One of the ways natural and synthetic systems regulate temperature is via circulating fluids through vasculatures embedded within their bodies. Because of the flexibility and availability of proven fabrication techniques, vascular-based thermal regulation is attractive for thin microvascular systems. Although preliminary designs and experiments demonstrate the feasibility of thermal modulation by pushing fluid through embedded micro-vasculatures, one has yet to optimize the performance before translating the concept into real-world applications. It will be beneficial to know how two vital design variables -- host material's thermal conductivity and fluid's heat capacity rate -- affect a thermal regulation system's performance, quantified in terms of the mean surface temperature. This paper fills the remarked inadequacy by performing adjoint-based sensitivity analysis and unravels a surprising non-monotonic trend. Increasing thermal conductivity can either increase or decrease the mean surface temperature; the increase happens if countercurrent heat exchange -- transfer of heat from one segment of the vasculature to another -- is significant. In contrast, increasing the heat capacity rate will invariably lower the mean surface temperature, for which we provide mathematical proof. The reported results (a) dispose of some misunderstandings in the literature, especially on the effect of the host material's thermal conductivity, (b) reveal the role of countercurrent heat exchange in altering the effects of design variables, and (c) guide designers to realize efficient microvascular active-cooling systems. The analysis and findings will advance the field of thermal regulation both on theoretical and practical fronts.

翻译：自然与人工系统中调节温度的途径之一，是通过嵌入其体内的脉管网络循环流体。得益于成熟制造工艺的灵活性与可及性，基于脉管的热调控对薄层微脉管系统具有吸引力。尽管初步设计与实验已证明通过驱动流体穿越嵌入式微脉管网络实现热调控的可行性，但在将该概念转化为实际应用前，仍需优化其性能。明确两个关键设计变量——基体材料热导率与流体热容率——如何影响以平均表面温度量化的热调控系统性能，将具有重要价值。本文通过基于伴随的灵敏度分析填补上述不足，并揭示出令人惊讶的非单调趋势：增大热导率既可能降低也可能提高平均表面温度——当反向热交换（脉管某段向另一段传递热量）显著时，温度反而升高；而增大热容率必然降低平均表面温度，我们对此给出了数学证明。所报告的结果：（a）澄清了文献中的若干误解，尤其是关于基体材料热导率的影响；（b）揭示了反向热交换在改变设计变量效应中的作用；（c）为设计者实现高效微脉管主动冷却系统提供指导。该分析与发现将从理论与实践两方面推动热调控领域的发展。