Effect of temperature-dependent material properties on thermal regulation in microvascular composites

TL;DR

This work addresses how temperature-dependent thermophysical properties influence vascular-based thermal regulation in microvascular composites. It develops a temperature-dependent reduced-order ROM for a thin domain with embedded vasculature, characterizes material properties, proves that minimum and maximum principles hold under TDMP for steady states, and analyzes mean surface temperature and outlet-temperature invariance under flow reversal. Numerical experiments across multiple vasculature layouts and host materials show TDMP yields only small quantitative differences in MST and thermal efficiency, with invariants preserved and steady-state results aligning with CMP cases. The findings provide practical guidance for designing thermal regulation in FRCs under realistic temperature dependencies and motivate future thermo-mechanical coupling studies.

Abstract

Fiber-reinforced composites (FRC) provide structural systems with unique features that appeal to various civilian and military sectors. Often, one needs to modulate the temperature field to achieve the intended functionalities (e.g., self-healing) in these lightweight structures. Vascular-based active cooling offers one efficient way of thermal regulation in such material systems. However, the thermophysical properties (e.g., thermal conductivity, specific heat capacity) of FRC and their base constituents depend on temperature, and such structures are often subject to a broad spectrum of temperatures. Notably, prior active cooling modeling studies did not account for such temperature dependence. Thus, the primary aim of this paper is to reveal the effect of temperature-dependent material properties -- obtained via material characterization -- on the qualitative and quantitative behaviors of active cooling. By applying mathematical analysis and conducting numerical simulations, we show this dependence does not affect qualitative attributes, such as minimum and maximum principles (in the same spirit as \textsc{Hopf}'s results for elliptic partial differential equations). However, the dependence slightly affects quantitative results, such as the mean surface temperature and thermal efficiency. The import of our study is that it provides a deeper understanding of thermal regulation systems under practical scenarios and can guide researchers and practitioners in perfecting associated designs.

Figures (12)

• Figure 1: This figure depicts A) the temperature field in the entire domain and B) the variation of the temperature ($\vartheta$) along the arc-length ($s$) of the vasculature. The left image shows the U-shaped vasculature in a carbon-fiber-reinforced polymer (CFRP) host whose thermophysical properties depend on the temperature. Inference: For two different applied heat fluxes, $1000$ and $2000 \; \mathrm{W/m^2}$, numerical results reveal that the temperature-dependent material properties (TDMP) did not significantly influence the solution field compared to assumed constant material properties (CMP).
• Figure 1: Problem setup: The figure illustrates a thin domain $\Omega$ of area 100 mm x 100 mm and thickness $d$. The lateral boundaries $\partial\Omega$ are adiabatic. A U-shaped vasculature $\Sigma$ with spacing $s$ is embedded with an inlet and outlet through which coolant flows. $\widehat{\mathbf{n}}^{\pm}(\mathbf{x})$ denote the unit normals on either side of $\Sigma$ and the tangent vector along the vasculature is denoted by $\widehat{\mathbf{t}}(\mathbf{x})$. A constant heat flux is applied on the bottom face of the domain, and the top surface is free to radiate and convect.
• Figure 2: Solid host material properties: This figure shows the variations of the A) specific heat capacity and B) thermal conductivity --- in the temperature range 296.15--423.15 K for three candidate host materials: CFRP, GFRP, and epoxy. The figure also provides the best-fit polynomial for each curve. The specific heat capacity varies significantly with temperature for all three materials. However, the thermal conductivity remains relatively constant except for CFRP.
• Figure 3: Liquid coolant (fluid) properties:A) The density and specific heat capacity of water (coolant) vary only 4.30% and 0.95%, respectively, over the temperature range 0--100 $^\circ\mathrm{C}$. These data were sourced from scienceschool and engineeringtoolbox, respectively. B) The heat capacity rate (i.e., the product of the density, specific heat capacity, and the volumetric flow rate) also varies merely 4.39% over the chosen temperature range for the volumetric flow rate $Q = 1 \, \mathrm{mL/min}$. Hence, in this paper, we have taken the fluid's heat capacity, which is an input to the mathematical model, to be constant.
• Figure 4: Problem description. The figure shows three different vascular layouts used in the study: A) U-shaped, B) serpentine, and C) asymmetric. Blue lines represent channels, which begin at the inlet and end at the outlet. In all cases, the computational domain is a square of size $100 \times 100 \, \mathrm{mm}$ with thickness $d = 5 \, \mathrm{mm}$. Active cooling is achieved by flowing fluid into the vasculature at the inlet with fluid's temperature equal to the ambient (i.e., $\vartheta_{\mathrm{inlet}} = \vartheta_{\mathrm{amb}}$). At the bottom face, a source supplies a uniform heat flux (i.e., $f(\mathbf{x}) = f_0$). The top surface is free to exchange heat via convection and radiation. The lateral boundaries are thermally isolated (i.e., adiabatic). All the figures are drawn to the scale.

Theorems & Definitions (5)

• Theorem 4.1: minimum principle
• proof
• Theorem 4.2: maximum principle
• proof
• Remark 4.1