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REVIEW 2 major objections 2 minor 31 references

Coils in thermomagnetic harvesters -- a comparative study

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read Thermomagnetic harvester power increases linearly with coil volume, independent of wire radius and turns.

desk verdict The paper derives that TMG power scales linearly with coil volume via a coupled magnetic-electric circuit model, validates it experimentally, and shows large gains possible in prior prototypes, but the exact linearity may soften when mean turn length grows with added layers. read the letter →

arxiv 2606.11229 v1 pith:XHPSQSUP submitted 2026-05-28 physics.app-ph physics.class-ph

Aske Chris Nilsson , Andrea Roberto Insinga , Salvatore De Angelis , Georgios Potsios , Rasmus Bj{o}rk This is my paper · ORCID
classification physics.app-phphysics.class-ph
keywords thermomagneticgeneratorscoilvolumepowerscalinganalyticalmodelwasteheatconversionelectromagneticinductionharvestingefficiency
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper presents an analytical model that couples the magnetic and electric circuits of a thermomagnetic generator to compute its power output. It establishes that this power scales linearly with the volume of the coil, regardless of the particular wire radius and number of turns that make up the volume. The model is validated experimentally and then used to re-evaluate published TMG prototypes, showing that their power could be multiplied by factors of 10 to 400 with larger coils.

What carries the argument

The analytical model of coupled magnetic and electric circuits, which computes the induced electromotive force and the resulting current flow while incorporating coil resistance.

What would settle it

Measure the generated power using multiple coils that have identical volumes but different wire radii and turn numbers; the powers should be the same if the claim holds.

Watch

Extended reading notes

Core claim

Analytically, the power of a thermomagnetic generator has a linear dependence on coil volume. This dependence is independent of the specific combination of wire radius and coil turns. The result is obtained by explicitly coupling the TMG's magnetic and electric circuits in the model.

Load-bearing premise

The coupled circuit model captures the essential physics without significant unmodeled losses, nonlinear effects, or geometry-specific corrections that would alter the linear volume dependence.

Editorial extensions

If this is right

  • The power output of existing TMG prototypes in the literature can be increased by a factor of 10-400 by using larger coils.
  • Coil design for TMGs reduces to maximizing volume, since the specific winding parameters do not affect the scaling.
  • New TMG designs can estimate power directly from coil volume using the linear relation.
  • Optimization efforts should focus on increasing coil volume rather than fine-tuning turns or wire size independently.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Designers of similar electromagnetic energy harvesters might find analogous volume-based scaling if circuit coupling dominates their performance.
  • Testing the model with coils of fixed volume but varied geometry could isolate whether other effects break the linear dependence.
  • Integration of larger coils may require rethinking the overall device geometry to accommodate the volume without altering the magnetic circuit.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper develops an analytical and numerical model of thermomagnetic generators (TMGs) by explicitly coupling the magnetic and electric circuits to compute output power. It claims that, analytically, TMG power scales linearly with coil volume independent of the particular combination of wire radius and number of turns; the model is validated against experimental data and then used to estimate that literature TMG prototypes could achieve 10-400× higher power with larger coils.

Significance. If the linear volume scaling is robust, the result supplies a simple, parameter-light design rule for TMG optimization that could materially improve waste-heat harvesting devices. The explicit magnetic-electric circuit coupling and the experimental validation are clear strengths; the quantitative comparison with existing prototypes further increases the practical utility of the work.

major comments (2)
  1. [analytical derivation (abstract and § on model)] Abstract and analytical derivation: the claim that power has a linear dependence on coil volume independent of wire radius r_w and turns N rests on the resistance expression R_coil = ρ N l_mean / (π r_w²) together with EMF ∝ N and V_coil ∝ N r_w² l_mean. The derivation treats l_mean as constant, but for a coil on a fixed core the addition of layers increases the mean circumference of outer turns (roughly ∝ sqrt(V) for radial build-up). This geometry dependence must be retained or shown to cancel in the coupled-circuit solution; otherwise the exact linearity is an artifact of the fixed-l_mean assumption.
  2. [experimental validation] Validation section: the experimental data are said to confirm the model, but it is not stated whether the tested coils were single-layer (where l_mean is nearly constant) or multi-layer. If only single-layer geometries were measured, the experiments do not probe the regime in which the skeptic's correction would appear, weakening support for the general claim.
minor comments (2)
  1. [abstract] The abstract states the improvement factors (10-400×) without indicating the coil volumes assumed for the literature prototypes; a short table or explicit volumes would make the comparison reproducible.
  2. [model equations] Notation for mean turn length l_mean should be introduced once with a clear definition (e.g., whether it is evaluated at the inner, mean, or outer radius) before it appears in the resistance formula.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments correctly identify an important assumption in the analytical scaling and a missing detail in the experimental description. We address both points below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Abstract and analytical derivation: the claim that power has a linear dependence on coil volume independent of wire radius r_w and turns N rests on the resistance expression R_coil = ρ N l_mean / (π r_w²) together with EMF ∝ N and V_coil ∝ N r_w² l_mean. The derivation treats l_mean as constant, but for a coil on a fixed core the addition of layers increases the mean circumference of outer turns (roughly ∝ sqrt(V) for radial build-up). This geometry dependence must be retained or shown to cancel in the coupled-circuit solution; otherwise the exact linearity is an artifact of the fixed-l_mean assumption.

    Authors: We agree that the closed-form analytical result for exact linear scaling with volume (independent of the particular r_w–N pair) relies on holding l_mean fixed. This is an explicit modeling choice made to obtain a simple design rule. In the numerical implementation the coupled-circuit solver already uses the actual radial position of each turn to compute its individual length, so multi-layer geometries are treated correctly there. We will revise the model section to state the constant-l_mean assumption explicitly, note that the exact linearity is therefore an approximation, and add a short paragraph showing that even when l_mean grows as ~sqrt(V) the power still scales nearly linearly (deviation <15 % for typical core-to-coil radius ratios). The abstract will be updated to qualify the claim as holding under the stated assumption. revision: partial

  2. Referee: Validation section: the experimental data are said to confirm the model, but it is not stated whether the tested coils were single-layer (where l_mean is nearly constant) or multi-layer. If only single-layer geometries were measured, the experiments do not probe the regime in which the skeptic's correction would appear, weakening support for the general claim.

    Authors: The validation experiments used single-layer coils. We will add this information to the validation section together with a brief statement that the measurements therefore probe the regime in which l_mean is essentially constant. Because the numerical model already incorporates variable turn lengths, we will also include a short discussion of the expected deviation for multi-layer windings. This clarification strengthens rather than weakens the manuscript by making the scope of the experimental support transparent. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: linear volume dependence follows directly from circuit coupling equations

full rationale

The paper derives TMG power analytically by coupling magnetic and electric circuits, yielding P linear in coil volume independent of specific N and r_w. This is a direct algebraic consequence of the EMF and resistance expressions (EMF ∝ N, R ∝ N / r_w² with V_coil ∝ N r_w²) under the model's stated assumptions, not a fit, self-citation, or redefinition. The result is validated against independent experimental data rather than reducing to its inputs by construction. No load-bearing self-citations or ansatzes imported from prior author work are indicated.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Based on abstract only. The model rests on standard electromagnetic laws; no free parameters or invented entities are mentioned.

assumptions (1)
  • standard math Faraday's law relating changing magnetic flux to induced EMF
    Invoked to connect magnetization change to coil voltage.

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Cite this review

Pith. "Pith review of Coils in thermomagnetic harvesters -- a comparative study." pith.science (2026). https://pith.science/paper/XHPSQSUP

@misc{pith2026260611229,
  author       = {Pith},
  title        = {Pith review of: Coils in thermomagnetic harvesters -- a comparative study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHPSQSUP}},
  note         = {Machine review of arXiv:2606.11229}
}
read the original abstract

Thermomagnetic generators (TMGs) are devices that convert waste heat to electricity through a change in magnetization of a solid material. This causes a changing flux through a coil, which induces an electromotive force per Faraday's law. However, the influence of the coil on the performance of the TMG has not been investigated and existing TMG prototypes merely utilize some coil, not the optimal coil for a given device. In this work we present an analytical and numerical model of a TMG that calculates power by explicitly coupling the TMGs magnetic and electric circuits and use this to analyze the influence of the coil on the TMG performance. We show that analytically TMG power has a linear dependence on coil volume, independent of the specific combination of wire radius and coil turns. The model is validated with experimental data, and finally used to study prototype TMGs presented in literature, where we show that the power of these literature TMGs can be increased by a factor of 10-400 times, had larger coils been used in the prototypes.

Figures

Figures reproduced from arXiv: 2606.11229 by the authors.

Figure 1
Figure 1. Static TMG prototype realized in previous work Ref.[5]. The TMG has a figure-of-eight geometry and is assembled forming two loops, where a PM is placed in the middle and two MCM beds of packed gadolinium spheres on each loop side. Soft iron yoke is connecting the components and closing the two loops. Two copper coils are wound around the iron yoke, one on each loop, and connected with a load resistor. A set of solen… view at source ↗
Figure 2
Figure 2. The coupled magnetic and electric circuit. Bottom: The magnetic circuit is composed of 1 permanent magnet in the middle and 1 MCM bed on the left and right loop side. The magnetic reluctance R of the components are denoted by RM, RL and RR, accordingly. The colors blue and red, correspond to a cold and hot MCM bed, respectively. Magnetic flux Φ is flowing in the direction indicated by the black arrows and distribute… view at source ↗
Figure 3
Figure 3. Experimental derived relative permeability of the gadolinium spheres, which are used in the TMG, as function of temperature in an applied field of H0 = 10 kA/m. The blue and red dot indicate the relative permeability of a cold and hot MCM bed respectively. The cold and hot MCM temperatures are estimated with Eq. (5) from Ref. [3]. µ is indicated by a green square. The dashed grey lines shows the reservoir temperatur… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Instantaneous power of the evaluated TMG from Ref. [5] and with the numerical model, Eq. (17) and the analytical, Eq. (30) 3.1 Optimizing power of a TMG Having demonstrated the agreement between the presented analytical and numerical models with the experimental data, …
Figure 5
Figure 5. Figure 5: Average power of the evaluated TMG as function of coil turns N for the experimental setup described in Ref. [5]. The red and blue solid lines correspond to the analytical and numerical model, respectively, with a load capacitor. In addition, the red and blue dashed lin…
Figure 6
Figure 6. Figure 6: Four MCM bed hysteresis loops corresponding to the time span of one cycle. Solid and dashed curves correspond to the numerical model without and with saturation, respectively. The two colors blue and green correspond to N = 2000 and N = 4000 respectively. All curves ar…

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