  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.
