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[The-Anh Nguyen](https://orcid.org/0000-0002-5694-759X), [Naoto Kakuta](https://orcid.org/0000-0002-3303-3955), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Hosei Nagano](https://orcid.org/0000-0003-4926-2768)

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[Near-infrared imaging of heat transfer behavior between gadolinium and fluid during magnetization/demagnetization process of magnetocaloric effect](https://mdr.nims.go.jp/datasets/5743b662-2852-414b-bc45-be5f582f6156)

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Near-infrared imaging of heat transfer behavior between gadolinium and fluid during magnetization/demagnetization process of magnetocaloric effectViewOnlineExportCitationRESEARCH ARTICLE |  MAY 15 2024Near-infrared imaging of heat transfer behavior betweengadolinium and fluid during magnetization/demagnetizationprocess of magnetocaloric effectSpecial Collection: Multicalorics IIThe-Anh Nguyen  ; Naoto Kakuta  ; Ken-ichi Uchida  ; Hosei Nagano  J. Appl. Phys. 135, 193904 (2024)https://doi.org/10.1063/5.0207290 CHORUS 27 May 2024 04:18:20https://pubs.aip.org/aip/jap/article/135/19/193904/3293843/Near-infrared-imaging-of-heat-transfer-behaviorhttps://pubs.aip.org/aip/jap/article/135/19/193904/3293843/Near-infrared-imaging-of-heat-transfer-behavior?pdfCoverIconEvent=citehttps://pubs.aip.org/jap/collection/387022/Multicalorics-IIjavascript:;https://orcid.org/0000-0002-5694-759Xjavascript:;https://orcid.org/0000-0002-3303-3955javascript:;https://orcid.org/0000-0001-7680-3051javascript:;https://orcid.org/0000-0003-4926-2768https://crossmark.crossref.org/dialog/?doi=10.1063/5.0207290&domain=pdf&date_stamp=2024-05-15https://doi.org/10.1063/5.0207290https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0207290/19953182/193904_1_5.0207290.am.pdfhttps://servedbyadbutler.com/redirect.spark?MID=176720&plid=2372057&setID=592934&channelID=0&CID=872259&banID=521836438&PID=0&textadID=0&tc=1&scheduleID=2290742&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&matches=%5B%22inurl%3A%5C%2Fjap%22%5D&mt=1716783500726260&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0207290%2F19953181%2F193904_1_5.0207290.pdf&hc=ed62578b7566033eacd18bfa3e7bd6d03767595b&location=Near-infrared imaging of heat transfer behaviorbetween gadolinium and fluid duringmagnetization/demagnetization processof magnetocaloric effectCite as: J. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290View Online Export Citation CrossMarkSubmitted: 7 March 2024 · Accepted: 2 May 2024 ·Published Online: 15 May 2024The-Anh Nguyen,1 Naoto Kakuta,2 Ken-ichi Uchida,3 and Hosei Nagano1,aAFFILIATIONS1Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8601, Japan2Department of Mechanical Systems Engineering, Tokyo Metropolitan University, Tokyo 191-0065, Japan3National Institute for Materials Science, Tsukuba 305-0047, JapanNote: This paper is part of the special topic, Multicalorics II.a)Author to whom correspondence should be addressed: nagano@mech.nagoya-u.ac.jpABSTRACTThis paper reports on the application of a near-infrared (NIR) imaging system for visualizing heat transfer dynamics from a bulkgadolinium (Gd) sample to the surrounding water during the magnetization/demagnetization process of the magnetocaloric effect (MCE).The suggested approach relied on the spectral variation in water absorption band at 1150 nm wavelength within the NIR spectrum. An experi-mental setup integrated a telecentric uniform-illumination system, a halogen lamp, and an NIR camera to enable real-time monitoring of asingle magnetization and demagnetization cycle induced by an external magnetic field, which was generated by a permanent-magnet-basedmagnetic circuit. Two-dimensional absorbance images captured during this cycle clearly depicted the thermal energy generated by the MCEin water. Furthermore, an analysis of the thermal boundary layer and the quantification of heat transfer from Gd to water provided insightsinto the dynamics over time. These results indicated the potential of our NIR imaging techniques in optimizing thermal–fluid interactionswithin MCE systems, thereby improving the design and efficiency of magnetic refrigeration systems.© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0207290I. INTRODUCTIONMagnetic refrigeration has developed rapidly during the pastthree decades as an alternative to vapor compression technologybecause of its potential from both energy and environmentalviewpoints.1–4 It is a type of solid-state cooling technology thatdoes not use evaporative coolant or mechanical compressors.Specifically, the attained efficiency of this system can reach up to60% without the need for detrimental fluids.5 Magnetocaloric effect(MCE) relies on specific magnetocaloric materials that exhibit tem-perature changes in response to fluctuations in a magnetic field. Inrecent years, a large number of magnetocaloric materials haveemerged as potential candidates for MCE applications, including(Mn,Fe)2P,6 MnAs,7,8 polymer-bonded La(Fe,Si)13 composites,9,10Ni-Mn-based Heusler alloys,11,12 or La0.8Sr0.2MnO3/La0.7Ca0.3MnO3bilayer films,13 besides the well-established benchmark material, gad-olinium (Gd). The MCE is directly related to the magnetic momentswithin magnetocaloric materials, where the changes in the magneticfield cause these moments to align (entropy decreasing) or disperse(entropy increasing), leading to the generation or absorption of heat[Fig. 1(a)]. One prevalent MCE-based refrigeration technology is theactive magnetic refrigeration (AMR), which incorporates the regener-ator (such as a parallel plate, a bed of powdered material, or a pinarray, all composed of magnetocaloric materials), magnetic fieldsource, heat transfer fluid, and heat exchanger. As illustrated inFig. 1(b), the AMR system undergoes cyclic magnetization anddemagnetization of the magnetocaloric material through the appliedJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-1© Author(s) 2024 27 May 2024 04:18:20https://doi.org/10.1063/5.0207290https://doi.org/10.1063/5.0207290https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0207290http://crossmark.crossref.org/dialog/?doi=10.1063/5.0207290&domain=pdf&date_stamp=2024-05-15https://orcid.org/0000-0002-5694-759Xhttps://orcid.org/0000-0002-3303-3955https://orcid.org/0000-0001-7680-3051https://orcid.org/0000-0003-4926-2768mailto:nagano@mech.nagoya-u.ac.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0207290https://pubs.aip.org/aip/japmagnetic field. During magnetization, the fluid flows from thecold reservoir to the hot, dissipating heat to the surroundings.Subsequently, during demagnetization, as the applied field dimin-ishes, the temperature of the material decreases. At this stage, thereis a flow of the fluid from the hot reservoir to the cold, accepting acooling load. Enhancing how heat moves between the magneto-caloric material and the surrounding fluid, known as thermal–fluidinteraction, is crucial for developing better cooling systems. Forinstance, efficient interaction ensures complete heat removal fromthe magnetocaloric material during demagnetization, allowing it toabsorb more heat in the subsequent magnetization state, resulting inaccelerated cooling. Therefore, much research efforts have beendirected toward this aspect in recent years to optimize AMR systemsfor real-world applications.A growing number of publications focused on numericalmodels to describe thermal–fluid interaction, mainly in packed-bedand parallel-plate AMR. In the case of the former, Nemec andLevec14 and du Toit15 found that the ratio between the outer AMRdimensions and the particle diameter significantly influenced theheat transfer effectiveness. Furthermore, Tusek et al.16 highlightedthat the interplay between heat and fluid dynamics primarilydepends on the geometry of AMR and the fluid flow rate; this hasalso been demonstrated in the case of parallel-plate AMR.17–20Nielsen et al.18,21 have contributed significantly by developing atechnique to estimate the Nusselt scaling factor, offering valuableinsights into the relationship between the effective Nusselt numberof a specific regenerator and the ideal Nusselt number of a uni-formly distributed one. Experimental studies have also been con-ducted to validate the findings, involving the thermocouplemeasurement of temperature spans between hot and coldAMRs.16,22,23 While previous works have made substantial progressin assessing the overall efficiency of AMRs, an experimentalresearch gap exists in comprehensively understanding the interac-tion between the heat transfer fluid and the magnetocaloric mate-rial, which holds the potential for efficiency enhancements.Addressing this limitation necessitates an exploration of transientspatial-resolved data, offering insights into localized heat transferbehaviors and potential areas for improvement. However, onlya few studies have delved into this area. Lei et al.24 utilized aMach–Zehnder interferometer to delineate the dynamics of stag-nant fluid behavior within the thermal boundary layer. Althoughthis study provided valuable insights, it is important to acknowl-edge the challenges associated with the precise alignment of opticalcomponents in the Mach–Zehnder interferometer technique, aswell as the ability to measure the time-dependent changes in heattransfer rate due to the MCE, both of which remain open areas forfurther investigation and exploration. To initiate our exploration inthis field of research, we employ a promising method known as anear-infrared (NIR) imaging method, which relies on thetemperature-dependent absorption band of water in the NIRregion. This method operates via transmission and furnishesaverage temperature assessments along the optical path withinwater or aqueous solutions. This characteristic makes it suitable forapplications where surface measurements are insufficient, allowingthe study of the temperature distribution inside the medium andproviding more detailed and comprehensive data. Previous studieshave confirmed the effectiveness of this method in measuring thetemperature of the water and aqueous solutions near variousobjects without the need for adiabatic conditions, such as thinmetal wires,25 steel spheres,26,27 micro-magnetic particle layers,28and microfluidic channels,29 achieving a high temperature resolu-tion of better than 0.2 K.This study aims to establish and validate the NIR imagingsystem capable of visualizing the heat development from themagnetocaloric material to its surrounding water environment.The experimental setup involved employing a telecentric uniform-illumination system, with the magnetocaloric material beingsubjected to a magnetization/demagnetization cycle induced by apermanent magnet. The specific magnetocaloric material used inthis study was pure Gd slab. Absorbance images at a wavelength of1150 nm obtained during this cycle were analyzed to derivetemperature data, which in turn were utilized for calorimetryFIG. 1. (a) Magnetocaloric effect (MCE) definition and (b) the schematic of the active magnetic refrigeration (AMR).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-2© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japcalculations to determine the heat transferred to water. We furtherdiscussed the temporal behavior of the thermal boundary layerthickness and heat transfer rate, providing insights for futureresearch directions. The novelty of this study lies in its use of asimple optical imaging configuration, which not only enables real-time monitoring of thermal energy distribution in the heat transferfluid but also allows for a quantitative assessment of how heattransfer rates evolve over time in the MCE.Sections II–VI of this paper are organized as follows. InSec. II, we explain the principles of the NIR temperature imagingtechnique. Section III describes the experimental methodology, out-lining the specific procedures and equipment for data collection. InSec. IV, visual and quantitative findings from the magnetizationand demagnetization processes are presented and analyzed. Thediscussion on heat transfer is thoroughly explored in Sec. V.Finally, Sec. VI summarizes this study.II. VARIATIONS IN THE NIR ABSORPTION BAND OFWATER WITH TEMPERATUREOur previous papers detailed the temperature-related changesin the NIR absorption spectrum of water.25–27,30 Hence, we providea concise overview of the theory below. Water molecules exhibitthree vibration modes: symmetric stretching (ν1), symmetricbending (ν2), and asymmetric stretching (ν3) of the covalent bonds,each characterized by an absorption peak specific to its distinct fre-quency [Fig. 2(a)]. The bands detected in the NIR wavelengthrange (800–2500 nm) solely arise from overtones and combinationsof these three modes. These encompass not just basic combinationslike ν1 + ν2 but also higher-order combinations such as ν1 + 2ν2.31In spectroscopy, the vibration frequency correlates with theabsorbed light wavelength. The presence of hydrogen bondsreduces the vibration frequency, shifting the absorption peaktoward longer wavelengths in the spectrum. With an increase intemperature, the number of hydrogen bonds decreases, leading to ashift of the absorption band toward shorter wavelengths.To quantify the amount of light absorbed by a substance at aparticular wavelength and temperature, the absorbance, A, and theabsorbance difference, ΔA, are used as follows:A(λ, T) ¼ �log10I(λ , T)I0(λ), (1)ΔA(λ, T) ¼ A(λ, T)� Ar(λ, T) ¼ �log10I(λ, T)Ir(λ, T), (2)where λ is the wavelength of light, T is the temperature of water,and I and I0 are the intensities of the incident and transmittedlight, respectively. Ir is the intensity of transmitted light at a refer-ence state (16.0 °C). Figure 2(b) shows the ΔA spectra (on the leftvertical axis) over the temperature range from 16.0 to 44.0 °C witha 2.0 °C increment, where 16.0 °C is Ar. These spectra were aroundthe wavelength range from 1100 to 1250 nm, corresponding to thecombination of ν1, ν2, and ν3 (ν1 + ν2 + ν3). At approximately 1150,1193, and 1240 nm (illustrated by dotted lines), there are observ-able positive peaks, an isosbestic point (ΔA remains constantregardless of temperature), and negative peaks, respectively. Weselected the 1150 nm wavelength for temperature imaging in thisstudy due to its highest sensitivity to temperature changes withinthis wavelength range. The images were detected using a narrow-bandpass filter with a 10 nm bandwidth, with details provided inSec. III. Furthermore, the spectrum presented in Fig. 2(b) isoptimal for water layers with an optical path length ranging from 5to 20 mm. Specifically, detection becomes saturated when the thick-ness is below 5 mm and becomes undetectable beyond 20 mm.However, because the various water absorption bands differ inmagnitude, they can be selectively employed depending on thethickness. For instance, when the thickness falls between 0.2 and2 mm, it is preferable to utilize the absorption band resulting fromthe combination of ν1 and ν3 (found within the wavelength rangeof 1350–1500 nm), as it possesses a higher absorption coefficientcompared to the ν1 + ν2 + ν3 absorption band.28III. EXPERIMENTAL DETAILSA. Sample preparationThe measurement sample involved the use of Gd, a commonlyutilized material in AMR systems, and a quartz cell with innerdimensions of 30 × 10 × 45mm3 (the optical path length is 10 mm),as shown in Fig. 3(a). The advantages of Gd-based alloys lie intheir well-defined properties and high MCE near room tempera-ture. A commercial-grade rectangular prism of Gd (Neco-DyUmn,Japan) measuring 5 × 10 × 5mm3 was prepared and polished usingan automatic polishing machine (MA-150; Musashino DenshiCorp., Tokyo, Japan) [Fig. 3(a)]. This prism was affixed to thecentral rectangular hole of a plastic holder and securely bonded tothe bottom surface of the quartz cuvette. Distilled water wasinjected into the cuvette using a syringe with a total volume of6 ml. The cuvette was then covered with a plastic cap. The initialwater temperature was set to 20 °C, matching the roomFIG. 2. (a) Three fundamental vibrational modes of water and their wavenum-bers. (b) Absorbance difference spectra, ΔA(λ) (left scale) for a 10-mm thickwater sample across temperatures ranging from 16.0 to 40.0 °C in 4.0 K inter-vals (the absorbance at 16.0 °C serves as the reference) and transmittancespectrum (right scale) of the narrow-bandpass filter.26Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-3© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japtemperature. During the experiment (approximately 200 s), theroom temperature was carefully monitored and maintained at 20 °Cusing a standard air conditioner. The high heat capacity of thewater ensured that its average temperature remained close to theinitial 20 °C throughout the experiment.B. ApparatusFigures 3(b) and 3(c) show a schematic and a photo of theimaging setup. A halogen lamp (FHL-102; Asahi Spectra, Japan)emitted light along the x axis, passing through a telecentric back-light illuminator composed of a 1X collimator lens (RLQL80-1;Asahi Spectra, Japan) and a telecentric lens unit (TOU-1-31; AsahiSpectra, Japan); this system increased the edge contrast of thesample and made the light parallel and homogeneous within a31 × 31mm2 area. The narrow-bandpass filter (65–785; EdmondOptics) allowed light at λ = 1150 nm to be incorporated into thefilter wheel. The light beam was detected using an InGaAs short-wave infrared camera (Goldeye G-033 TEC1; Allied Vision,Canada). The camera has a pixel pitch of 15 × 15 μm2 and a 640(horizontal) × 512 (vertical) pixels. The auto-brightness functional-ity in the NIR camera settings was adjusted dynamically fromframe to frame. To prevent perspective errors, we used a telecentriclens system with a 0.36× magnification (58–257; Edmond Optics),which was positioned between the sample and the camera, main-taining spatial resolution at about 40 μm based on pixel size andmagnification.A U-shaped magnetic circuit was used to generate a magneticfield comprising two Nd–Fe–B permanent magnets (NirokuSeisakusho Co., Ltd., Japan) and a ferromagnetic yoke. The gapbetween the Nd–Fe–B magnets is 38 mm, and the dimensions ofthe magnetic poles are 101.6 × 65.8 mm2. A Tesla meter (MG-801;Magna, Japan) was utilized to evaluate and visualize the externalmagnetic flux density distribution, μ0Hext within this air gap, whereHext is the applied external field and μ0 is the vacuum permeability.The results are mapped in the inset in Fig. 3(b). This magneticcircuit was installed on an electric actuator slider with a step motorto create a linear reciprocation motion. The sample (described inSec. III A) was hung on a steel frame 15mm above the optical table.In consideration of the four states of the MCE, detailed inSec. I, the experimental process involved four primary stages.(1) Magnetization: The magnet was accelerated toward the sampleutilizing the electric actuator; the initiation of movementmarked the time origin, t = 0. It took approximately 0.5 s forthe sample to reach the center of the two poles, where a mag-netic field of up to 0.56 T was generated [as illustrated in theinset of Fig. 3(b)].(2) Heat rejection: Sustaining the magnetic field for 100 s allowedthe sample to attain thermal equilibrium with the surroundings.(3) Demagnetization: The magnetic field was gradually reducedfrom 0.56 T to zero by retracting the magnet from the sampleat the same speed employed during the magnetization process.(4) Heat absorption: The magnet was propelled away from thesample and subsequently returned to its original position.A software (Vimba; Allied Vision, Canada) was utilized tocapture a real-time sequence of twelve-bit digital images, compris-ing multiple frames at a rate of 30 frames per second, saved in theFIG. 3. (a) Dimensions of a water cuvette and a rectangular prism of gadolinium (Gd). (b) Schematic of the experimental apparatus. The inset shows the magnetic fluxdensity. (c) Photograph of the experimental device.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-4© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japtiff format. MATLAB R2023a (MathWorks, MA, USA) was usedfor the subsequent image analysis.Before the MCE measurement, we confirmed that the magneticfield does not affect the water in this study. This verification is vitaldue to the Moses effect, wherein the surface of a diamagnetic liquidundergoes distortion when exposed to a magnetic field. Since wateris diamagnetic, exposing it to a magnetic field of significant strengthcan influence the behavior of water molecules, especially in terms oftheir vibrational states and interactions. This influence can result inobservable changes in the NIR spectrum due to modifications in themolecular vibrations or their responses to the magnetic field.32,33The procedure and results are shown in Appendix.IV. TIME-DEPENDENT MAGNETIZATION/DEMAGNETIZATION IMAGINGA. 2D temperature distribution estimationThe light intensity image detected by the NIR camera aftertransmitting to the narrow-bandpass filter at λ = 1150 nm, If (x, z),is expressed as follows:If (x, z) ¼ðλ2λ1τ(λ)I(λ; x, z)dλ¼ðλ2λ1τ(λ)I0(λ; x, z)� 10�A(λ;x, z)� �dλ, (3)where τ(λ) is the transmittance spectrum of the narrow-bandpassfilter [depicted on the right vertical axis in Fig. 2(b)]. λ1 and λ2denote the minimum and maximum wavelengths of the narrow-bandpass filter, respectively. Then, the absorbance difference image forthis filtered measurement is defined in the same manner as Eq. (2),ΔAf (x, z) ¼ �log10If (x, z)I f ,r(x, z), (4)where I f ,r(x, z) is the reference for If (x, z), and it was acquired byaveraging 50 frames before starting the MCE measurement. Based onthe proportional relationship between T and A, along with theFIG. 4. (a) ΔAf (x, z) images and (b) enlargement of ΔTm(x, z) in the red dashed rectangle in (a) during heating mode.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-5© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japassumption of uniform temperature along the light path (the meanvalue), the temperature difference, ΔTm, images can be determined asfollows:ΔTm(x, z) ¼ ΔAf (x, z)αd, (5)where d is the optical path length and α is the temperature coefficient,which has a value of 2.76 × 10−4 K−1 mm−1 at 1150 nm.34 To enhancethe quality of the data by mitigating noise or fluctuations, we achievedspatial smoothing through a 3 × 3 mean filter, while temporal smooth-ing employed an 11-point fifth-order Savitzky–Golay filter.B. ResultsThe magnetization state was examined by observing asequence of ΔAf (x, z) images capturing the application of a mag-netic field to Gd over a duration of 100 s, as shown in Fig. 4(a).Due to the backlight illumination used in this experimental setup,small debris particles in the water cast shadows with lower intensityvalues, indicating higher absorbance values compared to their sur-roundings. These were observed as certain bright dots in theimages. Additionally, the presence of black dots was attributed tostatic artifacts resulting from light scattered by dust particles on thesurface of the cuvette. To provide a detailed view of the thermaldistribution within the water during the magnetization state,enlarged 2D temperature estimation images, ΔTm(x, z) wereobtained using Eq. (5) [Fig. 4(b)]. As the magnet approached theGd sample at t = 0.3 s, causing alignment of magnetic moments,the temperature of the Gd rose, initiating heat transfer from Gd tothe water. This heat transfer continued, gradually increasing thetemperature of the water. Following the peak at t = 0.9 s, thetemperature gradually began to decrease toward ambient conditionsdue to thermal dissipation. This state demonstrated a steadydecrease in temperature, eventually reaching thermal equilibriumaround t = 63.5 s. No further temperature changes were observed atthis point, indicating that the heat exchange rate with the surround-ings balanced the heat generation rate within the material.Figures 5(a) and 5(b) depict ΔTm(z) plots at different positionsand time points within the water region. In Fig. 5(a), the ΔTm(z)profiles at the central axis (x = 0mm) exhibited a notable increasenear the vicinity of the Gd surface at t = 0.3 s, reaching a maximumat 1.38 K by t = 0.9 s, and gradually diminishing to zero byt = 63.5 s due to heat loss to the surrounding water. Additionally,the observed decrease in ΔTm with increasing distance from Gd val-idated heat diffusion from the source. Abnormal peak values, e.g.,z = 1mm, were observed and attributed to the presence of dust par-ticles; these particles dispersed over time due to temperature gradi-ents. It is noteworthy that the observed peak ΔTm (1.38 K) closelyapproximated 81% of the expected maximum value of the adiabatictemperature change in pure Gd reported by Almeida et al.,35within an external magnetic field of 0.6 T. This deviation can beattributed to two factors. First, the orthorhombic prism shape ofthe Gd sample utilized in our experiment may have influenced theinternal magnetic field within the material, resulting in a reductioncompared to the externally applied field.36,37 Second, the dynamicsof heat transfer between Gd and the surrounding water, as dis-cussed in Sec. V, contributed to reducing the temperature changeexperienced by Gd.In Fig. 5(b), ΔTm(z) across five positions along the x axis(x =−5, −2.5, 0, 2.5, and 5 mm) at t = 0.9 s and t = 3.3 s, respec-tively, were examined. Notably, the peak ΔTm(z) values were nearlyidentical at all five positions, measuring approximately 1.3 K att = 0.9 s and 0.65 K at t = 3.3 s. This uniformity suggested consistentFIG. 5. Vertical line profiles of ΔTm(z) and their fitting curves (4th-order polynomial function) in the water region at (a) the central axis (x = 0 mm) and (b) five positionsalong the x axis (x =−5, −2.5, 0, 2.5, and 5 mm) at t = 0.9 and 3.3 s, respectively.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-6© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japthermal behavior within the water region, implying a likelyuniform temperature distribution across the Gd surface. The slightdiscrepancy among the plots and curves at t = 0.9 and 3.3 s furtheremphasized the predominance of thermal conduction in theprocess.Figure 6 illustrates the demagnetization state, where thegradual reduction of the magnetic field applied to Gd is accompa-nied by a decrease in its temperature. This observed temperaturedrop was a direct consequence of the magnetic moments returningto their random orientation. As they relaxed, the previouslyabsorbed energy was released back into the surroundings, primarilyin the form of heat transferred to the water. This heat transfereffectively lowered the internal energy of Gd, resulting in itscooling. Similar to the magnetization process, vertical line profilesof ΔTm(z) at various positions along the x axis and different timepoints were utilized to provide quantitative insights into the tempo-ral variations, as shown in Fig. 7. In Fig. 7(a), following the with-drawal of the magnetic field from Gd at t = 100.3 s, an immediatedecrease in temperature near the Gd surface was observed,ΔTm =−0.79 K. This was followed by a further drop of 0.48 K overthe subsequent 0.6 s, reaching a maximum ΔTm =−1.27 K. As Gdlost thermal energy to the water, it began to warm up again due toheat exchange with the surroundings. This increasing trend contin-ued until thermal equilibrium was reached around t = 163.5 s,where the temperature stabilized. In Fig. 7(b), five vertical ΔTm(z)profiles (x =−5, −2.5, 0, 2.5, and 5 mm) at t = 100.9 s andt = 103.3 s exhibited almost identical behavior within each timepoint. These findings underscored the continued dominance ofthermal conduction in the demagnetization state, mirroring thefindings from the magnetization state.Figure 8 shows the comparison plot between the average tem-perature difference near the vicinity of the Gd surface, ΔTs, and thetemperature difference at the center of the Gd surface recorded bya T-type thermocouple, ΔTc. Based on the discussion in Figs. 5(b)and 7(b), we can derive the values of ΔTs using an averaging calcu-lation method,ΔTs ¼ 1WXWi ¼ 1max�ΔT im(z)�, (6)FIG. 6. (a) ΔAf (x, z) images and (b) enlargement of ΔTm(x, z) in the red dashed rectangle in (a) during cooling mode.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-7© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japwhere W is the ΔTm(x, z) image width. The comparison demon-strated a close agreement between the two data, indicating the reli-ability of our methodology. However, we observed discrepancies(up to 78 mK) in the ΔTs during the magnetic field-on and field-offstates. This irreversibility can primarily be attributed to the slowcycling process employed in the experiment, wherein the initialtemperature of Gd during demagnetization approached nearly thesame level as during magnetization. According to the reversibilityof the MCE, the adiabatic temperature changes during magnetization,ΔTad,mag, and demagnetization states, ΔTad,demag, follow the relation:ΔTad,mag(T) ¼ �ΔTad,demag(T þ ΔTad,mag(T)).38 Consequently, at thesame initial temperature (20 °C), ΔTad,mag could be slightly higherthan ΔTad,demag, consistent with this study.V. THERMAL ENERGY TRANSFER ANALYSISThe spatial-temporal temperature distribution images obtainedduring the magnetization and demagnetization states provide valu-able insights into the heat transfer dynamics within the system. Inthis section, we will focus on the thermal boundary layer develop-ment and the thermal energy transferred into the heat transferfluid, i.e., water, in the region of interest within the red dashed rect-angle (10 × 5mm2) in Figs. 4(a) and 6(a).Figure 9 shows the definition of thermal boundary layer thick-ness based on the analysis of binary images. Thermal boundarylayer refers to the region near a surface where the temperature gra-dient transitions from the boundary condition (e.g., the surfaceFIG. 7. Vertical line profiles of ΔTm(z) and their fitting curves (4th-order polynomial function) in the water region at (a) the central axis (x = 0 mm) and (b) five positionsalong the x axis (x =−5, −2.5, 0, 2.5, and 5 mm) at t = 100.9 and 103.3 s, respectively.FIG. 8. Comparison of ΔTs and ΔTc .FIG. 9. The definition of thermal boundary layer thickness using the binaryimage.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-8© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japtemperature) to the surrounding temperature. In this study, the Otsumethod was employed for thresholding, enabling the identificationof an optimal threshold that minimizes the intraclass variance ofthresholded black and white pixels.39 Subsequent to thresholding,individual images at discrete time intervals were transformed intobinary ones, B(t), with values of one and zero denoting white andblack regions, respectively. Then, the calculation of the averagethermal boundary layer thickness, �ξ, involved determining the ratiobetween the area of this layer, ψ, defined by the total count of whitepixels during magnetization and, conversely, black pixels duringdemagnetization, and the image width, W.Temporal development of �ξ during magnetization and demag-netization is plotted in Fig. 10(a). We observed that the evolutionof �ξ occurred in two distinct periods. Initially, �ξ increased graduallythroughout 13 s in both cases, with the maximum value of �ξ was2.9 and 2mm for magnetization and demagnetization, respectively.The rate of increase in �ξ depended on the thermal diffusivity of thefluid and time, consistent with previous studies on purely diffusivecases with flat-surface boundaries.30,40,41 Indeed, the inset ofFig. 10(a) demonstrates that �ξ is proportional to (κt)1/2, where κrepresents the thermal diffusivity of water. As time progressed, heatcontinued to transfer between Gd and water, leading to a decreasein �ξ. Eventually, the system achieved thermal equilibrium, with thetemperature gradient between the Gd surface and surroundingfluid becoming negligible. At this point, the boundary layer essen-tially vanished, resulting in a uniform temperature distributionFIG. 10. (a) Dependences of jQj (left scale) and �ξ (right scale) on time. The enlargement of �ξ in the black dashed rectangle with the linear fitting curves. Gradient of (b)�ξ and (c) Q over time.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-9© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/japacross the fluid. This transition in �ξ correlated with the total amountof heat transferred from Gd to water, Q [the left y axis in Fig. 10(a)];for clarity, the absolute values of Q were used to ensure that bothdatasets appear positive. This cumulative heat transfer reflects theamount of energy exchanged between Gd and water. Mathematically,we can express Q as the area-weighted average equation,Q ¼ðð ðd0ρcΔTdxdydz ¼ ρcððΔAfαdxdz¼ ρcσαXNi, jΔAijf ¼ρcχαNXNi, jΔAijf , (7)where ρ is the density and c is the specific heat at constantpressure, both assumed constant: ρ = 9.93 × 10−7 kg/mm3 andc = 4180 J/(kg K). σ is the real area corresponding to one pixel, χ isthe real area of the region of interest, N is the number of pixels, andi and j is the image pixel number in the x and z directions, respec-tively. Because of the irreversibility of this system, as explained inSec. IV B, Q was not the same in two cases; Q in demagnetizationwas smaller by approximately 25% compared to the magnetization.However, it should be noted that a thicker thermal boundarylayer or a larger amount of energy transferred to the water corre-sponded to a reduction in the temperature gradient, as illustratedin Figs. 5(a) and 7(a). This phenomenon implied that heat wastransferred over a greater distance, resulting in a slower rate of tem-perature change across that distance and, consequently, a lowertemperature gradient or heat transfer rate. Figure 10(b) shows thebehavior of the rate of change in �ξ over time, represented by thegradient, @�ξ/@t. It was observed that @�ξ/@t increased rapidly forabout 1.8 s after both magnetization and demagnetization, suggest-ing a rapid change in the thermal boundary layer and potentiallyefficient heat transfer. As time progresses beyond this initial period,the value of @�ξ/@t gradually diminished. This decline marked thepoint at which the heat began to spread more evenly throughoutthe layer rather than just transferring from the surface to the fluid.The significant transition can be referred to as the onset of heat dif-fusion, ttransition, occurred at 1.8 s for magnetization and 101.8 s fordemagnetization. Figure 10(c) shows the heat transfer rate, @Q/@t.As expected, the maximum values of @Q/@t were observed beforettransition, measuring 0.047 and −0.038W during magnetization anddemagnetization, respectively.Understanding the relationship between the thermal boundarylayer thickness and heat transfer efficiency is crucial for optimizingMCE systems, particularly in microchannel parallel-plate regenera-tors. While initially, a thicker boundary layer might increase thelocal heat transfer rate due to the larger contact area betweenthe solid surface and the fluid, it can also lead to a decrease in theoverall heat transfer rate over time due to factors like increased heattravel distance and potentially reduced temperature gradient. Thistrade-off needs careful consideration during design. Additionally,addressing flow maldistribution in these microchannels is essentialfor maintaining optimal cooling or heating performance andupholding the coefficient of performance of the MCE system, asuneven flow can create localized inefficiencies in heat transferregardless of the thermal boundary layer.42,43 This aspect will beconsidered in future research.VI. CONCLUDING REMARKSIn conclusion, we demonstrated the effectiveness of the NIRimaging method for visualizing and quantifying heat transferdynamics during an MCE from the magnetocaloric material to thesurrounding water. By exploiting the water absorption coefficientvariation at 1150 nm, the NIR system effectively captured two-dimensional absorbance images throughout a single magnetizationand demagnetization cycle induced by a center magnetic field of0.56 T, which was generated by a permanent-magnet-based mag-netic circuit. Temperature images revealed peak temperature differ-ences of 1.38 and −1.27 K near the Gd surface duringmagnetization (0.9 s) and demagnetization (100.9 s), respectively.Utilizing binary processing, we determined the thermal boundarylayer thickness, observing its increase proportional to the squareroot of the product of thermal diffusivity of water and time.Additionally, the heat quantity transferred from Gd to water corre-lated with the development of the thermal boundary layer thick-ness. Notably, the maximum heat transfer rate of 0.047 and−0.038W occurred before the onset of heat diffusion at 0.9 and100.9 s in the magnetization and demagnetization states, respec-tively. Future research should build upon these findings to explorethe broader applicability of NIR imaging to diverse MCE systemconfigurations and operating conditions. This could involve investi-gating different regenerator geometries, flow rates, and magneticfield strengths to evaluate the thermal–fluid interaction acrossvarious scenarios. Exploring various NIR wavelengths may offerinsights into alternative heat transfer fluids, such as ethylene glycol,and facilitate the construction of a data set on heat transfer coeffi-cients for assessing the performance of MCE systems. Furthermore,this method shows potential for application beyond MCE, extend-ing to other caloric effects like electrocaloric, elastocaloric, and bar-ocaloric effects, by replacing magnetic fields with electric fields,strain, and pressure.ACKNOWLEDGMENTSThe authors thank H. Sepehri-Amin, F. Ando, and A. Alaslifor valuable discussions. This work was supported by ERATO“Magnetic Thermal Management Materials” (No. JPMJER2201)from JST, Japan.AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsThe-Anh Nguyen: Conceptualization (equal); Formal analysis(equal); Investigation (equal); Methodology (equal); Writing –original draft (equal); Writing – review & editing (equal). NaotoKakuta: Methodology (equal); Writing – review & editing (equal).Ken-ichi Uchida: Funding acquisition (equal); Project administra-tion (equal); Validation (equal); Writing – review & editingJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-10© Author(s) 2024 27 May 2024 04:18:20https://pubs.aip.org/aip/jap(equal). Hosei Nagano: Conceptualization (equal); Funding acqui-sition (equal); Project administration (equal); Supervision (equal);Validation (equal); Writing – review & editing (equal).APPENDIX: EFFECT OF MAGNETIC FIELDS ON THEABSORPTION SPECTRUM OF WATERA quartz cuvette with inner dimensions of 30 × 10 × 45 mm3(with an optical path length of 10 mm) was utilized to verifywhether the magnetic field affects water itself. Distilled water (6 ml)was injected into the cuvette using a syringe, and the cuvette wassealed with a plastic cap.Initially, the intensity of transmitted light through the cuvettecontaining water was measured as a reference state without themagnet and denoted as Iw. Subsequently, this cuvette was placed atthe center of the two poles, exposing it to a magnetic field of up to0.56 T for a duration of 100 s. The intensity of light under this con-dition was recorded as Im. The change in absorbance, ΔA, was thencalculated using the logarithmic ratio of Im to Iw:� log10(Im/Iw).Figure 11 shows the plotted ΔA profiles within the whitedashed rectangle under the magnetic flux value of 0.56 T.Throughout the entire duration, the resulting absorption data con-sistently exhibited minimal variation or remained unchanged.Occasional minor deviations in ΔA data were observed, likelyattributed to minor impurities in the water or the cuvette. Thisobservation implies that under those experimental conditions(e.g., μ0Hext = 0.56 T and λ = 1150 nm), any influences of themagnetic field, beyond temperature effects, on ΔA were notablyinsignificant. This outcome remained consistent when applyinganother temperature-sensitive wavelength, λ = 1240 nm, within the1100–1250 nm range.DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1H. Johra, K. Filonenko, P. Heiselberg, C. Veje, S. Dall’Olio, K. Engelbrecht, andC. Bahl, “Integration of a magnetocaloric heat pump in an energy flexible resi-dential building,” Renew. Energy 136, 115–126 (2019).2A. Kitanovski, “Energy applications of magnetocaloric materials,” Adv. EnergyMater. 10(10), 1903741 (2020).3X. Moya and N. D. Mathur, “Caloric materials for cooling and heating,”Science 370(6518), 797–803 (2020).4J. Y. Law, L. M. Moreno-Ramírez, Á Díaz-García, and V. Franco, “Current per-spective in magnetocaloric materials research,” J. Appl. Phys. 133(4), 040903(2023).5L. M. Maier, P. Corhan, A. Barcza, H. A. Vieyra, C. Vogel, J. D. Koenig,O. Schäfer-Welsen, J. Wöllenstein, and K. Bartholomé, “Active magnetocaloricheat pipes provide enhanced specific power of caloric refrigeration,” Commun.Phys. 3(1), 1–6 (2020).6O. Tegus, E. Brück, K. H. J. Buschow, and F. R. de Boer,“Transition-metal-based magnetic refrigerants for room-temperature applica-tions,” Nature 415(6868), 150–152 (2002).7H. Wada and Y. Tanabe, “Giant magnetocaloric effect of MnAs1-xSbx,”Appl. Phys. Lett. 79(20), 3302–3304 (2001).8L. Tocado, E. Palacios, and R. Burriel, “Entropy determinations and magneto-caloric parameters in systems with first-order transitions: Study of MnAs,”J. Appl. Phys. 105(9), 093918 (2009).9H. Zhang, Y. Sun, E. Niu, F. Hu, J. Sun, and B. Shen, “Enhanced mechanicalproperties and large magnetocaloric effects in bonded La(Fe, Si)13-based mag-netic refrigeration materials,” Appl. Phys. Lett. 104(6), 062407 (2014).10K. P. Skokov, D. Y. Karpenkov, M. D. Kuz’Min, I. A. Radulov, T. Gottschall,B. Kaeswurm, M. Fries, and O. Gutfleisch, “Heat exchangers made of polymer-bonded La(Fe,Si)13,” J. Appl. Phys. 115(17), 4–6 (2014).11J. Liu, T. Gottschall, K. P. Skokov, J. D. Moore, and O. Gutfleisch, “Giant mag-netocaloric effect driven by structural transitions,” Nat. Mater. 11(7), 620–626(2012).12R. Modak, R. Iguchi, H. Sepehri-Amin, A. Miura, and K. Uchida,“Simultaneous direct measurements of conventional and inverse magnetocaloriceffects in Ni-Mn-based Heusler alloys using lock-in thermography technique,”AIP Adv. 10(6), 065005 (2020).13R. Yuan, P. Lu, H. Han, D. Xue, A. Chen, Q. Jia, and T. Lookman, “Enhancedmagnetocaloric performance in manganite bilayers,” J. Appl. Phys. 127(15),154102 (2020).14D. Nemec and J. Levec, “Flow through packed bed reactors: 1. Single-phaseflow,” Chem. Eng. Sci. 60(24), 6947–6957 (2005).15C. G. du Toit, “Radial variation in porosity in annular packed beds,”Nucl. Eng. Des. 238(11), 3073–3079 (2008).16J. Tušek, A. Kitanovski, and A. Poredoš, “Geometrical optimization ofpacked-bed and parallel-plate active magnetic regenerators,” Int. J. Refrig. 36(5),1456–1464 (2013).17K. K. Nielsen, J. Tusek, K. Engelbrecht, S. Schopfer, A. Kitanovski,C. R. H. Bahl, A. Smith, N. Pryds, and A. Poredos, “Review on numerical model-ing of active magnetic regenerators for room temperature applications,”Int. J. Refrig. 34(3), 603–616 (2011).18K. K. Nielsen, K. Engelbrecht, D. V. Christensen, J. B. Jensen, A. Smith, andC. R. H. Bahl, “Degradation of the performance of microchannel heat exchangersdue to flow maldistribution,” Appl. Therm. Eng. 40, 236–247 (2012).19T. Lei, K. Engelbrecht, K. K. Nielsen, and C. T. Veje, “Study of geometries ofactive magnetic regenerators for room temperature magnetocaloric refrigeration,”Appl. Therm. Eng. 111, 1232–1243 (2017).FIG. 11. Temporal changes in the absorbance difference ΔA of water atλ = 1150 and 1240 nm under 0.56 T for the white dashed rectangular area.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-11© Author(s) 2024 27 May 2024 04:18:20https://doi.org/10.1016/j.renene.2018.12.102https://doi.org/10.1002/aenm.201903741https://doi.org/10.1002/aenm.201903741https://doi.org/10.1126/science.abb0973https://doi.org/10.1063/5.0130035https://doi.org/10.1038/s42005-020-00450-xhttps://doi.org/10.1038/s42005-020-00450-xhttps://doi.org/10.1038/415150ahttps://doi.org/10.1063/1.1419048https://doi.org/10.1063/1.3093880https://doi.org/10.1063/1.4865236https://doi.org/10.1063/1.4868707https://doi.org/10.1038/nmat3334https://doi.org/10.1063/5.0005865https://doi.org/10.1063/1.5139946https://doi.org/10.1016/j.ces.2005.05.068https://doi.org/10.1016/j.nucengdes.2007.12.018https://doi.org/10.1016/j.ijrefrig.2013.04.001https://doi.org/10.1016/j.ijrefrig.2010.12.026https://doi.org/10.1016/j.applthermaleng.2012.02.019https://doi.org/10.1016/j.applthermaleng.2015.11.113https://pubs.aip.org/aip/jap20Q. Hou, Y. Xuan, W. Lian, Y. Xu, and Y. Ma, “A novel approach for suppress-ing flow maldistribution in mini-channel heat exchangers,” Int. J. Therm. Sci.184, 108020 (2023).21K. K. Nielsen, K. Engelbrecht, and C. R. H. Bahl, “The influence of flow mal-distribution on the performance of inhomogeneous parallel plate heat exchang-ers,” Int. J. Heat Mass Transfer 60(1), 432–439 (2013).22J. Tušek, A. Kitanovski, S. Zupan, I. Prebil, and A. Poredoš, “A comprehensiveexperimental analysis of gadolinium active magnetic regenerators,” Appl. Therm.Eng. 53(1), 57–66 (2013).23T. Xiong, G. Liu, S. Huang, G. Yan, and J. Yu, “Two-phase flow distribution inparallel flow mini/micro-channel heat exchangers for refrigeration and heat pumpsystems: A comprehensive review,” Appl. Therm. Eng. 201(PB), 117820 (2022).24Z. Lei, X. Yang, C. Haberstroh, B. Pulko, S. Odenbach, and K. Eckert, “Space-and time-resolved interferometric measurements of the thermal boundary layerat a periodically magnetized gadolinium plate,” Int. J. Refrig. 56, 246–255(2015).25N. Kakuta, K. Kondo, H. Arimoto, and Y. Yamada, “Reconstruction of cross-sectional temperature distributions of water around a thin heating wire byinverse Abel transform of near-infrared absorption images,” Int. J. Heat MassTransfer 77, 852–859 (2014).26N. Kakuta, Y. Arakawa, M. Kyoda, T. Miyake, K. Mishiba, and K. Kondo,“Near-infrared measurement of axisymmetric temperature field formed by freeconvection from a 1-mm-diameter heating sphere in water,” Int. J. Heat MassTransfer 137, 847–856 (2019).27T. A. Nguyen, K. Kondo, and N. Kakuta, “Near-infrared measurement of tem-perature fields formed by mixed convection from a small heating sphere inwater,” Int. J. Therm. Sci. 176, 107498 (2022).28V. C. Han and N. Kakuta, “Near-infrared measurement of water temperaturenear micro-magnetic particle layer in a fluidic channel under induction heating,”Exp. Therm. Fluid Sci. 115, 110087 (2020).29T. Uema, T. Ohata, Y. Washizuka, R. Nakanishi, D. Kawashima, andN. Kakuta, “Near-infrared imaging in a microfluidic channel of aqueous acid–base reactions,” Chem. Eng. J. 403, 126338 (2021).30T. A. Nguyen and N. Kakuta, “Experimental study on the initial thermalplumes produced by small heating plates in water,” Exp. Therm. Fluid Sci. 142,110803 (2023).31Y. Ozaki, C. W. Huck, S. Tsuchikawa, and S. B. Engelsen, Near-InfraredSpectroscopy (Springer, Singapore, 2021).32M. Iwasaka and S. Ueno, “Structure of water molecules under 14 T magneticfield,” J. Appl. Phys. 83(11), 6459–6461 (1998).33K. X. Zhou, G. W. Lu, Q. C. Zhou, J. H. Song, S. T. Jiang, and H. R. Xia,“Monte Carlo simulation of liquid water in a magnetic field,” J. Appl. Phys.88(4), 1802–1805 (2000).34N. Kakuta, K. Nishijima, K. Kondo, and Y. Yamada, “Near-infrared measure-ment of water temperature near a 1-mm-diameter magnetic sphere and its heatgeneration rate under induction heating,” J. Appl. Phys. 122(4), 044901 (2017).35R. Almeida, S. C. Freitas, C. R. Fernandes, R. Kiefe, J. P. Araújo, J. S. Amaral,J. O. Ventura, J. H. Belo, and D. J. Silva, “Rotating magnetocaloric effect in poly-crystals—Harnessing the demagnetizing effect,” J. Phys. Energy 6(1), 015020(2024).36A. Aharoni, “Demagnetizing factors for rectangular ferromagnetic prisms,”J. Appl. Phys. 83(6), 3432–3434 (1998).37Y. Hirayama, R. Iguchi, X. F. Miao, K. Hono, and K. Uchida,“High-throughput direct measurement of magnetocaloric effect based on lock-inthermography technique,” Appl. Phys. Lett. 111(16), 163901 (2017).38K. K. Nielsen, C. R. H. Bahl, and A. Smith, “Constraints on the adiabatic tem-perature change in magnetocaloric materials,” Phys. Rev. B 81(5), 1–5 (2010).39N. Otsu, “A threshold selection method from gray-level histograms,”IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).40Y. Jiang, B. Nie, Y. Zhao, J. Carmeliet, and F. Xu, “Scaling of buoyancy-drivenflows on a horizontal plate subject to a ramp heating of a finite time,”Int. J. Heat Mass Transfer 171, 121061 (2021).41Y. Fan, Y. Zhao, J. F. Torres, F. Xu, C. Lei, Y. Li, and J. Carmeliet, “Naturalconvection over vertical and horizontal heated flat surfaces: A review of recentprogress focusing on underpinnings and implications for heat transfer and envi-ronmental applications,” Phys. Fluids 33(10), 101301 (2021).42K. K. Nielsen, C. R. H. Bahl, and K. Engelbrecht, “The effect of flow maldistri-bution in heterogeneous parallel-plate active magnetic regenerators,” J. Phys. D:Appl. Phys. 46(10), 105002 (2013).43S. Li, H. Zhang, J. Cheng, X. Li, W. Cai, Z. Li, and F. Li, “A state-of-the-artoverview on the developing trend of heat transfer enhancement by single-phaseflow at micro scale,” Int. J. Heat Mass Transfer 143, 118476 (2019).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 193904 (2024); doi: 10.1063/5.0207290 135, 193904-12© Author(s) 2024 27 May 2024 04:18:20https://doi.org/10.1016/j.ijthermalsci.2022.108020https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.018https://doi.org/10.1016/j.applthermaleng.2013.01.015https://doi.org/10.1016/j.applthermaleng.2013.01.015https://doi.org/10.1016/j.applthermaleng.2021.117820https://doi.org/10.1016/j.ijrefrig.2015.01.004https://doi.org/10.1016/j.ijheatmasstransfer.2014.05.046https://doi.org/10.1016/j.ijheatmasstransfer.2014.05.046https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.127https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.127https://doi.org/10.1016/j.ijthermalsci.2022.107498https://doi.org/10.1016/j.expthermflusci.2020.110087https://doi.org/10.1016/j.cej.2020.126338https://doi.org/10.1016/j.expthermflusci.2022.110803https://doi.org/10.1063/1.367737https://doi.org/10.1063/1.1305324https://doi.org/10.1063/1.4995284https://doi.org/10.1088/2515-7655/ad1c61https://doi.org/10.1063/1.367113https://doi.org/10.1063/1.5000970https://doi.org/10.1103/PhysRevB.81.054423https://doi.org/10.1109/TSMC.1979.4310076https://doi.org/10.1016/j.ijheatmasstransfer.2021.121061https://doi.org/10.1063/5.0065125https://doi.org/10.1088/0022-3727/46/10/105002https://doi.org/10.1088/0022-3727/46/10/105002https://doi.org/10.1016/j.ijheatmasstransfer.2019.118476https://pubs.aip.org/aip/jap