Heat transfer modulation in Phase Change Materials via fin insertion

We leverage a large set of numerical simulations to study optimized geometrical configurations for Phase Change Materials (PCMs) cells. We consider a PCM cell as a square enclosure with a solid substance that undergoes melting under the effect of a heat source from one side and under the effects of buoyancy forces. Moreover, an additional source fin with prescribed length $l$ and height $h$ protrudes into the cell perpendicularly from the heat source. The fin prompts enhanced heat transfer and convection within the PCM cell, thus shortening (in comparison to a finless cell) the melting time $t_m$ needed for all the PCM material to melt and transit from the solid to the liquid phase. This improvement is systematically studied as a function of the fin geometrical details ($l$, $h$), as well as the Rayleigh number $\operatorname{Ra}$ -- encoding the importance of buoyancy forces with respect to diffusion/dissipation effects -- and the Stefan number $\operatorname{St}$ -- encoding the importance of sensible heat with respect to latent heat. Overall, our systematic study in terms of the free parameters $l$, $h$, $\operatorname{Ra}$ and $\operatorname{St}$ offers inspiring insights to optimize the structure of a PCM cell during its manufacturing process and suggests optimal operating conditions for such geometrical configurations.