structure. The results also show that the heat transfer performance increases as the configuration of the ground volume and the buried structure evolves to the most slender shape possible.