Modeling thermal regulation in thin vascular systems: A mathematical analysis

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 with mentioned functionalities benefit various aerospace, military, and civilian applications. Although heat transfer is a mature field, control of thermal characteristics in synthetic microvascular systems is new, and the fundamental comprehension is hazy. What will benefit designers are predictive mathematical models and an in-depth qualitative understanding of vasculature-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 use mathematical analysis tools for this reduced-order model and reveal many heat transfer properties in fluid-sequestered vasculature systems. We derive point-wise properties (minimum, maximum, and comparison principles) and global properties (such as bounds on performance metrics such as the mean surface temperature and cooling efficiency). These newfound results deepen our understanding of active cooling/heating and propel the perfecting of thermal regulation systems.