Modeling heat flow in materials with dual pore sizes

What is it about?

This paper investigates bi-dispersed porous media, which are complex materials composed of clusters of large particles that are themselves agglomerations of smaller particles. Because these materials naturally contain both large macro-pores between the clusters and micro-pores within them, we developed a mathematical model that accounts for the fact that fluids move at different velocities and hold different temperatures in each type of pore space. We specifically looked at the physics of heat transfer when a fluid is forced through a channel of this porous material situated between two parallel walls. To make the model highly applicable, we analyzed and solved for two distinct operational scenarios: one where the channel walls are maintained at a uniform temperature, and another where the walls supply a uniform heat flux.

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Photo by Spring Fed Images on Unsplash

Photo by Spring Fed Images on Unsplash

Why is it important?

Our work is unique because it formulates a specialized two-velocity, two-temperature model to accurately capture local thermal non-equilibrium in these intricate structures. Traditional models often treat porous media as having a single, uniform solid phase and fluid phase, which falls short when analyzing bi-dispersed materials where the "solid" phase actually acts as a secondary porous medium with its own distinct flow and temperature characteristics. This research is highly valuable because it provides engineers with exact analytic solutions for predicting heat transfer efficiency. By allowing researchers to calculate the Nusselt number based on specific parameters—like the thermal conductivity ratio, velocity ratio, volume fraction, and internal heat exchange—we offer precise tools needed to optimize the design of advanced filters, heat exchangers, and thermal management systems.

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