Mimicking vascular systems in living beings, designers have realized microvascular composites to achieve thermal regulation and other functionalities, such as electromagnetic modulation, sensing, and healing. Such material systems avail circulating fluids through embedded vasculatures to accomplish the mentioned functionalities that benefit various aerospace, military, and civilian applications. Although heat transfer is a mature field, control of thermal characteristics in synthetic microvascular systems via circulating fluids is new, and a theoretical underpinning is lacking. What will benefit designers are predictive mathematical models and an in-depth qualitative understanding of vascular-based active cooling/heating. So, the central focus of this paper is to address the remarked knowledge gap. \emph{First}, we present a reduced-order model with broad applicability, allowing the inlet temperature to differ from the ambient temperature. \emph{Second}, we apply mathematical analysis tools to this reduced-order model and reveal many heat transfer properties of fluid-sequestered vascular systems. We derive point-wise properties (minimum, maximum, and comparison principles) and global properties (e.g., bounds on performance metrics such as the mean surface temperature and thermal efficiency). These newfound results deepen our understanding of active cooling/heating and propel the perfecting of thermal regulation systems.

翻译：模仿生物体血管系统，设计者已实现微血管复合材料以达成热调控及其他功能，如电磁波调节、传感与自修复。此类材料系统通过嵌入的脉管网络利用循环流体实现上述功能，服务于航空航天、军事及民用领域。尽管传热学已发展成熟，但在合成微血管系统中通过循环流体控制热特性仍属新兴领域，且缺乏理论支撑。能够助力设计者的当属预测性数学模型及对基于血管的主动冷却/加热机制的深度定性理解。因此，本文的核心目标是填补上述知识空白。首先，我们提出一个具有广泛适用性的降阶模型，允许入口温度与环境温度存在差异。其次，运用数学分析工具对该降阶模型进行解析，揭示流体密闭血管系统的多项传热特性。我们推导了点态性质（最小值、最大值及比较原理）与全局性质（例如均表面温度、热效率等性能指标的边界）。这些新发现深化了对主动冷却/加热的理解，并推动了热调控系统的完善。