A methodology for measuring heat transfer coefficient and self-similarity of thermal regulation in microvascular material systems

Abstract

Fluid transport through microvascular networks—a hallmark for homeostasis in living systems—has transcended to engineered materials, primarily made possible because of modern manufacturing advancements. Vascular-enabled multifunctionality, including thermal regulation and self-healing, holds great potential for extending the lifetime of structural materials and expanding the operational envelope. Prior studies on vascular-based active cooling use a “combined” heat transfer coefficient (HTC): a single parameter lumps convection and radiation effects. Although the resulting mathematical models are linear—an attractive feature for computational modeling, the combined coefficient approach may not be accurate or even applicable if the operating temperature is unknown, which is the case with many thermal regulation applications (e.g., space probes). In this paper, we illustrate the remarked limitations of the lumped approach and advocate the need to use a decoupled HTC by splitting convective and radiative heat transfer modes. We show the broad applicability of the proposed method by applying it to three material systems: glass and carbon fiber-reinforced polymer composites and an additive manufactured metal. We show, using numerical simulations, the differences in the predictions from the decoupled approach with that of the combined HTC; these differences are prominent at higher heat fluxes. Also, the decoupling has enabled us to establish a scaling law that allows transferring of solutions fields across material systems, strengthening further the validity and utility of our approach. This work's significance is two-fold. First, the research is fundamental, providing accurate measurement protocols for critical model parameters. Second, this work facilitates the development of mathematical models for vascular-based thermal regulation that are predictive even for hostile environments (which are often difficult to realize in laboratories), such as outer space.