Modeling Thermal Regulation in Thin Vascular Systems: A Mathematical Analysis (Communications in Computational Physics, 2023)
Mimicking vascular systems in living beings, designers have realized microvascular composites to achieve thermal regulation and other functionalities, suchas 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 heattransfer is a mature field, control of thermal characteristics in synthetic microvascularsystems via circulating fluids is new, and a theoretical underpinning is lacking. Whatwill benefit designers are predictive mathematical models and an in-depth qualitativeunderstanding of vascular-based active cooling/heating. So, the central focus of thispaper is to address the remarked knowledge gap. First, we present a reduced-ordermodel with broad applicability, allowing the inlet temperature to differ from the ambient temperature. Second, we apply mathematical analysis tools to this reduced-ordermodel 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 surfacetemperature and thermal efficiency). These newfound results deepen our understanding of active cooling/heating and propel the perfecting of thermal regulation systems.