If you’ve ever kept a drink cool on a hot summer day by placing it inside a frozen, gel-filled sleeve, you’ll understand the appeal of phase change materials (PCMs). The reason these sleeves work so well (and so much better than simply putting your drink in a cold bath or cool room) is that the solid inside them has a high latent heat, meaning it can absorb relatively large quantities of energy before melting and beginning to warm up.
But what if surrounding your drink with a frozen PCM isn’t enough? What if you want to cool your drink more quickly and evenly? One option would be to create a PCM sleeve with fin-shaped extensions that protrude into your drinking vessel. These fins would cool your drink – or, equivalently, allow your drink to melt the PCM – much more efficiently than a simple sleeve. But what should the fins look like? How far apart should they be? And how many of them do you need?
These are the questions that Paolo Proia, Mauro Sbragaglia and Giacomo Falcucci considered in a study published in EPL – though not with the aim of keeping their drinks cold. As researchers at the University Tor Vergata of Rome, Italy, Proia, Sbragaglia and Falcucci are interested in PCMs that store and release heat like a battery. Such materials are useful in fields such as electronics and refrigeration where heat is a common byproduct. Other applications include maintaining the efficiency of solar panels by preventing them from getting too hot and keeping buildings cool in the daytime via insulation.
Physics World spoke with them about their work.
What was your motivation for doing this research?
Our interest in PCMs stems, in part, from our interest in their many applications, especially in the ecological transition to less carbon-intensive fuels. PCMs are particularly good at managing heat in hydrogen storage with metal hydrides, for example, because storing hydrogen in these materials produces heat, while releasing the hydrogen requires it. Using a PCM to store the heat of the adsorption process and give it back during the release means that the produced heat doesn’t go to waste. Instead, it improves the efficiency of the process.
We’re also fascinated by the complexity of the equations involved. The coupling of fluid and temperature dynamics already causes interesting phenomena such as convection. By adding a phase transition to the mix, you introduce a moving boundary that complicates the system even more, both phenomenologically and analytically, since the describing equations must account for it.
We started this paper as a way of extending our previous work on the insertion of fins inside a PCM to three dimensions. PCMs are exceptionally good in latent heat but severely lacking in sensible heat; in other words, they store heat well, but they absorb and release it poorly. Fins are useful in relieving this flaw since they enhance the heat transfer surface and provide a horizontal heat source, which is instrumental for the development of convection, the main driver of heat transfer in this kind of system. By switching to a 3D system, we had more freedom to explore complex layouts of multiple fins and the importance of their relative position.
What is the most important advance in the paper?
The most important result is that naively inserting fins too close to each other can cause interference. If there are overlaps in the fins’ “influence zone”, the system will waste energy by, in effect, trying to melt something that was already molten from heating by a nearby fin. Moreover, by comparing a single fin and multiple fins with the same total surface, we found that the latter configuration benefits from the gaps between the fins. This is because the substance in these gaps melts early and starts acting as an extra heating surface, contributing to the development of bigger convective structures.
Why is it so challenging to model melting in phase change materials in 3D?
Beyond the analytical requirements we already mentioned, the success of this type of modelling depends on having a resolution that is high enough to capture correctly all the phenomena in the system. This means the number of computational sites N must be sufficiently large. In 2D, we “only” have N2 sites to model, but in 3D, this scales to N3. That creates a challenge because making N too large would severely slow down the simulation. Moreover, we must be sure to respect the restraints on the physical parameters for which the lattice Boltzmann method is a correct approximation of the equations involved. So, we underwent a thorough validation process to pinpoint the best parameters for the algorithm.
What do you plan to do next?
First, we’d like to further optimize the code. The main bottleneck is the speed of a single iteration. Ideally, we’d like to study a wider range of layouts and physical conditions, but with the code we have now, that would impact heavily on performance. For example, a slower-melting substance requires more iterations to completely melt, which translates into more real-life time to model, sometimes outside the limits of feasibility. This problem would obviously be solved if we can make a single iteration faster.
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Another issue we have is that some ranges of physical parameters can make the simulation unstable. Fortunately, there exist some remedies to this, and we plan to eventually adopt them.
Finally, we would be happy to see other researchers use these findings in their own optimization studies on fin shapes and spatial layouts. It would also be very interesting to see someone study this problem from an analytical angle or to see some experimental validation. In the medium term, we are planning to conduct our own experiments to use as a benchmark for our computational results.
