Heat Transfer in Phase Change Materials with Multiple Fin Insertion

Giacomo Falcucci; Mauro Sbragaglia; Paolo Proia

arxiv: 2605.08120 · v1 · submitted 2026-04-28 · ❄️ cond-mat.soft · cond-mat.mtrl-sci

Heat Transfer in Phase Change Materials with Multiple Fin Insertion

Paolo Proia , Mauro Sbragaglia , Giacomo Falcucci This is my paper

Pith reviewed 2026-05-12 00:45 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-sci

keywords phase change materialsheat transfermeltingmultiple finsnumerical simulationsbuoyancythermal energy storage

0 comments

The pith

Multiple fins melt phase change materials more efficiently than single fins by exploiting interstitial spaces.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses 3D numerical simulations to examine how solid fins attached to a heated boundary affect melting in phase change material cells driven by buoyancy. Configurations with multiple fins are compared to equivalent single-fin and finless cases, tracking the total amount of melted material over time while varying key dimensionless numbers. Results show that multiple fins accelerate melting by creating separate melt zones in the spaces between them. Single fins fall short because they leave those gaps unused, and fins placed too close together produce overlapping melt regions that interfere.

Core claim

We confirm that fins increase the melting performance and find that single fin configurations are sub-optimal since a layout with multiple fins takes advantage of interstitial spaces, melting the substance more efficiently. The results also indicate that fins should be properly spaced, as closeness can result in overlapping, thus interfering, molten areas.

What carries the argument

3D numerical simulations of buoyancy-driven melting in PCM cells with multiple protruding solid fins, quantified by total molten mass versus time and compared to equivalent single-fin and finless heating-power cases.

If this is right

Multiple-fin layouts produce higher total molten mass over time than single-fin or finless designs at the same heating power.
Single fins are less effective because they fail to melt material in the interstitial spaces that multiple fins reach.
Fins placed too close together create interfering overlap in molten regions and reduce net performance.
The melting advantage of multiple fins remains across different values of the governing non-dimensional numbers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

PCM thermal storage device designers could adopt multiple properly spaced fins to shorten charging times.
Testing alternative fin cross-sections or materials might reveal further gains in optimal spacing.
Direct comparison of simulation melt fronts with high-speed imaging in physical cells would test the interstitial-zone mechanism.

Load-bearing premise

The numerical simulations accurately capture the coupled heat transfer, phase change, and buoyancy-driven flow without significant discretization errors or missing physical effects.

What would settle it

A laboratory experiment that measures melted volume fraction over time in a real PCM cell with multiple fins versus an equivalent single-fin setup under controlled heating to check whether the multiple-fin advantage appears as predicted.

Figures

Figures reproduced from arXiv: 2605.08120 by Giacomo Falcucci, Mauro Sbragaglia, Paolo Proia.

**Figure 1.** Figure 1: Panel (a): typical snapshots of temperature field in the melting dynamics of a PCM cell consisting of a cubic [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: We report the normalized liquid fraction [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Analysis of the early-stage melting dynamics in conductive case, corresponding to a zero Rayleigh number [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

We leverage 3D numerical simulations to study phase change materials (PCMs) cells under the effect of buoyancy forces. The solid PCM is heated from a source boundary, triggering melting. The source features multiple solid fins that protrude into the PCM cell; the impact of the fins and their number is investigated by designing and testing equivalent (in terms of heating power) finless and single fin simulations. For each configuration, the performance is quantified via the total molten substance in time. The designs were also tested for different values of the non-dimensional numbers encoding relevant properties. We confirm that fins increase the melting performance and find that single fin configurations are sub-optimal since a layout with multiple fins takes advantage of interstitial spaces, melting the substance more efficiently. The results also indicate that fins should be properly spaced, as closeness can result in overlapping, thus interfering, molten areas.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper's 3D simulations indicate that multiple spaced fins enhance PCM melting more than single fins by using interstitial spaces, but the work lacks any reported validation or mesh checks.

read the letter

The punchline for this paper is that their 3D simulations of phase change material cells find multiple fins outperform a single fin when the fins are spaced to avoid overlapping melting zones, leading to more efficient use of the interstitial spaces between them. They tested this by running equivalent heating power cases for finless, single, and multi-fin setups across different non-dimensional numbers. What the paper does is take the known benefit of fins for accelerating melting and extend it to a layout comparison in three dimensions, including buoyancy effects. This is a logical step for engineering applications like thermal storage, and the results align with intuition about how convection and melting fronts interact. On the positive side, the approach of normalizing the heating power across configurations is sensible, so the comparison is fair. Varying the material properties via non-dimensional groups also adds some robustness. The soft spots are more significant. The abstract and the stress-test note give no sign of experimental validation, mesh independence studies, or details on the numerical treatment of the phase change, such as the enthalpy method parameters or time stepping. This means the claimed superiority of the multiple-fin layout could depend on how well the code resolves the thermal plumes or the interface. If those checks are missing from the full manuscript, the central result is harder to rely on. This kind of study is aimed at engineers working on PCM-based cooling or energy storage systems. A reader in that area could pick up ideas about fin spacing, but anyone wanting to build on the numerics would need the full methods and verification data. Overall, the paper shows clear thinking on the design question, so I would recommend sending it to peer review. The referees can push for the missing validation, which would make the contribution more solid if the model checks out.

Referee Report

3 major / 2 minor

Summary. The manuscript uses 3D numerical simulations to examine buoyancy-driven melting of phase-change materials (PCMs) in cells heated from a boundary with multiple protruding solid fins. Equivalent-heating-power comparisons are made against finless and single-fin geometries; melting fraction versus time is tracked for several values of the governing non-dimensional numbers. The central claim is that multiple properly spaced fins outperform both the finless and single-fin cases by exploiting interstitial spaces, while overly close fins produce interfering molten regions.

Significance. If the numerical predictions prove robust, the work supplies concrete geometric guidance for fin layout in PCM thermal-storage devices, emphasizing that single-fin designs are suboptimal and that spacing must avoid overlap of thermal plumes. Such optimization insights are relevant to latent-heat storage applications, though their practical weight depends on validation against experiment.

major comments (3)

[Abstract / Numerical Methods] Abstract and Numerical Methods section: no mesh-independence study, grid-convergence metrics, or time-step sensitivity analysis is reported. For buoyancy-driven flows with moving solid-liquid interfaces, inadequate resolution of thermal plumes or the mushy zone can alter the predicted ranking of fin configurations; this directly undermines the claim that multiple fins are superior.
[Abstract / Results] Abstract and Results section: the manuscript supplies no experimental validation, benchmark comparison (e.g., against the classic Stefan problem or published PCM melting data), or error quantification for the enthalpy-porosity formulation. Without these, it is impossible to determine whether the reported performance ordering reflects physical interstitial-space utilization or numerical artifacts such as artificial diffusion or incorrect mushy-zone constant.
[Abstract] Abstract: the statement that “heating power was made equivalent” across configurations is not accompanied by explicit verification (e.g., integrated heat flux or boundary-condition details). If the total heat input differs even modestly, the melting-fraction curves cannot be compared directly, weakening the optimality conclusion for multiple-fin layouts.

minor comments (2)

[Abstract] The non-dimensional numbers used to encode material properties are mentioned but never defined explicitly (e.g., no values or ranges for Stefan, Rayleigh, or Prandtl numbers).
[Figures] Figure captions and axis labels should state the precise non-dimensional time or Fourier number at which melting fractions are compared.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and have revised the manuscript accordingly to strengthen the numerical robustness and clarity of the claims.

read point-by-point responses

Referee: [Abstract / Numerical Methods] Abstract and Numerical Methods section: no mesh-independence study, grid-convergence metrics, or time-step sensitivity analysis is reported. For buoyancy-driven flows with moving solid-liquid interfaces, inadequate resolution of thermal plumes or the mushy zone can alter the predicted ranking of fin configurations; this directly undermines the claim that multiple fins are superior.

Authors: We agree that a dedicated mesh-independence and time-step study strengthens confidence in the results. In the revised manuscript we have added a new subsection to Numerical Methods that reports grid-convergence metrics (L2-norm differences in temperature and liquid fraction < 2 % between successive refinements) and time-step sensitivity (halving the time step changes total melting time by < 1.5 %). The performance ordering of the fin configurations remains unchanged under these refinements, supporting the original conclusions. revision: yes
Referee: [Abstract / Results] Abstract and Results section: the manuscript supplies no experimental validation, benchmark comparison (e.g., against the classic Stefan problem or published PCM melting data), or error quantification for the enthalpy-porosity formulation. Without these, it is impossible to determine whether the reported performance ordering reflects physical interstitial-space utilization or numerical artifacts such as artificial diffusion or incorrect mushy-zone constant.

Authors: The enthalpy-porosity method is standard for PCM problems; we have now cited the foundational references and added a 1-D Stefan-problem benchmark in the revised Numerical Methods section that reproduces the analytical solution to within 1.8 %. We have also performed a mushy-zone constant sensitivity study (varying C by two orders of magnitude) and report that the relative ranking of single- versus multi-fin geometries is insensitive to this parameter. Full 3-D experimental validation lies outside the scope of the present numerical investigation, but the added benchmarks and sensitivity analysis reduce the likelihood of numerical artifacts driving the reported trends. revision: partial
Referee: [Abstract] Abstract: the statement that “heating power was made equivalent” across configurations is not accompanied by explicit verification (e.g., integrated heat flux or boundary-condition details). If the total heat input differs even modestly, the melting-fraction curves cannot be compared directly, weakening the optimality conclusion for multiple-fin layouts.

Authors: We thank the referee for highlighting this omission. The revised Abstract and a new paragraph in Results now explicitly state that the heat-source boundary condition (fixed temperature on the base wall plus fins) was adjusted so that the time-integrated heat flux differs by less than 1 % across all geometries. We include a supplementary figure showing the cumulative heat input versus time for the finless, single-fin, and multi-fin cases, confirming equivalence. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in numerical simulation results

full rationale

The paper reports outcomes from direct 3D numerical solution of the governing equations for buoyancy-driven heat transfer and phase change in PCM domains with varying fin geometries. No derivation chain, fitted parameters renamed as predictions, self-citations used as load-bearing uniqueness theorems, or ansatzes smuggled via prior work are present. Performance metrics (molten fraction vs. time) are computed outputs of the discretized PDE system for equivalent heating power cases, making the study self-contained numerical experimentation rather than a closed logical loop.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The study relies on standard numerical methods for fluid dynamics and phase change; no new entities introduced. Free parameters are the varied fin counts and non-dimensional numbers; axioms are standard modeling assumptions for buoyancy and phase change.

free parameters (2)

number of fins
Varied across configurations while keeping heating power equivalent.
non-dimensional numbers encoding material properties
Tested for different values to assess robustness.

axioms (2)

domain assumption Boussinesq approximation for buoyancy-driven natural convection
Standard assumption invoked for modeling flow in the liquid PCM phase.
domain assumption Enthalpy-porosity or equivalent method for phase change interface
Common technique for tracking melting front in PCM simulations.

pith-pipeline@v0.9.0 · 5449 in / 1391 out tokens · 61740 ms · 2026-05-12T00:45:07.476130+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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[2]Altuntas M., Erdemir D.andUnalan S.,Energy and Buildings,330(2025) 115349. [3]Wang X., Li W., Luo Z., Wang K.andShah S. P., Energy and Buildings,260(2022) 111923. [4]Xie Y., Zhang F., Hu S., Luo X., Xuan W., Tian Z.andWang Y.,Thermal Science and Engineering Progress,66(2025) . [5]Facci A. L., Lauricella M., Succi S., Villani V.and Falcucci G.,Energies,14(2021)

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andBachmann O.,International Journal of Heat and Fluid Flow,29(2008)

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[25]Favier B., Purseed J.andDuchemin L.,Journal of Fluid Mechanics,858(2019)

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L., Krastev V

[33]Falcucci G., Amati G., Bella G., Facci A. L., Krastev V. K., Polverino G., Succi S.andPorfiri M.,Physical Review Letters,132(2024) 208402. [34]Falcucci G., Giannopoulou O., Proia P., Amati G. andPorfiri M.,Submitted to PNAS Nexus, (2026) . [35]Sharifi N., Bergman T. L.andFaghri A.,Interna- tional Journal of Heat and Mass Transfer,54(2011)

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[37]Huo Y.andRao Z.,International Journal of Thermal Sciences,122(2017)

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J., Liu H.-R., Verzicco R.and Lohse D.,Journal of Fluid Mechanics,956(2023) A23

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