Electromagnetic Induction Heating of Polymer Nanocomposites – A Computational Study on Design Parameters

Electromagnetic Induction Heating of Polymer Nanocomposites – A Computational Study on Design Parameters | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Electromagnetic Induction Heating of Polymer Nanocomposites – A Computational Study on Design Parameters Taha Najam, Suhail Hyder Vattathurvalappil, Mahmoodul Haq, Abrar H Baluch This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6539415/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Electromagnetic induction technology enables rapid, non-contact heating of conductive polymer nanocomposites, yet uncontrolled localized heating during this process can induce significant thermomechanical damage. Key influencing factors include nanoparticle dispersion, agglomeration, magnetic field frequency, and coil geometry. This study presents a multiphysics computational model to simulate the induction heating of acrylonitrile butadiene styrene (ABS) reinforced with iron oxide (Fe₃O₄) nanoparticles, assessing the impact of these variables on heating efficiency. Numerical predictions were validated against experimental data at four Fe₃O₄ weight concentrations, demonstrating strong agreement and confirming a positive correlation between nanoparticle content and heating rate. Additionally, higher frequencies substantially enhanced heating, while nanoparticle agglomeration was found to promote localized overheating, posing a risk of material degradation. Although parameters such as particle size, coil design, and polymer positioning influenced heating rates, their effects were comparatively minor. The developed computational framework, experimentally validated, proves reliable and adaptable for modeling induction heating in diverse polymer nanocomposite systems. Physical sciences/Materials science Physical sciences/Mathematics and computing Electromagnetic Induction Heating Nano Composite Iron Oxide Particles Computational Modeling magnetite Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction The market size of electromagnetic induction heating is projected to exceed 2.8 billion USD due to its increasing popularity and extensive range of applications [1]. This efficient, contactless, and consistent heating technique increases the temperature of a magnetic and/or electrically conductive material by exposing it to an alternating magnetic field. This technology serves several polymer-based applications, including welding of thermoplastic systems, curing of thermosetting systems, polymer systems with shape memory and self-healing properties, molding techniques, membrane distillation methods, pyrolysis processes, and roller embossing operations [2]. Iron oxides, which are conductive nanoparticles, are embedded in polymers to serve as nano heaters when exposed to electromagnetic induction waves. This property makes them extremely valuable for applications such as adhesive bonding and cancer therapy [3–17]. These conductive nanoparticles might vary in terms of their size, morphology, and electromagnetic properties [18]. Despite the advantages in induction heating, several studies have revealed thermo-mechanical degradation in polymer nanocomposites. This deterioration is attributed to the inability to control the rate of heating, which results from a limited understanding of the many components included in the induction heating of polymer nanocomposites. This emphasizes the crucial need for study on several process factors, such as frequency, susceptor particle size, particle agglomeration, coil geometry, and the placement of nanocomposite material within the coil. It is evident that induction heating of nano composites is a multi-physics problem that requires precise understanding of complex physical principles. Therefore, an experimentally validated computational model is of paramount importance to study the effect of various parameters involved in it. To the best of authors understanding scant research has been conducted on developing computational models to predict electromagnetic induction-based heating in polymer nanocomposites. Xiang Z, et al. [19] developed a computational model to examine the impact of induction heating on thermoplastic polymer composites that contain ferromagnetic nanoparticles (FMNP) as susceptors. However, this work only concentrated on low frequencies and did not account for micromechanical aspects of the composite material. Sha Z et al. [20] conducted computational analysis of induction heating in polymer nanocomposite. In this work, authors implemented an in-situ alignment technique to enhance the induction heating efficiency for different weight percentages of FMNPs. Cheng X et al. [21] studied Fe₃O₄ nanoparticles-based ethylene methacrylic acid (EMAA) thermoplastic adhesive to develop an on-demand bonding/debonding system activated by induction heating. Brassard D et al. [22] computationally modeled the induction welding process for carbon nanotube-reinforced PEI polymer composites, achieving an enhancement in lap shear strength (LSS) of welded joints by up to 28%. The aforementioned findings provide substantial experimental and computational data, underscoring the necessity for a validated computational tool. The experimental measurements in these works depended on homogenized surface temperature measurements, which cannot be deemed an acceptable measuring approach, given the heating sources are the nanoparticles scattered throughout the polymer matrix. It is important to emphasize that these studies measure the uniform temperature distribution of the adhesive using surface temperature, which is a poor predictor of the homogeneous thermal condition of the composite. Furthermore, the existing models fail to clarify the time-temperature variations caused by dispersion, loop formation, particle size, and location-specific heating. Electromagnetic (EM) induction heating offers rapid and targeted heating mechanisms for polymer nanocomposites, significantly enhancing manufacturing and maintenance across several applications. Aspects like ideal nanoparticle concentration, distribution, and temperature regulation have a significant impact on the effectiveness of heating. In the case of ABS polymers, it requires a minimum of 8 weight percent of Fe 3 O 4 nanoparticles; however, variations in the melting temperatures of different polymers necessitate adjustments in nanoparticle concentration [5]. Electromagnetic induction heating is recently identified as an effective heating technique for adhesive bonding applications. Rapid heating and cooling due to this process can generate residual stresses and can cause premature failure [5,7]. With the help of guided waves and fiber-optic sensors, these problems can be fixed in real time by precisely controlling the heating process and lowering the risk of damage caused by heat [9]. Further, mechanical and electromagnetic heating are greatly influenced by factors such as functionalization and dispersion of nanoparticles [5,6]. In addition to the aforementioned points, incorporation of non-destructive assessment techniques and customization of electromagnetic heating settings to address material inconsistencies continue to provide problems that require further exploration to enhance the effectiveness of electromagnetic induction heating in polymer nanocomposites [6,8] Implementing electromagnetic induction heating in thermoplastic nanocomposites has a lot of potential for a wide range of uses. However, there is a noticeable lack of knowledge in the existing literature about how particle size, coil geometry, and frequency affect the heating rate of FMNP-based polymer composites during electromagnetic induction heating. The limited attention has overlooked essential elements such as nanoparticle concentration and dispersion, leading to suboptimal outcomes. This study presents a robust computational model that is experimentally validated using a multiphysics computational program. It also includes a comprehensive parametric analysis examining the effects of frequency, exposure distance, coil geometry, agglomeration, and inter-particle distance, as depicted in Fig. 1 . This work offers insights to enhance the induction heating method for polymer nanocomposites. 2. Experimental Procedure 2.1. Experimental Setup This study builds on the work of Vattathurvalappil et al. [5] to develop an experimentally validated computational tool for the induction heating of polymer nanocomposites. Acrylonitrile Butadiene Styrene (ABS), CYPOLACTM Resin MG94 from SABIC®, was chosen as the thermoplastic polymer due to its exceptional toughness and favorable equilibrium of mechanical properties, cost, and chemical resistance [23]. The versatility of ABS renders it a prevalent material across several industries. It possesses a melting temperature of 240°C. Iron oxide (Fe 3 O 4 ) nano-particles, sourced from Sigma Aldrich, with a diameter of around 50–100 nm, served as particulate reinforcement inside the ABS matrix. The experimental approach utilized the Across International IHG06A1 induction heater, which utilized 30A of maximum input current, 100–500 kHz output frequency range, and 6.6 kW of peak oscillation power. The induction technique employed a copper coil (IHHC 2x1), sourced from Across International. The six-turn coil features internal dimensions of 50.8 mm by 25.4 mm and is constructed from copper tubing with a square cross-section of 6.35 mm by 6.35 mm. Effective heating of the adhesive bond-line depends on the configuration of the coil. The schematic representation of the experimental equipment arrangement is illustrated in Fig. 2 . 2.2. Temperature Characterization Using Electromagnetic Induction Heating The high-definition distributed temperature sensing capabilities of LUNA technology (Luna ODiSI-B) were used to accurately measure the heating rate of the ABS reinforced with Fe 3 O 4 . Six distinct concentrations of Fe 3 O 4 were combined with ABS and exposed to electromagnetic induction: Neat ABS (0 wt%) and ABS with 4 wt%, 8 wt%, 12 wt%, 16 wt%, and 20 wt% respectively. Time-temperature characterization was conducted for each composition. This device utilizes an optical fiber with a 1 mm diameter that provides a continuous line of temperature readings with submillimeter spatial resolution. This enables temperature monitoring at several points inside the nanocomposites during its exposure to induction radiation. The fiber optic sensing wire is affixed between two nanocomposite plates measuring 25mm x 25mm x 1mm, as seen in Fig. 2 .. During the heating process, time-temperature profiles were obtained to document the thermal response to the electromagnetic field. The optical sensor measured the time taken for each material system to attain 220°C, which denotes the processing temperature for the ABS thermoplastic matrix. The geometric center of the material sample was designated as the focal point for measuring the heating rate. This location was selected due to its anticipated maximum magnetic flux density, resulting in the highest heating rate. 3. Computational Modeling A multiphysics computational model was established to simulate the induction heating and predict the heating rate in polymer nanocomposites (ABS + Fe 3 O 4 nano-particles) exposed to electromagnetic induction radiation. The model was created by integrating the "Heat Transfer in Solids" and "Magnetic Fields" modules included in COMSOL Multiphysics program [24]. This paper presents a frequency-transient model in which the changing current I(t) is shown as an equation-based function of alternating frequency, which is related to the changing magnetic field in the induction coil (1). At each time step, the “magnetic fields” module estimates the electromagnetic fields inside the domain employing Ampere’s law derived from Maxwell’s equations, which incorporates time-varying eddy and displacement currents, as seen in the Eq. (2). The displacement current is often insignificant for high-frequency exposures and can be disregarded, particularly in cases where eddy currents prevail. The correlation between magnetic flux density and magnetic vector potential is defined in Eq. (3), allowing for the reformulation of Ampere’s law as shown in the subsequent Eq. (4). \(\:I\left(t\right)={I}_{o}sin\left(2\pi\:ft\right)\) – (1) \(\:\nabla\:\times\:H=J+\frac{\partial\:D}{\partial\:t}\) – (2) \(\:B=\nabla\:\times\:A\) – (3) \(\:J=\nabla\:\times\:\left(\frac{1}{\mu\:}\left(\nabla\:\times\:A\right)\right)\) - (4) A high-frequency induction heater (> 100 KHz) is essential for heating nano/micro particles using the induction heating method. Nevertheless, these magnetic fields affect the surface layer and do not penetrate the particle's depth during high-frequency exposures. This process is known as skin effect, and the extent of penetration is called skin depth. According to the Eq. ( 5 ), skin depth ( \(\:\delta\:\) ) depends on the applied frequency and the material characteristics, such as the susceptor's permeability and conductivity. Because of this, the skin effect limits the eddy current density (J eddy (x,t) ) to the surfaces of the Fe3O4 particles. This means that the formula needs to be changed to include an exponential drop in current densities when measured at a certain depth from the surface, as shown in the equations ( 6 ). Eqs. ( 7 ) and ( 8 ) defines the surface eddy current density as a function of electrical conductivity and the time-dependent electric field. $$\:\delta\:=\sqrt{\frac{1}{\pi\:\mu\:f\sigma\:}}$$ 5 $$\:{J}_{eddy}\left(x,t\right)={J}_{surface}\left(t\right){e}^{-x/\delta\:}$$ 6 $$\:{J}_{surface}\left(t\right)=\sigma\:.E\left(t\right)$$ 7 $$\:E\left(t\right)=-\frac{\partial\:A}{\partial\:t}$$ 8 As shown in (9), the changing nature of the vector potential makes the electric field and eddy currents change all the time. This causes Joule heating \(\:{Q}_{Joule}\left(t\right)\) in the Fe 3 O 4 particles. The heat produced in the particles is time-dependent and is calculated at each time step in the simulation before being sent to the “Heat Transfer in Solids” module as a heat source. COMSOL also figures out an extra source of heat that changes over time at each time step. This source is made up of magnetic hysteresis losses, \(\:{Q}_{hysteresis}\left(t\right)\) for the ferromagnetic particles. As shown in (10), hysteresis losses are directly linked to frequency, coercive force \(\:{H}_{c}\) , and the permeabilities \(\:{u}_{0}\:\&\:{u}_{r}\) of the Fe3O4 susceptor particles. As the material is heated, the magnetic and thermal characteristics of the particles and polymer matrix may alter. This can be incorporated into the COMSOL model by establishing temperature-dependent functions. $$\:{Q}_{Joule}\left(t\right)={J}_{eddy}\left(x,t\right).E\left(t\right)=\sigma\:{\left|E\right|}^{2}$$ 9 $$\:{Q}_{hysteresis}\left(t\right)={u}_{0}{u}_{r}{H}_{c}2f$$ 10 With each time step, the afore-mentioned heat generations are computed iteratively and play a crucial role by contributing to the heat transfer equation as a singular source \(\:{Q}_{total}\left(t\right)\) , see Eq. ( 11 ) for subsequent calculations. The complete time dependent heat transfer equation is provided by Eq. ( 12 ). $$\:{Q}_{total}\left(t\right)={Q}_{Joule}\left(t\right)+{Q}_{Hysteresis}\left(t\right)$$ 11 $$\:\rho\:{C}_{p}\frac{\partial\:T}{\partial\:t}={Q}_{total}\left(t\right)+\nabla\:\cdot\:\left(k\nabla\:T\right)$$ 12 Where \(\:{C}_{p}\) is the matrix specific-heat capacity, \(\:\rho\:\) is the matrix density, absolute temperature is defined by \(\:T\) , heat generation is labelled \(\:{Q}_{total}\left(t\right),\:\) and the thermal conductivity is given by \(\:k\) . The nano-particle susceptors are assumed to have anisotropic heat transfer is accordance to the model proposed by Wirtz et. al. [25] and Holmes et. al [26]. The outer boundaries of the matrix were modeled for radiative heat transfer using the Stefan–Boltzmann law, accounting for non-black body behavior. The radiative heat flux between the matrix and the surrounding air was determined by the material's emissivity \(\:ϵ\) , as defined in Eq. ( 13 ). $$\:{Q}_{L}=ϵ\sigma\:\left({T}_{surface}^{4}-{T}_{ambient}^{4}\right)$$ 13 Figure 3 illustrates the electromagnetic heating setup as a two-dimensional CAD model created for computational simulations. The model was discretized utilizing tetrahedral elements with a predefined element size specified as "very fine". The six-turn coil is represented with the outer rectangular segment and has an electrical conductivity of 6 × 10^7 S/m. The ambient air, with an initial temperature of 20 ◦ C, was maintained at a stationary state, and heat transport by radiation was accounted for by using a surface emissivity of 0.9 during the simulation to guarantee alignment with the experimental setup. Twelve Fe 3 O 4 particles, each having a diameter of 0.7 mm, were uniformly dispersed within a film of ABS matrix of size 25 mm X 1 mm. The film was positioned near the center of the rectangular coil. Figure 3 illustrates the computational domain and the outcomes of the magnetic flux distribution with an induction current of 30A at a frequency of 200 kHz. 4. Results and Discussion 4.1. Experimental Validation of Computational Model The time-temperature relationship for ABS thermoplastic reinforced with different weight percentages of fe₃O₄ nanoparticles, as determined by Vattathurvalappil et al. [5], is examined alongside data from the multi-physics computational model developed during this study. Figure 4 (a) depicts the time-temperature relationship for ABS blended with 8, 12, 16, and 20 weight percent of fe 3 O 4 , respectively. It shows that an increase in exposure duration correlates with a rise in temperature within the polymer nanocomposite. The initial heating rate for all compositions demonstrated a significant divergence from the experimental results. Nonetheless, with time, the error diminished, leading to a robust alignment with the thermal equilibrium state. The initial discrepancy between the experimental and computational analyses can be attributed to differences in the size, shape, and distribution of particles in both the experiments and the model. Additionally, the fiber Bragg grating (FBG) sensor measured the ambient temperature, which was documented as the experimental temperature. The computer model evaluated the temperature in the core of the adhesive layer, located between two bigger conductive particles (refer to Fig. 3 ). The variability in temperature measurement contexts influences the early measurements, particularly before the system attains thermal equilibrium. As such, the discrepancy can be resolved by incorporating the similar dimensions and dispersion pattern of nanoparticles into the computational framework. The particle size employed is a crucial component contributing to the initial disparity as well. The actual nanoparticles were described at the nanoscale; however, the computer model included bigger particles to streamline the simulation process and reduce computing time. This difference could be fixed by matching the nanoparticle size and distribution between the experimental and computational models. However, this would make the computations a lot more expensive. The current model's weight percent of conductive particles was based on the experiment. However, the particle size was changed to a millimeter scale to find the best balance between accuracy and computer speed. Figure 4 a indicates that the experimental correlation during the last heating phase is superior at elevated fe 3 O 4 concentrations. Figure 4 b illustrates the temperature contour of the polymer nanocomposite following 15 seconds of exposure. The data indicates a substantial rise in temperature next to the nanoparticle clusters, signifying localized thermal impacts. Even though there was good agreement between all of the material compositions, ABS with 16% wt of fe 3 O 4 has been chosen as the starting point for computational experiments for the brevity of the research. 4.2. Effect of Frequency This study applied five distinct frequencies, ranging from 1 kHz (low) to 750 kHz (very high), to ABS nanocomposite that consists of 16 wt.% fe₃O₄ nanoparticles. Time-temperature curves were generated from this computation experiment and are shown in Fig. 5 . The data indicates a clear link between frequency and heating rate. With an increase in frequency, the heating rate also increased. This result between frequency and heating rate can be attributed to two interconnected causes. Initially, elevated frequencies induce a rapid modification of the magnetic field, subsequently producing stronger eddy currents within the conductive nanoparticles. The occurrence of these eddy currents results in an increase in resistive (Joule) heating. Further, an increase in frequency can lead to an increase in magnetic domain realignment in magnetically responsive materials such as fe 3 O 4 nanoparticles. This process leads to enhanced hysteresis losses, thereby augmenting the overall heat generated within the material. In this way, there is a clear link between frequency and heating behavior in FMNP-reinforced thermoplastics, which validates the understandings derived from Maxwell's equations. 4.3. Effect of position within the coil In electromagnetic induction bonding, the positioning of the susceptor (polymer nanocomposite) within the induction coil is crucial. In this section of the study, the susceptor's location was relocated from its initial placement at the top edge of the coil to the geometric center of the coil, located at 9.675 mm from the top or bottom. The impact of this positional alteration on the heating rate was examined and shown in Fig. 6 . The findings reveal that the relocation has minimal impact on the heating rate. This behavior is primarily due to the uniform magnetic field generated by the rectangular coil, especially within its central area. In a rectangular coil configuration, the magnetic flux is uniformly dispersed across the inner region, resulting in uniform heating irrespective of the adhesive's precise location within the coil. The configuration of the coil is essential in ascertaining the distribution of magnetic flux. In a rectangular coil, the magnetic field exhibits more concentration in some regions; nevertheless, in this instance, the disparity between the edge and center positions is negligible. This differs from other coil geometries, such as circular or helical coils, where the distribution of magnetic flux can vary substantially with location, potentially influencing heating rates. In conclusion, although the placement of the susceptor within the rectangular coil had negligible influence on heating rates, the coil shape continues to be a critical determinant of magnetic flux production and heating efficiency. 4.4. Effect of interparticle distance When subjected to electromagnetic induction heating, each nanoparticle functions as a nanoheater. The inter-particle distance, or the space between fe 3 O 4 nanoparticles, is very important for controlling the rate of heating and making sure that the temperature in the polymer nanocomposite is the same all over. Changes in interparticle spacing result in fluctuations in thermal conduction mechanisms. This enables diverse heat transfer among particles, perhaps resulting in variable overall heating rates. This research examines five interparticle distances, varying from 0.75 mm (extremely near) to 2.25 mm (far). The weight percentage of fe 3 O 4 is maintained at 16%, while other electromagnetic characteristics remain consistent with those defined in the experimental validation. Figure 7 a shows the time-temperature variation over all interparticle distances. The variation in interparticle distance indicates a high particle concentration in the center; hence, measuring the temperature in that region would yield an inaccurate forecast of the homogeneous thermal state. As such, the area-average temperature of the ABS matrix is plotted with respect to time. As the distance between the particles increases, the average temperature of the matrix increases more swiftly, as seen in Fig. 7 a. The heating rate for a 1.0 mm interparticle distance is about double that of the 0.75 mm, whereas no significant variation in heating rate is observed with further dispersion (i.e., 2.0 mm and 2.25 mm distances). Temperature contours after 10 seconds of exposure for all the samples are shown in Fig. 7 b. The output of this study asserts the importance of homogenous dispersion of fe 3 O 4 particles within the thermoplastic matrix, as this parameter can be controlled during the mixing process to optimize the heating rate for a multitude of applications. 4.5. Effect of agglomeration The agglomeration of nanoparticles can cause stress concentration, resulting in premature failure. Further, heat transmission dynamics of systems with tightly packed particles vary from those of more scattered systems. Also, achieving perfect dispersion of nanoparticles inside the polymer matrix is impractical, necessitating an examination of the effects of agglomeration. Figure 8 a shows that this study looked at five different agglomeration situations. Four of them had random particle agglomeration, and the fifth was a baseline situation with a uniform distribution of nanoparticles. This investigation maintains a constant concentration of fe₃O₄ and electromagnetic characteristics. Temperature observations were documented as the area-average in the ABS matrix for each instance to alleviate local temperature biases that may result from agglomerates. In all agglomerated instances, the heating rate was seen to be substantially the same, albeit somewhat lower, in comparison to the baseline. This results from the uniform distribution in the baseline, which promotes improved heat transmission and, thus, an increased heating rate. Agglomeration, by causing clustering, impeded the homogeneity of heat transfer, hence diminishing the area average heating rate inside the matrix. Nonetheless, it is important to acknowledge that the aggregation of particles elevates the localized temperature, as seen in Fig. 8 b. This may result in localized heat breakdown of the polymer, as reported by Vattathurvalappil et al. [8]. However, the differences in heating rates among the four agglomerated examples were comparable, suggesting that the degree of random clustering did not markedly affect the overall thermal behavior (refer to Fig. 8 b). The findings highlight the essential requirement for consistent nanoparticle dispersion to improve heating efficiency and to avert thermomechanical deterioration in fe 3 O 4 reinforced thermoplastics. 4.6. Effect of coil geometry Induction coil geometry plays a crucial role in defining the magnetic field and thereby the heating behavior. This section of the computational experiment investigates the induction coil geometry effects on magnetic flux and heating performance of fe 3 O 4 reinforced ABS thermoplastics. Replacing the six-turn rectangular coil configuration, as established by the selected baseline, to a six-turn circular coil, modifies the magnetic field distribution, potentially influencing the heating rate due to changes in induced eddy currents. Temperature measurements were area-averaged across the ABS matrix to accurately capture the thermal state. As shown in Fig. 9 a, the time-temperature profiles reveal that the heating rates for both coil geometries are nearly identical, indicating that the overall heating performance is relatively unaffected by coil shape changes. Figure 9 b illustrates the difference in magnetic flux pattern for both coil geometries indicating the consequent flux density variation across the domain. These results highlight the significance of coil design in induction heating applications, suggesting that maintaining equal internal and external areas minimizes magnetic flux variations between the two coil configurations, reinforcing that geometry alone does not significantly alter the heating performance of Fe 3 O 4 reinforced thermoplastics. 5. Conclusion Induction heating of polymer-reinforced fe 3 O 4 nanocomposites is extensively utilized in several technical and medical sectors. However, a lack of experimentally verified predictive models in this field leads to expensive and time-consuming production phases. A multiphysics computational model was developed in this study to predict the heating behavior in acrylonitrile butadiene styrene polymer reinforced with fe 3 O 4 subjected to electromagnetic induction heating. The 2D model was developed with COMSOL multiphysics software and was validated by experimental investigations done by Vattathurvalappil et al. [5]. The model predicted the heating rate with approximately five percent error margin. The error margin was improved once a homogenized temperature distribution was achieved within the polymer nanocomposite. The validated model was subsequently utilized to perform computational experiments analyzing the impacts of frequency, interparticle distances, particle agglomeration, and coil morphology. The interparticle distance significantly affected heat transfer, with larger distances increasing the heating rate until a certain limit was reached. Agglomeration resulted in localized temperature rises; nevertheless, its overall impact on average heating rates was minimal, suggesting that appropriate dispersion is beneficial to avert localized thermal degradation. Increased frequencies significantly enhanced heating rates, confirming the understandings based on electromagnetic principles. Furthermore, coil configuration had no impact on overall heating performance, highlighting design versatility without compromising efficiency. These results provide significant insights for both facilitating and enhancing induction heating across many applications. Overall, the multiphysics based computational model established in this work can be utilized for predicting the induction-based heating behavior in various polymer-based nanocomposites. Declarations Author contributions Suhail Hyder Vattathurvalappil: Conceptualization, Formal Analysis, Investigation, Data Curation, Supervision, Writing-original draft, writing-review and editing Taha Najam: Software, Data Curation, Writing-original draft, writing-review and editing Mahmoodul Haq: Formal Analysis, Writing-review and editing Abrar H Baluch: Formal Analysis, Writing-review and editing Acknowledgements The authors would also like to acknowledge the support from King Fahd University of Petroleum & Minerals. Data Availability Statement All data obtained from experimental tests are available upon request. The request can be raised to the corresponding author, Dr. Suhail Hyder Vattathurvalappil. Conflicts of interest/Competing interests Authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 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Song, M., Zhang, Y., Hu, S., Song, L., Dong, J., Chen, Z., and Gu, N., “Influence of Morphology and Surface Exchange Reaction on Magnetic Properties of Monodisperse Magnetite Nanoparticles,” Colloids and Surfaces A: Physicochemical and Engineering Aspects , Vol. 408, 2012, pp. 114–121. https://doi.org/https://doi.org/10.1016/j.colsurfa.2012.05.039 Xiang, Z., Jakkpat, K. I., Ducharne, B., Capsal, J. F., Mogniotte, J. F., Lermusiaux, P., Cottinet, P. J., Schiava, N. Della, and Le, M. Q., “Enhancing the Low-Frequency Induction Heating Effect of Magnetic Composites for Medical Applications,” Polymers , Vol. 12, No. 2, 2020. https://doi.org/10.3390/polym12020386 Sha, Z., Cheng, X., Charles, A. D. M., Zhou, Y., Islam, M. S., Rider, A. N., Peng, S., Lim, M., Timchenko, V., and Wang, C. H., “In-Situ Aligning Magnetic Nanoparticles in Thermoplastic Adhesives for Contactless Rapid Joining of Composite Structures,” Composite Structures , Vol. 321, No. May, 2023, p. 117304. https://doi.org/10.1016/j.compstruct.2023.117304 Cheng, X., Zhou, Y., Charles, A. D. M., Yu, Y., Islam, M. S., Peng, S., Wang, J., Rider, A. N., Lim, M., Timchenko, V., and Wang, C. H., “Enabling Contactless Rapid On-Demand Debonding and Rebonding Using Hysteresis Heating of Ferrimagnetic Nanoparticles,” Materials and Design , Vol. 210, 2021, p. 110076. https://doi.org/10.1016/j.matdes.2021.110076 Brassard, D., Dubé, M., and Tavares, J. R., “Modelling Resistance Welding of Thermoplastic Composites with a Nanocomposite Heating Element,” Journal of Composite Materials , Vol. 55, No. 5, 2021, pp. 625–639. https://doi.org/10.1177/0021998320957055 Polli, H., Pontes, L. A. M., Araujo, A. S., Barros, J. M. F., and Fernandes, V. J., “Degradation Behavior and Kinetic Study of ABS Polymer,” Journal of Thermal Analysis and Calorimetry , Vol. 95, No. 1, 2009, pp. 131–134. https://doi.org/10.1007/s10973-006-7781-1 “The Joule Heating Interface.” Retrieved 30 September 2024. https://doc.comsol.com/5.5/doc/com.comsol.help.comsol/comsol_ref_heattransfer.21.15.html Xu, J., and Wirtz, R. A., “In-Plane Effective Thermal Conductivity of Plain-Weave Screen Laminates,” IEEE Transactions on Components and Packaging Technologies , Vol. 25, No. 4, 2002, pp. 615–620. https://doi.org/10.1109/TCAPT.2002.807993 Holmes, S. T., and Gillespie, J. W., “Thermal Analysis for Resistance Welding of Large-Scale Thermoplastic Composite Joints,” Journal of Reinforced Plastics and Composites , Vol. 12, No. 6, 1993, pp. 723–736. https://doi.org/10.1177/073168449301200609 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 13 Jun, 2025 Reviews received at journal 05 Jun, 2025 Reviews received at journal 03 Jun, 2025 Reviews received at journal 02 Jun, 2025 Reviewers agreed at journal 30 May, 2025 Reviewers agreed at journal 27 May, 2025 Reviewers agreed at journal 16 May, 2025 Reviewers invited by journal 14 May, 2025 Editor assigned by journal 08 May, 2025 Editor invited by journal 08 May, 2025 Submission checks completed at journal 08 May, 2025 First submitted to journal 27 Apr, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6539415","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":456325500,"identity":"4b0b23c3-b30a-418d-a48a-8097839791ae","order_by":0,"name":"Taha Najam","email":"","orcid":"","institution":"King Fahd University of Petroleum and Minerals","correspondingAuthor":false,"prefix":"","firstName":"Taha","middleName":"","lastName":"Najam","suffix":""},{"id":456325501,"identity":"cbfa1498-e32a-41cc-b0b3-a77acda88bf1","order_by":1,"name":"Suhail Hyder Vattathurvalappil","email":"data:image/png;base64,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","orcid":"","institution":"King Fahd University of Petroleum and Minerals","correspondingAuthor":true,"prefix":"","firstName":"Suhail","middleName":"Hyder","lastName":"Vattathurvalappil","suffix":""},{"id":456325502,"identity":"e2973b60-cd06-4829-8b2a-836b16c3371c","order_by":2,"name":"Mahmoodul Haq","email":"","orcid":"","institution":"Michigan State University","correspondingAuthor":false,"prefix":"","firstName":"Mahmoodul","middleName":"","lastName":"Haq","suffix":""},{"id":456325503,"identity":"f51ceef1-a9ac-40bd-b347-ca388374bc80","order_by":3,"name":"Abrar H Baluch","email":"","orcid":"","institution":"King Fahd University of Petroleum and Minerals","correspondingAuthor":false,"prefix":"","firstName":"Abrar","middleName":"H","lastName":"Baluch","suffix":""}],"badges":[],"createdAt":"2025-04-27 09:23:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6539415/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6539415/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82859086,"identity":"34d0c4d0-a9f1-4153-b982-1eae33d04a7f","added_by":"auto","created_at":"2025-05-16 06:15:26","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":50550,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of methodology adopted in this work\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/465fe5a9956b95886b046cd5.jpg"},{"id":82859088,"identity":"5cc2c525-a0fc-4758-9985-0b2a424fe69e","added_by":"auto","created_at":"2025-05-16 06:15:26","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":82960,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental setup adopted from Vattathurvalappil et al. [5].\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/eed1e87715adbe1c47b0cde5.jpg"},{"id":82859293,"identity":"6fec16d4-a0c1-48c4-9cd7-5333f23e5339","added_by":"auto","created_at":"2025-05-16 06:23:26","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":39902,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Displays a schematic of the RVE model with clear labelling. (b) Shows magnetic flux distribution with an induction current of 30A at a frequency of 200 kHz.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/564cdb0ef3f79396d7e56eb8.jpg"},{"id":82859863,"identity":"408ede30-206f-4298-bd28-386366910604","added_by":"auto","created_at":"2025-05-16 06:31:26","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":79593,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Time-temperature correlation between experimental and computational experiments for different weight percent of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e particles in ABS. (b) Temperature contour in polymer nanocomposites after 15 seconds of induction exposure in various weight percent of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e particles in ABS.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/0c44ca40181bc6c56fdfcee4.jpg"},{"id":82859294,"identity":"62272de3-525d-48e8-b109-669414a9a6fa","added_by":"auto","created_at":"2025-05-16 06:23:26","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":74181,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Time-temperature correlation that shows the effect of electromagnetic induction frequencies. (b) Temperature contour in the polymer nanocomposites after 10 seconds of induction exposure for various frequencies.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/cd72074d78b525bd4f42e91f.jpg"},{"id":82859095,"identity":"50d385bb-bb4e-4ed1-85a2-32e5a611e22b","added_by":"auto","created_at":"2025-05-16 06:15:26","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":40341,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Heating rate in susceptor with respect to its position within the coil (b) Position of substrate in the coil.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/9f68b8fedb18a074de86416d.jpg"},{"id":82859090,"identity":"7e86da49-95b2-40a3-92c6-8745ebba9b7e","added_by":"auto","created_at":"2025-05-16 06:15:26","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":71283,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Time-temperature correlation that shows the effect of interparticle distance. (b) Temperature contour in the polymer nanocomposites after 10 seconds of induction exposure for various interparticle distances.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/b18a50f54c01650333faee86.jpg"},{"id":82859300,"identity":"6cf659e3-bb4e-41f0-8372-0feca0b4ac53","added_by":"auto","created_at":"2025-05-16 06:23:26","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":69393,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eTime-temperature correlation that shows the effect of particle agglomeration. (b) Temperature contour in the polymer nanocomposites after 10 seconds of induction exposure for various cases of agglomeration.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/944b21014a6f9c6b79066d1d.jpg"},{"id":82859865,"identity":"83e5d92d-eadf-4429-ac0e-270e3a0cabb2","added_by":"auto","created_at":"2025-05-16 06:31:26","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":48614,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Time-temperature correlation indicates identical behavior for both coil types. (b) Temperature contour in the polymer nanocomposites after 10 seconds of induction exposure for different cases of coil geometry.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/69122aee19a7e856311572d7.jpg"},{"id":82860241,"identity":"b61b4e64-6af8-43c7-b0eb-fc92f5d662f8","added_by":"auto","created_at":"2025-05-16 06:39:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1134777,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6539415/v1/911d2172-42d4-45c6-97ed-e54f9476aed9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Electromagnetic Induction Heating of Polymer Nanocomposites – A Computational Study on Design Parameters","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe market size of electromagnetic induction heating is projected to exceed 2.8\u0026nbsp;billion USD due to its increasing popularity and extensive range of applications [1]. This efficient, contactless, and consistent heating technique increases the temperature of a magnetic and/or electrically conductive material by exposing it to an alternating magnetic field. This technology serves several polymer-based applications, including welding of thermoplastic systems, curing of thermosetting systems, polymer systems with shape memory and self-healing properties, molding techniques, membrane distillation methods, pyrolysis processes, and roller embossing operations [2]. Iron oxides, which are conductive nanoparticles, are embedded in polymers to serve as nano heaters when exposed to electromagnetic induction waves. This property makes them extremely valuable for applications such as adhesive bonding and cancer therapy [3\u0026ndash;17]. These conductive nanoparticles might vary in terms of their size, morphology, and electromagnetic properties [18]. Despite the advantages in induction heating, several studies have revealed thermo-mechanical degradation in polymer nanocomposites. This deterioration is attributed to the inability to control the rate of heating, which results from a limited understanding of the many components included in the induction heating of polymer nanocomposites. This emphasizes the crucial need for study on several process factors, such as frequency, susceptor particle size, particle agglomeration, coil geometry, and the placement of nanocomposite material within the coil.\u003c/p\u003e \u003cp\u003eIt is evident that induction heating of nano composites is a multi-physics problem that requires precise understanding of complex physical principles. Therefore, an experimentally validated computational model is of paramount importance to study the effect of various parameters involved in it. To the best of authors understanding scant research has been conducted on developing computational models to predict electromagnetic induction-based heating in polymer nanocomposites. Xiang Z, et al. [19] developed a computational model to examine the impact of induction heating on thermoplastic polymer composites that contain ferromagnetic nanoparticles (FMNP) as susceptors. However, this work only concentrated on low frequencies and did not account for micromechanical aspects of the composite material. Sha Z et al. [20] conducted computational analysis of induction heating in polymer nanocomposite. In this work, authors implemented an in-situ alignment technique to enhance the induction heating efficiency for different weight percentages of FMNPs. Cheng X et al. [21] studied Fe₃O₄ nanoparticles-based ethylene methacrylic acid (EMAA) thermoplastic adhesive to develop an on-demand bonding/debonding system activated by induction heating. Brassard D et al. [22] computationally modeled the induction welding process for carbon nanotube-reinforced PEI polymer composites, achieving an enhancement in lap shear strength (LSS) of welded joints by up to 28%. The aforementioned findings provide substantial experimental and computational data, underscoring the necessity for a validated computational tool. The experimental measurements in these works depended on homogenized surface temperature measurements, which cannot be deemed an acceptable measuring approach, given the heating sources are the nanoparticles scattered throughout the polymer matrix. It is important to emphasize that these studies measure the uniform temperature distribution of the adhesive using surface temperature, which is a poor predictor of the homogeneous thermal condition of the composite. Furthermore, the existing models fail to clarify the time-temperature variations caused by dispersion, loop formation, particle size, and location-specific heating.\u003c/p\u003e \u003cp\u003eElectromagnetic (EM) induction heating offers rapid and targeted heating mechanisms for polymer nanocomposites, significantly enhancing manufacturing and maintenance across several applications. Aspects like ideal nanoparticle concentration, distribution, and temperature regulation have a significant impact on the effectiveness of heating. In the case of ABS polymers, it requires a minimum of 8 weight percent of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nanoparticles; however, variations in the melting temperatures of different polymers necessitate adjustments in nanoparticle concentration [5]. Electromagnetic induction heating is recently identified as an effective heating technique for adhesive bonding applications. Rapid heating and cooling due to this process can generate residual stresses and can cause premature failure [5,7]. With the help of guided waves and fiber-optic sensors, these problems can be fixed in real time by precisely controlling the heating process and lowering the risk of damage caused by heat [9]. Further, mechanical and electromagnetic heating are greatly influenced by factors such as functionalization and dispersion of nanoparticles [5,6]. In addition to the aforementioned points, incorporation of non-destructive assessment techniques and customization of electromagnetic heating settings to address material inconsistencies continue to provide problems that require further exploration to enhance the effectiveness of electromagnetic induction heating in polymer nanocomposites [6,8]\u003c/p\u003e \u003cp\u003eImplementing electromagnetic induction heating in thermoplastic nanocomposites has a lot of potential for a wide range of uses. However, there is a noticeable lack of knowledge in the existing literature about how particle size, coil geometry, and frequency affect the heating rate of FMNP-based polymer composites during electromagnetic induction heating. The limited attention has overlooked essential elements such as nanoparticle concentration and dispersion, leading to suboptimal outcomes. This study presents a robust computational model that is experimentally validated using a multiphysics computational program. It also includes a comprehensive parametric analysis examining the effects of frequency, exposure distance, coil geometry, agglomeration, and inter-particle distance, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This work offers insights to enhance the induction heating method for polymer nanocomposites.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Experimental Procedure","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Experimental Setup\u003c/h2\u003e \u003cp\u003eThis study builds on the work of Vattathurvalappil et al. [5] to develop an experimentally validated computational tool for the induction heating of polymer nanocomposites.\u003c/p\u003e \u003cp\u003eAcrylonitrile Butadiene Styrene (ABS), CYPOLACTM Resin MG94 from SABIC\u0026reg;, was chosen as the thermoplastic polymer due to its exceptional toughness and favorable equilibrium of mechanical properties, cost, and chemical resistance [23]. The versatility of ABS renders it a prevalent material across several industries. It possesses a melting temperature of 240\u0026deg;C. Iron oxide (Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e) nano-particles, sourced from Sigma Aldrich, with a diameter of around 50\u0026ndash;100 nm, served as particulate reinforcement inside the ABS matrix.\u003c/p\u003e \u003cp\u003eThe experimental approach utilized the Across International IHG06A1 induction heater, which utilized 30A of maximum input current, 100\u0026ndash;500 kHz output frequency range, and 6.6 kW of peak oscillation power. The induction technique employed a copper coil (IHHC 2x1), sourced from Across International. The six-turn coil features internal dimensions of 50.8 mm by 25.4 mm and is constructed from copper tubing with a square cross-section of 6.35 mm by 6.35 mm. Effective heating of the adhesive bond-line depends on the configuration of the coil. The schematic representation of the experimental equipment arrangement is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Temperature Characterization Using Electromagnetic Induction Heating\u003c/h2\u003e \u003cp\u003eThe high-definition distributed temperature sensing capabilities of LUNA technology (Luna ODiSI-B) were used to accurately measure the heating rate of the ABS reinforced with Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e. Six distinct concentrations of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e were combined with ABS and exposed to electromagnetic induction: Neat ABS (0 wt%) and ABS with 4 wt%, 8 wt%, 12 wt%, 16 wt%, and 20 wt% respectively. Time-temperature characterization was conducted for each composition. This device utilizes an optical fiber with a 1 mm diameter that provides a continuous line of temperature readings with submillimeter spatial resolution. This enables temperature monitoring at several points inside the nanocomposites during its exposure to induction radiation. The fiber optic sensing wire is affixed between two nanocomposite plates measuring 25mm x 25mm x 1mm, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.. During the heating process, time-temperature profiles were obtained to document the thermal response to the electromagnetic field. The optical sensor measured the time taken for each material system to attain 220\u0026deg;C, which denotes the processing temperature for the ABS thermoplastic matrix. The geometric center of the material sample was designated as the focal point for measuring the heating rate. This location was selected due to its anticipated maximum magnetic flux density, resulting in the highest heating rate.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Computational Modeling","content":"\u003cp\u003eA multiphysics computational model was established to simulate the induction heating and predict the heating rate in polymer nanocomposites (ABS\u0026thinsp;+\u0026thinsp;Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nano-particles) exposed to electromagnetic induction radiation. The model was created by integrating the \"Heat Transfer in Solids\" and \"Magnetic Fields\" modules included in COMSOL Multiphysics program [24].\u003c/p\u003e \u003cp\u003eThis paper presents a frequency-transient model in which the changing current I(t) is shown as an equation-based function of alternating frequency, which is related to the changing magnetic field in the induction coil (1). At each time step, the \u0026ldquo;magnetic fields\u0026rdquo; module estimates the electromagnetic fields inside the domain employing Ampere\u0026rsquo;s law derived from Maxwell\u0026rsquo;s equations, which incorporates time-varying eddy and displacement currents, as seen in the Eq.\u0026nbsp;(2). The displacement current is often insignificant for high-frequency exposures and can be disregarded, particularly in cases where eddy currents prevail. The correlation between magnetic flux density and magnetic vector potential is defined in Eq.\u0026nbsp;(3), allowing for the reformulation of Ampere\u0026rsquo;s law as shown in the subsequent Eq.\u0026nbsp;(4).\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:I\\left(t\\right)={I}_{o}sin\\left(2\\pi\\:ft\\right)\\)\u003c/span\u003e \u003c/span\u003e \u003cem\u003e\u0026ndash; (1)\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\nabla\\:\\times\\:H=J+\\frac{\\partial\\:D}{\\partial\\:t}\\)\u003c/span\u003e \u003c/span\u003e \u003cem\u003e\u0026ndash; (2)\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:B=\\nabla\\:\\times\\:A\\)\u003c/span\u003e \u003c/span\u003e \u003cem\u003e\u0026ndash; (3)\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:J=\\nabla\\:\\times\\:\\left(\\frac{1}{\\mu\\:}\\left(\\nabla\\:\\times\\:A\\right)\\right)\\)\u003c/span\u003e \u003c/span\u003e \u003cem\u003e- (4)\u003c/em\u003e\u003c/p\u003e \u003cp\u003eA high-frequency induction heater (\u0026gt;\u0026thinsp;100 KHz) is essential for heating nano/micro particles using the induction heating method. Nevertheless, these magnetic fields affect the surface layer and do not penetrate the particle's depth during high-frequency exposures. This process is known as skin effect, and the extent of penetration is called skin depth. According to the Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e5\u003c/span\u003e), skin depth (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\delta\\:\\)\u003c/span\u003e\u003c/span\u003e) depends on the applied frequency and the material characteristics, such as the susceptor's permeability and conductivity. Because of this, the skin effect limits the eddy current density (J \u003csub\u003eeddy (x,t)\u003c/sub\u003e) to the surfaces of the Fe3O4 particles. This means that the formula needs to be changed to include an exponential drop in current densities when measured at a certain depth from the surface, as shown in the equations (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Eqs.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e7\u003c/span\u003e) and (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e8\u003c/span\u003e) defines the surface eddy current density as a function of electrical conductivity and the time-dependent electric field.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\delta\\:=\\sqrt{\\frac{1}{\\pi\\:\\mu\\:f\\sigma\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{J}_{eddy}\\left(x,t\\right)={J}_{surface}\\left(t\\right){e}^{-x/\\delta\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{J}_{surface}\\left(t\\right)=\\sigma\\:.E\\left(t\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:E\\left(t\\right)=-\\frac{\\partial\\:A}{\\partial\\:t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAs shown in (9), the changing nature of the vector potential makes the electric field and eddy currents change all the time. This causes Joule heating \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{Joule}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e in the Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e particles. The heat produced in the particles is time-dependent and is calculated at each time step in the simulation before being sent to the \u0026ldquo;Heat Transfer in Solids\u0026rdquo; module as a heat source.\u003c/p\u003e \u003cp\u003eCOMSOL also figures out an extra source of heat that changes over time at each time step. This source is made up of magnetic hysteresis losses, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{hysteresis}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e for the ferromagnetic particles. As shown in (10), hysteresis losses are directly linked to frequency, coercive force \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{c}\\)\u003c/span\u003e\u003c/span\u003e, and the permeabilities \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{0}\\:\\\u0026amp;\\:{u}_{r}\\)\u003c/span\u003e\u003c/span\u003e of the Fe3O4 susceptor particles. As the material is heated, the magnetic and thermal characteristics of the particles and polymer matrix may alter. This can be incorporated into the COMSOL model by establishing temperature-dependent functions.\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{Joule}\\left(t\\right)={J}_{eddy}\\left(x,t\\right).E\\left(t\\right)=\\sigma\\:{\\left|E\\right|}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{hysteresis}\\left(t\\right)={u}_{0}{u}_{r}{H}_{c}2f$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWith each time step, the afore-mentioned heat generations are computed iteratively and play a crucial role by contributing to the heat transfer equation as a singular source \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{total}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e, see Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e11\u003c/span\u003e) for subsequent calculations. The complete time dependent heat transfer equation is provided by Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e12\u003c/span\u003e).\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{total}\\left(t\\right)={Q}_{Joule}\\left(t\\right)+{Q}_{Hysteresis}\\left(t\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:\\rho\\:{C}_{p}\\frac{\\partial\\:T}{\\partial\\:t}={Q}_{total}\\left(t\\right)+\\nabla\\:\\cdot\\:\\left(k\\nabla\\:T\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the matrix specific-heat capacity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e is the matrix density, absolute temperature is defined by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e, heat generation is labelled \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{total}\\left(t\\right),\\:\\)\u003c/span\u003e\u003c/span\u003eand the thermal conductivity is given by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e. The nano-particle susceptors are assumed to have anisotropic heat transfer is accordance to the model proposed by Wirtz et. al. [25] and Holmes et. al [26]. The outer boundaries of the matrix were modeled for radiative heat transfer using the Stefan\u0026ndash;Boltzmann law, accounting for non-black body behavior. The radiative heat flux between the matrix and the surrounding air was determined by the material's emissivity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ϵ\\)\u003c/span\u003e\u003c/span\u003e, as defined in Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e13\u003c/span\u003e).\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{L}=ϵ\\sigma\\:\\left({T}_{surface}^{4}-{T}_{ambient}^{4}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the electromagnetic heating setup as a two-dimensional CAD model created for computational simulations. The model was discretized utilizing tetrahedral elements with a predefined element size specified as \"very fine\". The six-turn coil is represented with the outer rectangular segment and has an electrical conductivity of 6 \u0026times; 10^7 S/m. The ambient air, with an initial temperature of 20 \u003csup\u003e◦\u003c/sup\u003eC, was maintained at a stationary state, and heat transport by radiation was accounted for by using a surface emissivity of 0.9 during the simulation to guarantee alignment with the experimental setup. Twelve Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e particles, each having a diameter of 0.7 mm, were uniformly dispersed within a film of ABS matrix of size 25 mm X 1 mm. The film was positioned near the center of the rectangular coil. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the computational domain and the outcomes of the magnetic flux distribution with an induction current of 30A at a frequency of 200 kHz.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Results and Discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Experimental Validation of Computational Model\u003c/h2\u003e \u003cp\u003eThe time-temperature relationship for ABS thermoplastic reinforced with different weight percentages of fe₃O₄ nanoparticles, as determined by Vattathurvalappil et al. [5], is examined alongside data from the multi-physics computational model developed during this study. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a) depicts the time-temperature relationship for ABS blended with 8, 12, 16, and 20 weight percent of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e, respectively. It shows that an increase in exposure duration correlates with a rise in temperature within the polymer nanocomposite. The initial heating rate for all compositions demonstrated a significant divergence from the experimental results. Nonetheless, with time, the error diminished, leading to a robust alignment with the thermal equilibrium state. The initial discrepancy between the experimental and computational analyses can be attributed to differences in the size, shape, and distribution of particles in both the experiments and the model. Additionally, the fiber Bragg grating (FBG) sensor measured the ambient temperature, which was documented as the experimental temperature. The computer model evaluated the temperature in the core of the adhesive layer, located between two bigger conductive particles (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The variability in temperature measurement contexts influences the early measurements, particularly before the system attains thermal equilibrium. As such, the discrepancy can be resolved by incorporating the similar dimensions and dispersion pattern of nanoparticles into the computational framework.\u003c/p\u003e \u003cp\u003eThe particle size employed is a crucial component contributing to the initial disparity as well. The actual nanoparticles were described at the nanoscale; however, the computer model included bigger particles to streamline the simulation process and reduce computing time. This difference could be fixed by matching the nanoparticle size and distribution between the experimental and computational models. However, this would make the computations a lot more expensive. The current model's weight percent of conductive particles was based on the experiment. However, the particle size was changed to a millimeter scale to find the best balance between accuracy and computer speed. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea indicates that the experimental correlation during the last heating phase is superior at elevated fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e concentrations. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb illustrates the temperature contour of the polymer nanocomposite following 15 seconds of exposure. The data indicates a substantial rise in temperature next to the nanoparticle clusters, signifying localized thermal impacts. Even though there was good agreement between all of the material compositions, ABS with 16% wt of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e has been chosen as the starting point for computational experiments for the brevity of the research.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Effect of Frequency\u003c/h2\u003e \u003cp\u003eThis study applied five distinct frequencies, ranging from 1 kHz (low) to 750 kHz (very high), to ABS nanocomposite that consists of 16 wt.% fe₃O₄ nanoparticles. Time-temperature curves were generated from this computation experiment and are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The data indicates a clear link between frequency and heating rate. With an increase in frequency, the heating rate also increased.\u003c/p\u003e \u003cp\u003eThis result between frequency and heating rate can be attributed to two interconnected causes. Initially, elevated frequencies induce a rapid modification of the magnetic field, subsequently producing stronger eddy currents within the conductive nanoparticles. The occurrence of these eddy currents results in an increase in resistive (Joule) heating. Further, an increase in frequency can lead to an increase in magnetic domain realignment in magnetically responsive materials such as fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nanoparticles. This process leads to enhanced hysteresis losses, thereby augmenting the overall heat generated within the material. In this way, there is a clear link between frequency and heating behavior in FMNP-reinforced thermoplastics, which validates the understandings derived from Maxwell's equations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Effect of position within the coil\u003c/h2\u003e \u003cp\u003eIn electromagnetic induction bonding, the positioning of the susceptor (polymer nanocomposite) within the induction coil is crucial. In this section of the study, the susceptor's location was relocated from its initial placement at the top edge of the coil to the geometric center of the coil, located at 9.675 mm from the top or bottom. The impact of this positional alteration on the heating rate was examined and shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe findings reveal that the relocation has minimal impact on the heating rate. This behavior is primarily due to the uniform magnetic field generated by the rectangular coil, especially within its central area. In a rectangular coil configuration, the magnetic flux is uniformly dispersed across the inner region, resulting in uniform heating irrespective of the adhesive's precise location within the coil.\u003c/p\u003e \u003cp\u003eThe configuration of the coil is essential in ascertaining the distribution of magnetic flux. In a rectangular coil, the magnetic field exhibits more concentration in some regions; nevertheless, in this instance, the disparity between the edge and center positions is negligible. This differs from other coil geometries, such as circular or helical coils, where the distribution of magnetic flux can vary substantially with location, potentially influencing heating rates. In conclusion, although the placement of the susceptor within the rectangular coil had negligible influence on heating rates, the coil shape continues to be a critical determinant of magnetic flux production and heating efficiency.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Effect of interparticle distance\u003c/h2\u003e \u003cp\u003eWhen subjected to electromagnetic induction heating, each nanoparticle functions as a nanoheater. The inter-particle distance, or the space between fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nanoparticles, is very important for controlling the rate of heating and making sure that the temperature in the polymer nanocomposite is the same all over. Changes in interparticle spacing result in fluctuations in thermal conduction mechanisms. This enables diverse heat transfer among particles, perhaps resulting in variable overall heating rates.\u003c/p\u003e \u003cp\u003eThis research examines five interparticle distances, varying from 0.75 mm (extremely near) to 2.25 mm (far). The weight percentage of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e is maintained at 16%, while other electromagnetic characteristics remain consistent with those defined in the experimental validation. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea shows the time-temperature variation over all interparticle distances. The variation in interparticle distance indicates a high particle concentration in the center; hence, measuring the temperature in that region would yield an inaccurate forecast of the homogeneous thermal state. As such, the area-average temperature of the ABS matrix is plotted with respect to time.\u003c/p\u003e \u003cp\u003eAs the distance between the particles increases, the average temperature of the matrix increases more swiftly, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea. The heating rate for a 1.0 mm interparticle distance is about double that of the 0.75 mm, whereas no significant variation in heating rate is observed with further dispersion (i.e., 2.0 mm and 2.25 mm distances). Temperature contours after 10 seconds of exposure for all the samples are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003eThe output of this study asserts the importance of homogenous dispersion of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e particles within the thermoplastic matrix, as this parameter can be controlled during the mixing process to optimize the heating rate for a multitude of applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Effect of agglomeration\u003c/h2\u003e \u003cp\u003eThe agglomeration of nanoparticles can cause stress concentration, resulting in premature failure. Further, heat transmission dynamics of systems with tightly packed particles vary from those of more scattered systems. Also, achieving perfect dispersion of nanoparticles inside the polymer matrix is impractical, necessitating an examination of the effects of agglomeration.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea shows that this study looked at five different agglomeration situations. Four of them had random particle agglomeration, and the fifth was a baseline situation with a uniform distribution of nanoparticles. This investigation maintains a constant concentration of fe₃O₄ and electromagnetic characteristics. Temperature observations were documented as the area-average in the ABS matrix for each instance to alleviate local temperature biases that may result from agglomerates.\u003c/p\u003e \u003cp\u003eIn all agglomerated instances, the heating rate was seen to be substantially the same, albeit somewhat lower, in comparison to the baseline. This results from the uniform distribution in the baseline, which promotes improved heat transmission and, thus, an increased heating rate. Agglomeration, by causing clustering, impeded the homogeneity of heat transfer, hence diminishing the area average heating rate inside the matrix. Nonetheless, it is important to acknowledge that the aggregation of particles elevates the localized temperature, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb. This may result in localized heat breakdown of the polymer, as reported by Vattathurvalappil et al. [8].\u003c/p\u003e \u003cp\u003eHowever, the differences in heating rates among the four agglomerated examples were comparable, suggesting that the degree of random clustering did not markedly affect the overall thermal behavior (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb). The findings highlight the essential requirement for consistent nanoparticle dispersion to improve heating efficiency and to avert thermomechanical deterioration in fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e reinforced thermoplastics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.6. Effect of coil geometry\u003c/h2\u003e \u003cp\u003eInduction coil geometry plays a crucial role in defining the magnetic field and thereby the heating behavior. This section of the computational experiment investigates the induction coil geometry effects on magnetic flux and heating performance of fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e reinforced ABS thermoplastics. Replacing the six-turn rectangular coil configuration, as established by the selected baseline, to a six-turn circular coil, modifies the magnetic field distribution, potentially influencing the heating rate due to changes in induced eddy currents.\u003c/p\u003e \u003cp\u003eTemperature measurements were area-averaged across the ABS matrix to accurately capture the thermal state. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea, the time-temperature profiles reveal that the heating rates for both coil geometries are nearly identical, indicating that the overall heating performance is relatively unaffected by coil shape changes. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb illustrates the difference in magnetic flux pattern for both coil geometries indicating the consequent flux density variation across the domain.\u003c/p\u003e \u003cp\u003eThese results highlight the significance of coil design in induction heating applications, suggesting that maintaining equal internal and external areas minimizes magnetic flux variations between the two coil configurations, reinforcing that geometry alone does not significantly alter the heating performance of Fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e reinforced thermoplastics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eInduction heating of polymer-reinforced fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nanocomposites is extensively utilized in several technical and medical sectors. However, a lack of experimentally verified predictive models in this field leads to expensive and time-consuming production phases. A multiphysics computational model was developed in this study to predict the heating behavior in acrylonitrile butadiene styrene polymer reinforced with fe\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e subjected to electromagnetic induction heating.\u003c/p\u003e \u003cp\u003eThe 2D model was developed with COMSOL multiphysics software and was validated by experimental investigations done by Vattathurvalappil et al. [5]. The model predicted the heating rate with approximately five percent error margin. The error margin was improved once a homogenized temperature distribution was achieved within the polymer nanocomposite. The validated model was subsequently utilized to perform computational experiments analyzing the impacts of frequency, interparticle distances, particle agglomeration, and coil morphology. The interparticle distance significantly affected heat transfer, with larger distances increasing the heating rate until a certain limit was reached. Agglomeration resulted in localized temperature rises; nevertheless, its overall impact on average heating rates was minimal, suggesting that appropriate dispersion is beneficial to avert localized thermal degradation. Increased frequencies significantly enhanced heating rates, confirming the understandings based on electromagnetic principles. Furthermore, coil configuration had no impact on overall heating performance, highlighting design versatility without compromising efficiency.\u003c/p\u003e \u003cp\u003eThese results provide significant insights for both facilitating and enhancing induction heating across many applications. Overall, the multiphysics based computational model established in this work can be utilized for predicting the induction-based heating behavior in various polymer-based nanocomposites.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAuthor contributions\u003c/p\u003e\n\u003cp\u003eSuhail Hyder Vattathurvalappil:\u0026nbsp;Conceptualization, Formal Analysis, Investigation, Data Curation, Supervision, Writing-original draft, writing-review and editing\u003c/p\u003e\n\u003cp\u003eTaha Najam:\u0026nbsp;Software, Data Curation, Writing-original draft, writing-review and editing\u003c/p\u003e\n\u003cp\u003eMahmoodul Haq:\u0026nbsp;Formal Analysis, Writing-review and editing\u003c/p\u003e\n\u003cp\u003eAbrar H Baluch:\u0026nbsp;Formal Analysis, Writing-review and editing\u003c/p\u003e\n\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThe authors would also like to acknowledge the support from King Fahd University of Petroleum \u0026amp; Minerals.\u003c/p\u003e\n\u003cp\u003eData Availability Statement\u003c/p\u003e\n\u003cp\u003eAll data obtained from experimental tests are available upon request. The request can be raised to the corresponding author, Dr. Suhail Hyder Vattathurvalappil.\u003c/p\u003e\n\u003cp\u003eConflicts of interest/Competing interests\u003c/p\u003e\n\u003cp\u003eAuthors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eGlobal Market Insights, \u0026ldquo;Induction Heating System Market Size - By Product (Portable, Stationary), By End-Use (Automotive, Aerospace, Power Generation, Shipbuilding, Oil \u0026amp; Gas) \u0026amp; Global Forecast Report, 2024 \u0026ndash; 2032,\u0026rdquo; 2023.\u003c/li\u003e\n\u003cli\u003eMariani, A., and Malucelli, G., \u0026ldquo;Insights into Induction Heating Processes for Polymeric Materials: An Overview of the Mechanisms and Current Applications,\u0026rdquo; \u003cem\u003eEnergies\u003c/em\u003e, Vol. 16, No. 11, 2023, p. 4535.\u003c/li\u003e\n\u003cli\u003eVattathurvalappil, S. 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W., \u0026ldquo;Thermal Analysis for Resistance Welding of Large-Scale Thermoplastic Composite Joints,\u0026rdquo; \u003cem\u003eJournal of Reinforced Plastics and Composites\u003c/em\u003e, Vol. 12, No. 6, 1993, pp. 723\u0026ndash;736. https://doi.org/10.1177/073168449301200609\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Electromagnetic Induction Heating, Nano Composite, Iron Oxide Particles, Computational Modeling, magnetite","lastPublishedDoi":"10.21203/rs.3.rs-6539415/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6539415/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eElectromagnetic induction technology enables rapid, non-contact heating of conductive polymer nanocomposites, yet uncontrolled localized heating during this process can induce significant thermomechanical damage. Key influencing factors include nanoparticle dispersion, agglomeration, magnetic field frequency, and coil geometry. This study presents a multiphysics computational model to simulate the induction heating of acrylonitrile butadiene styrene (ABS) reinforced with iron oxide (Fe₃O₄) nanoparticles, assessing the impact of these variables on heating efficiency. Numerical predictions were validated against experimental data at four Fe₃O₄ weight concentrations, demonstrating strong agreement and confirming a positive correlation between nanoparticle content and heating rate. Additionally, higher frequencies substantially enhanced heating, while nanoparticle agglomeration was found to promote localized overheating, posing a risk of material degradation. Although parameters such as particle size, coil design, and polymer positioning influenced heating rates, their effects were comparatively minor. The developed computational framework, experimentally validated, proves reliable and adaptable for modeling induction heating in diverse polymer nanocomposite systems.\u003c/p\u003e","manuscriptTitle":"Electromagnetic Induction Heating of Polymer Nanocomposites – A Computational Study on Design Parameters","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-16 06:15:21","doi":"10.21203/rs.3.rs-6539415/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-13T07:28:24+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-06T02:14:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-04T03:32:16+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-02T10:01:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"209777445165966616223161642833068837188","date":"2025-05-30T09:03:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"317253398533443151980963560902234984511","date":"2025-05-27T08:24:11+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"47435535444140761862406714231937713398","date":"2025-05-16T06:24:12+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-14T06:10:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-08T14:18:34+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-05-08T08:06:37+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-08T08:05:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-04-27T09:08:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6fb100bd-0c3a-44f2-8ed2-2cc41dccc5f4","owner":[],"postedDate":"May 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":48503035,"name":"Physical sciences/Materials science"},{"id":48503036,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2025-07-21T09:08:43+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-16 06:15:21","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6539415","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6539415","identity":"rs-6539415","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}