Session: 12-10-01: Heat Transfer in Natural and Build Environments

Paper Number: 191544

A Thermal Circuit Framework for Multimodal Heat Transfer in Porous Structures 

Thermal protection systems (TPS) are essential for atmospheric reentry vehicles. They protect the vehicles from the extreme aerothermal conditions generated by their propulsion systems and the high aerodynamic drag encountered during planetary entry. Porous materials have been widely used to build TPS due to their advantageous characteristics, such as low thermal conductivity, lightweight design, high reliability, and cost-effectiveness. Central to the design and application of porous TPS materials is a comprehensive understanding of the underlying coupled thermal transfer mechanisms within them, as well as our ability to accurately model and predict their thermal transport properties. Heat transfer through a porous medium includes combined contributions from conduction along the solid matrix, radiation across voids (pores), and conduction through gases filling the voids. Although this qualitative picture of the heat transfer mechanisms is well accepted, a quantitative understanding of the contribution of each individual mechanism is still lacking, primarily due to the complex morphology of the porous materials and the intrinsically coupling nature of different mechanisms across scales. To this end, a thermal circuit framework was developed where individual heat transport mechanisms were quantified with equivalent thermal resistances. Facilitated by novel experimental measurements, this approach enables the decomposition of the multimodal heat transfer into mechanism-specific contributions.

In the experiment, idealized model porous media, called micromodels, with well-defined morphology and thermophysical properties were fabricated using microfabrication techniques from silicon–glass wafers, and emissivity was modified when required by depositing a thin gold coating. Heat transfer measurements were conducted using a thermal test apparatus placed inside a vacuum chamber, where temperatures and heat fluxes were recorded using thermocouples and heat-flux sensors to quantify the contributions of solid conduction, gas conduction, and radiation. The approach allows for the isolation of individual heat transfer mechanisms by systematically controlling the surrounding pressure and the surface emissivity. For instance, gas conduction was suppressed under high-vacuum conditions ( Pa), effectively removing gas molecules from the pores, while radiative transfer was varied by tuning the surface emissivity. Analytical modeling was used to resolve the internal temperature field and to enable extraction of mechanism-specific thermal resistances. For solid and gas conduction, the temperature distribution was obtained from the three-dimensional steady-state heat diffusion equation with the experimentally relevant boundary conditions: a prescribed top-surface temperature and adiabatic sidewalls, together with a spatially localized heat-flux boundary condition at the bottom surface. The solution was constructed using separation of variables and eigenfunction expansions. Radiative heat transfer was modeled using a gray, diffuse far-field formulation based on the Stefan–Boltzmann law with an assumed unity view factor between the hot and cold surfaces.

Among the three heat transfer mechanisms investigated, radiation thermal resistance was found to be the dominant contributor, while solid conduction resistance was the least significant. Quantitatively, at 299°C, radiation thermal resistance was approximately 78 times greater than solid conduction resistance, while gas conduction resistance was approximately 7 times higher

Presenting Author: M. Ruhul Amin Montana State University

Presenting Author Biography: M. Ruhul Amin received his Ph.D. in Mechanical Engineering from the University of Tennessee, USA. He is currently a professor of mechanical engineering at Montana State University and has extensive experience in computational heat transfer and fluid flow. Dr. Amin serves as the program coordinator for the Mechanical Engineering Program at Montana State University and as a Program Evaluator for the Accreditation Board for Engineering and Technology (ABET). He is also a member of the ABET Commission. Dr. Amin is a Fulbright Scholar, a member of ASME, and serves on ASME technical committee. He is a registered professional engineer in the State of Montana. He has chaired and co-chaired numerous technical sessions at international conferences, and has co-chaired multiple international conferences on thermal sciences.

Authors:

Mahedi Hassan University of Colorado Boulder
M. Ruhul Amin Montana State University
Yaofa Li University of California Riverside