Modeling thermal regulation in thin vascular systems: A mathematical analysis

TL;DR

This paper develops a mathematical model for thermal regulation in microvascular systems, providing insights into heat transfer properties and aiding the design of active cooling and heating solutions in synthetic vascular materials.

Contribution

It introduces a reduced-order model applicable to various conditions and applies mathematical analysis to uncover fundamental heat transfer properties.

Findings

Derived bounds on surface temperature and thermal efficiency.

Identified minimum and maximum temperature points in vascular systems.

Provided theoretical insights to improve thermal regulation design.

Abstract

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.