Configuration-independent thermal invariants under flow reversal in thin vascular systems

Modulating temperature fields is indispensable for advancing modern technologies: space probes, electronic packing, and implantable medical devices, to name a few. Bio-inspired thermal regulation achieved via fluid flow within a network of embedded vesicles is notably desirable for slender synthetic material systems. This far-reaching study—availing theory, numerics, and experiments—reveals a counter-intuitive yet fundamental property of vascular-based fluid-flow-engendered thermal regulation. For such thin systems, the mean surface temperature and the outlet temperature—consequently, the heat extracted by the flowing fluid (coolant)—are invariant under flow reversal (i.e. swapping the inlet and outlet). Despite markedly different temperature fields under flow reversal, our newfound invariance—a discovery—holds for anisotropic thermal conductivity, any inlet and ambient temperatures, transient and steady-state responses, irregular domains, and arbitrary internal vascular topologies, including those with branching. The reported configuration-independent result benefits thermal regulation designers. For instance, the flexibility in the coolant’s inlet location eases coordination challenges between electronics and various delivery systems in microfluidic devices without compromising performance (e.g. soft implantable coolers for pain management). Last but not least, the invariance offers an innovative way to verify computer codes, especially when analytical solutions are unavailable for intricate domain and vascular configurations.