Beam search multiresolution optimization of buried fluid-thermal conduit paths under hard spatially distributed temperature constraints

Buried flow-thermal systems such as heated pavements and injection mold cooling channels require spatially reliable surface temperature control with low pressure loss. This article formulates such fluid distribution design tasks as an abstract shape optimization problem: a buried fluid conduit must be routed between fixed inlet and outlet locations so that both an inlet temperature cap and a distributed surface temperature constraint are satisfied while pressure loss is minimized. Along the path, the thermal control capacity of the fluid decreases, whereas pressure loss and thermal coverage increase. This article introduces a coupled 2.5D flow-thermal model that describes the interactions between conduit geometry, hydraulic losses, fluid temperature evolution and fluid–solid heat transfer. A Green function thermal surrogate is derived for fast candidate path evaluation. The optimization is performed by a staged graph-based beam search on triangulated domains. A multiresolution hierarchy of triangulations is used to identify promising coarse route topologies and then refine the local path geometry. Validation against high-fidelity 3D conjugate heat transfer CFD predictions shows good agreement: the predicted minimum surface temperatures differ by 0.18 °C–0.64 °C, while fluid temperature change and net heat inputs agree within about 2%–8%. For an analytically tractable validation case, the proposed optimization method recovers the global optimum (within triangulation accuracy). The results show that the method can find thermally feasible, hydraulically efficient conduit layouts in non-convex, non-simply-connected domains.