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Heat transfer modulation in Phase Change Materials via fin insertion

Paolo Proia, Mauro Sbragaglia, Giacomo Falcucci

TL;DR

The paper addresses improving heat transfer in phase-change materials (PCMs) by inserting a single fin inside a PCM cell. It employs 2D lattice Boltzmann simulations to solve coupled Navier–Stokes and energy equations with latent heat, while systematically varying fin geometry through $\hat{l}$ and $\hat{h}$ and non-dimensional parameters $Ra$ and $St$, to quantify melting-time reductions via $t_m$ and its normalized form $\hat{t}_m$. Key findings show that fins substantially accelerate melting due to buoyancy-driven convection, with speed-ups up to about $60\%$, and that optimal fin height depends non-trivially on $Ra$ and $St$, driven by competing convective structures beneath and above the fin. The work provides actionable design insights for PCM-based thermal energy storage, offering guidance on fin dimensions and operating regimes to enhance charging/discharging rates and informing manufacturing considerations and future 3D extensions.

Abstract

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.

Heat transfer modulation in Phase Change Materials via fin insertion

TL;DR

The paper addresses improving heat transfer in phase-change materials (PCMs) by inserting a single fin inside a PCM cell. It employs 2D lattice Boltzmann simulations to solve coupled Navier–Stokes and energy equations with latent heat, while systematically varying fin geometry through and and non-dimensional parameters and , to quantify melting-time reductions via and its normalized form . Key findings show that fins substantially accelerate melting due to buoyancy-driven convection, with speed-ups up to about , and that optimal fin height depends non-trivially on and , driven by competing convective structures beneath and above the fin. The work provides actionable design insights for PCM-based thermal energy storage, offering guidance on fin dimensions and operating regimes to enhance charging/discharging rates and informing manufacturing considerations and future 3D extensions.

Abstract

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 and height 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 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 (, ), as well as the Rayleigh number -- encoding the importance of buoyancy forces with respect to diffusion/dissipation effects -- and the Stefan number -- encoding the importance of sensible heat with respect to latent heat. Overall, our systematic study in terms of the free parameters , , and offers inspiring insights to optimize the structure of a PCM cell during its manufacturing process and suggests optimal operating conditions for such geometrical configurations.

Paper Structure

This paper contains 4 sections, 8 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Statement and set-up
  3. Results and discussion
  4. Conclusions

Figures (9)

  • Figure 1: Sketch of PCM cell geometry. The enclosure consists of a square cell with a side length of $L$. On the left side there is a source at fixed temperature $T_H$, from which a fin of fixed surface area $S$ and variable length $l$ protrudes at height $h$. The fin is an heat source at temperature $T_H$. Its height and length are normalized to the side length as $\hat{l}=l/L$ and $\hat{h}=h/L$. The three other sides are insulating wall for which $\partial_{\bar{n}}T=0$, with $\bar{n}$ being the normal to the wall. The enclosure is filled with the solid substance at the melting temperature $T_C$.
  • Figure 2: Comparison of the time evolution of the temperature field $T(\vec{x},t)$ for non-finned (upper plots) and finned (lower plots) cells with $\operatorname{Ra}=10^7,~\operatorname{St}=10$. Time increases from left to right. The space coordinates are normalized to the size of the cell $L$ as $\hat{x}=x/L$ and $\hat{y}=y/L$.
  • Figure 3: Comparison of the temperature field $T(\vec{x},t)$ and liquid fraction $\phi^\star(t)$ (see \ref{['eq:phi-star']}) for $\operatorname{Ra}=10^6,~\operatorname{St}=1$ for various fin height/length configurations at time $t=13000.0$. $\hat{h}$ increases from left to right, while $\hat{l}$ increases from top to bottom.
  • Figure 4: We report the liquid fraction $\phi^\star$ (see \ref{['eq:phi-star']}) as a function of $\hat{h}$ at time $t=13000.0$, for different values of $\hat{l},~\operatorname{Ra},~\operatorname{St}$. $\operatorname{Ra}$ changes between sub-figures in panels (a) and (b), while $\operatorname{St}$ increases from left to right. The different lengths are shown with different symbols and colors; the black square represents the value for the case without the fin.
  • Figure 5: Plot of the normalized melting time $\hat{t}_m$ (see \ref{['eq:norm-melting-time']}) at changing $\hat{l},~\hat{h},~\operatorname{Ra}~,\operatorname{St}$. $\operatorname{St}$ increases from left to right, while $\operatorname{Ra}$ increases from top to bottom. We also show contour lines for some selected values of $\hat{t}_m$ in the range $0.8-0.97$.
  • ...and 4 more figures