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. First, we present a reduced-order model with broad applicability, allowing the inlet temperature to differ from the ambient temperature. 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：尽管热传输是一个成熟的领域,但通过循环流体液对合成微型血管系统中的热特性的控制是新的,缺乏理论基础。设计者将获益于预测数学模型和对以血管为基础的活性冷却/热能的深入定性理解。因此,本文的中心重点是解决上述知识差距。首先,我们提出一个可广泛应用的减序模型,允许内温与环境温度不同。第二,我们对这一降序模型应用数学分析工具,并揭示流压血管系统的许多热转移特性。我们从中获取点性能(最小值、最大值和比较原则)和全球新特性(例如,对性能测量值的界限,例如,对地温和热温度的精确度和温度的精确度理解)。