Influence of Curved-quadra lateral sector Encapsulation shape and Orientation on the Performance of CuO/PCM- A CFD approach

The present work investigates the passive cooling capabilities of CuO nanoparticle-enhanced phase change materials (CPCMs), revealing that the orientation of the thermal energy storage system significantly influences the thermal behaviour and melting characteristics of CPCMs, ultimately affecting heat dissipation. Conventional shapes like rectangular or cylindrical enclosures do not effectively optimize heat transfer and phase change processes. Selecting a curved-quadrilateral sector as the encapsula- tion shape addresses these issues by enhancing heat transfer efficiency, promoting uniform melting, and optimizing the phase change process. Experimental validation confirms model accuracy, demonstrating minimal discrepancies between predicted and observed data. The results reveal that increasing the inclination angle leads to longer melting fraction durations. Furthermore, the concentration of CuO nanoparticles in PCMs significantly influences thermal conductivity and melting rates. The analysis of a CPCM3 reveals critical insights that in the early stage, rapid melting occurs near the heat source, resulting in a 150% performance improvement. This is followed by an intermediate stage where natural convection further enhances melting, yield- ing a 140% increase in liquid fraction. Eventually, as the PCM transitions predominantly to liquid, performance stabilizes at a 50% improvement. These findings emphasize the importance of enclosure geometry and orientation in PCM-based thermal management systems, particularly for energy storage and passive cooling applications. Influence of Curved-quadra lateral sector Encapsulation shape and Orientation on the Perfor- mance of CuO/PCM- A CFD approach Turubati Jagadeesh1, C.L.V.R.S.V Prasad2, G. Swami Naidu3 1 Research scholar, Mechanical Engineering department, JNTU-GV College of Engineering, AP, India. 2 Professor, Mechanical Engineering department, GMRIT, AP, India. 3 Professor, Metallurgical Engineering, JNTU-GV College of Engineering, AP, India Corresponding author: [email protected] data availability statementData generated during the research work is available in the manuscript. funding statementNot applicable conflict of interest disclosureThe authors declare no competing interests. • ethics approval statementAll authors agreed with the content, and necessary permissions were obtained from the concerned authorities. The experimental analysis has not harmed any human or animal. 1 Posted on 31 Mar 2025 | The copyright holder is the author/funder. All rights reserved. No reuse without permission. | https://doi.org/10.22541/au.174340277.79562610/v1 | This is a preprint and has not been peer-reviewed. Data may be preliminary. • patient consent statementAll authors agreed with the content, and no one objected to submitting the article to the journal • permission to reproduce material from other sourcesNot applicable • clinical trial registrationNot applicable Influence of Curved-quadra lateral sector Encapsulation shape and Orientation on the Perfor- mance of CuO/PCM- A CFD approach

The present work investigates the passive cooling capabilities of CuO nanoparticle-enhanced phase change

(CPCMs), revealing that the orientation of the thermal energy storage system significantly influ- ences the thermal behaviour and melting characteristics of CPCMs, ultimately affecting heat dissipation. Conventional shapes like rectangular or cylindrical enclosures do not effectively optimize heat transfer and phase change processes. Selecting a curved-quadrilateral sector as the encapsulation shape addresses these issues by enhancing heat transfer efficiency, promoting uniform melting, and optimizing the phase change process. Experimental validation confirms model accuracy, demonstrating minimal discrepancies between predicted and observed data. The results reveal that increasing the inclination angle leads to longer melting fraction durations. Furthermore, the concentration of CuO nanoparticles in PCMs significantly influences thermal conductivity and melting rates. The analysis of a CPCM3 reveals critical insights that in the early stage, rapid melting occurs near the heat source, resulting in a 150% performance improvement. This is followed by an intermediate stage where natural convection further enhances melting, yielding a 140% in- crease in liquid fraction. Eventually, as the PCM transitions predominantly to liquid, performance stabilizes at a 50% improvement. These findings emphasize the importance of enclosure geometry and orientation in PCM-based thermal management systems, particularly for energy storage and passive cooling applications.

Curved-quadra lateral TES, Nano PCM, Orientation, Liquidfraction, CFD.

In the rapidly evolving landscape of electronic devices, effective heat management has become crucial for ensuring uninterrupted and efficient performance within electronic circuits. As the proliferation of electronic components leads to increased heat generation, the need for innovative cooling solutions is more pressing than ever. Traditional methods, such as extended surfaces and heat pipes, have utilised conventional fluids. Integrating latent heat storage materials, particularly phase change materials (PCMs), presents a significant opportunity for improving cooling circuit systems. A thorough analysis of multiple studies utilizing numer- ical and experimental methods, emphasizing the capability of PCMs to improve the efficiency of electronic technologies, thus fostering cleaner and more sustainable solutions within the sector. The miniaturization of the electronic components we utilize daily has significantly advanced in recent years. It has streamlined our daily operations, as they have become more compact and portable (Hadiya and Shukla 2016). Along with miniaturisation, there is an expeditious enhancement of the performance of these electronic compo- nents. Due to the augmentation in the performance and efficiency of the electronic components, electricity consumption has increased, and more heat has started dissipating. As a result, thermal management of the components comes into the scenario. Thermal management is a crucial factor influencing the power of portable electronic components’ working and steadfastness or reliability (Kandasamy et al. 2008; Kalbasi and Salimpour 2015). Inadequate thermal management may increase heat production and temperature, po- tentially causing performance deterioration and eventual component failure. While there has been significant research on Phase Change Materials (PCMs) within Latent Heat Thermal Energy Storage (LHTES) systems for cooling electronic components, there remains a lack of comprehensive studies focusing on the integration and optimisation of TES systems specifically designed to mitigate high-temperature-induced failures in elec- tronic components. Additionally, the comparative effectiveness of different TES systems (SHTES, LHTES, and Thermochemical Energy Storage) in various operational environments and their long-term reliability in 2 Posted on 31 Mar 2025 | The copyright holder is the author/funder. All rights reserved. No reuse without permission. | https://doi.org/10.22541/au.174340277.79562610/v1 | This is a preprint and has not been peer-reviewed. Data may be preliminary. electronic applications have not been thoroughly explored (Al-Jethelah et al. 2019; Dora et al. 2021; Sunku Prasad et al. 2021; Nagaraju et al. 2022). While PCMs demonstrate potential for cooling electronic compo- nents due to their thermal properties, there is a significant gap in addressing the low thermal conductivity of traditional PCMs. This limitation hinders their application in high-power scenarios. Future research should focus on enhancing the thermal conductivity of PCMs or developing new materials that maintain the advantageous properties of PCMs while improving their performance (Zhao et al. 2017; Khan et al. 2020). PCM absorbs heat during the day and releases it at night, enhancing thermal mass in building envelopes. They are categorised into organic and inorganic types, further divided by encapsulation methods such as macro-encapsulation and microcapsules. PCM operates without external energy, contributing to passive cooling and heating, which can lower energy consumption and improve indoor comfort. Studies indicate that the effectiveness of PCMs in reducing temperature and energy use varies based on their thermophysical prop- erties, encapsulation techniques, integration methods, and local climate conditions (Li et al. 2016; Ruˇ cevskis et al. 2020). The review on battery thermal management systems (BTMS) emphasises advancements in immersion cooling techniques for lithium-ion batteries in electric vehicles. Immersion cooling, particularly with dielectric fluids, shows promise for improving heat transfer and safety. However, significant research gaps remain, including the long-term effects on battery lifespan, low-temperature performance, material compatibility, fluid stability, and environmental sustainability. Additionally, safety assessments of immer- sion cooling systems need further exploration. Addressing these issues is crucial for optimising immersion cooling technologies and developing high-performance, durable, safe electric vehicles. This review is a key resource for researchers and industry professionals focused on enhancing BTMS efficacy in future applications (Roe et al. 2022). The study successfully demonstrated that incorporating low concentrations of Graphene Nanoplatelets (GNPs) into a coolant mixture of Ethylene Glycol and water significantly improves the cooling efficiency of a customised Lithium Nickel Manganese Cobalt Oxide (NMC) battery pack. The simulations indicated a reduction in operating temperature by 12% to 29% with GNP concentrations of 0.001 vol% and 0.005 vol%, which is crucial for maintaining optimal conditions for Lithium-Ion Batteries in Electric Vehi- cles. The findings also highlight the potential of GNPs to enhance thermal management in battery systems, suggesting further increases in GNP concentration and structural redesigns (Jindal et al. 2022). Researchers have investigated the lithium-ion thermal management system utilising undulated battery walls for enhanced cooling performance (Singh et al. 2023). They demonstrate that increased air inflow rates significantly lower cell temperatures and that undulated walls improve thermal management compared to straight walls despite higher pressure drops. The thermal performance is assessed by varying mass flow rates and heat inputs, with

indicating that the microencapsulated slurry enhances heat transfer rates significantly compared to water (Santhosh Reddy et al. 2024). It is observed that the Nusselt number is notably higher in wavy and semi-wavy mini channels, indicating better heat transfer due to structural advantages. However, this comes with an increase in pressure drop. Overall, the study highlights the effectiveness of microencapsulated PCM in improving thermal management in mini-channel systems. The review on Battery Energy Storage Systems (BESSs) underscores their vital importance in modern energy systems, particularly in managing the fluc- tuations of renewable energy sources and improving grid stability. Despite the promising advancements in Battery Energy Storage Systems (BESS) and their applications, several critical research gaps remain. These include the need for enhanced safety and reliability through improved thermal management and predictive modelling, the establishment of standardisation and interoperability to streamline BESS deployment, the advancement of artificial intelligence (AI) and machine learning (ML) for real-time grid adaptation, and the reduction of costs through innovative battery technologies. Addressing these gaps is essential for optimising BESS operations and facilitating the transition to more resilient and sustainable energy systems (Srivastava et al. 2022; Kumar et al. 2024). A comprehensive table detailing the exploitation of PCMs provides a struc- tured overview of their performance metrics, applications, and inherent limitations, which has been presented in Table 1. By examining critical factors such as thermal conductivity, latent heat capacity, melting point, and cycling stability, this resource aids researchers and engineers in selecting the most appropriate PCM for their specific thermal management challenges. Table 1: Exploring PCM Performance across diverse applications 3 Posted on 31 Mar 2025 | The copyright holder is the author/funder. All rights reserved. No reuse without permission. | https://doi.org/10.22541/au.174340277.79562610/v1 | This is a preprint and has not been peer-reviewed. Data may be preliminary. Ref Domain of interest for analysis PCM Findings (Mosaffa et al. 2012) Shell and tube finned thermal storage calcium chloride hexahydrate(CaCl2 ·6H2O) PCM solidifies more rapidly in cylindrical shell storage than in rectangular storage. (Li et al. 2016) Thermal storage and thermal spreading(LMPCM+FHP) Liquid-Metal PCM The FHP–LMPCM module can regulate the temperature of electronic devices within an acceptable range, even when the PCM is fully melted under transient-state heating circumstances. (Shmueli et al. 2010) Vertical Cylinder Tube PCM Natural convection in the liquid becomes dominant, changing the solid shape to a conical one, which shrinks in size from the top to the bottom. (Seddegh et al. 2015) Heat transfer mechanism in a vertical shell and tube PCM A hybrid convection-conduction model may more accurately characterise heat transport in storage systems. (Yang et al. 2017) Shell and tube LHTES with Annular fins RT35(Paraffin Wax) Melting time could be maximally reduced by 65% by inserting annular fins into PCM (Sciacovelli et al. 2015) Vertical cylindrical shell-and-tube RT60 paraffin wax The solidification front moves along both radial and axial directions. (Huang et al. 2011) PCM-Heat Sink RT27&RT35 (Paraffin Wax) Internal fins improve temperature management of the solar module in a photovoltaic/phase change material configuration. (Bondareva and Sheremet 2017) PCM-Heat Sink n-Octadecane The Rayleigh number influences the flow structure of melt and the heat transfer rate. In contrast, the Ostrogradsky number indicates increased heat generation within a heater, leading to more intense melting of n-octadecane in the cavity. (Dhaidan and Khalaf 2020) hemicylindrical storage cell RT58 Increasing hot water temperature leads to a reduction of melting time and increases in the stored energy and the Nusselt number (Gharbi et al. 2015) PCM-Heat Sink Plastic-Paraffin, PCM/Silicon Matrix, PCM/Graphene Matrix Incorporating Phase Change Materials (PCM) can reduce component temperatures and significantly enhance the heat sink’s critical time, potentially doubling its effectiveness. A graphite matrix filled with PCM demonstrates greater thermal performance. (Zennouhi et al. 2017) Rectangular enclosure for different inclination angles Gallium The melting rate inside the rectangular chamber escalates when the inclination angle is reduced from 90 ° to 0°. (Seddegh et al. 2017) Rectangular enclosure with wavy surfaced bottom. The melting rate escalates with the rise in the amplitude of the wavy surface. (El Omari et al. 2011) Different enclosures paraffin wax The optimal efficiency for a vertically displaced enclosure about the cooled surface is achieved. (Kousksou et al. 2014) Maximisation of performance of LHTES using tree-shaped fins paraffin wax Implementing Y-shaped fins results in a 24% enhancement in system efficiency. Y-shaped fins with broad angles between the branches are advantageous for brief operational durations. This study formulates a problem centred on the design of an encapsulation shape for an energy-efficient configuration for battery cooling aimed at mitigating heatwave propagation. The novelty of the present investigation is to predict the best orientation when the encapsulation shape is filled with CuO nanoparticle- based PCM. The results are expected by developing the numerical model and ensuring the local temperature distribution and melting fraction time durations. The effect of PCM pack orientation on temperature dissipation, a previously overlooked aspect, and to determine the optimal positioning of the PCM pack to improve phase change uniformity and energy storage capacity. The CFD model will simulate various heat transfer mechanisms, including conduction, convection, and phase transition, with results focusing on liquid fraction evolution. Ultimately, the research seeks to provide insights into the role of orientation in PCM-based thermal management, contributing to improved cooling strategies for battery systems in various applications. Methodology The numerical methodology for the proposed encapsulation shape of phase change material (PCM) consists of designing a sector-based curved quadrilateral to improve battery thermal management. This design fea- tures a significant surface-area-to-volume ratio, facilitating effective heat dissipation and ensuring optimal thermal contact with battery cells. The curved geometry is designed to promote the movement of the liquid PCM driven by natural convection, which helps to minimise localised overheating and maintain thermal uni- formity throughout phase transitions. The tapered structure is engineered to optimise heat flow, facilitating the controlled melting and solidification of the PCM, thereby enhancing latent heat utilisation. The encap- sulation is designed to leverage gravity-assisted heat dissipation, effectively reducing thermal resistance. The modular design facilitates stackable configurations, rendering it suitable for compact thermal management systems in electric vehicles and high-performance energy storage devices. The computational domain of dimensions, 100mm diameter of Curved-quadrilateral, is modelled using Ansys-ICEM software and for mesh generation, followed by an analysis of meshing quality based on orthogonal quality metrics. The orthogonal quality of the generated mesh is 0.98. Additionally, it is essential for achieving precise outcomes in numerical simulations. Figure 1 presents the geometry and structured non-uniform mesh of the Curved-quadrilateral domain. 4 Posted on 31 Mar 2025 | The copyright holder is the author/funder. All rights reserved. No reuse without permission. | https://doi.org/10.22541/au.174340277.79562610/v1 | This is a preprint and has not been peer-reviewed. Data may be preliminary. (a) (b) Figure 1: (a) Curved quadrilateral computational domain (b) Meshing of curved quadrilateral The PCM encapsulation shape with a thickness of 20mm is considered, and 6 temperature locations, T1 to T6, are considered within the PCM centreline. Understanding local temperature variations is crucial for optimising the performance of phase change materials (PCM) in thermal energy storage and passive cooling. Accurate temperature predictions allow for complete melting and solidification cycles, enhancing latent heat capacity. This knowledge enables engineers to design systems with uniform heat distribution and efficient PCM utilisation. Additionally, reliable temperature modelling validates numerical methods. It aligns simulations with experimental results, while localised temperature data is essential for forecasting 5 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. the long-term performance and reliability of PCM-based thermal management systems. The influence of PCM encapsulation shape and its orientation is analysed while considering the CuO-based PCM (CPCM). Three concentrations have been considered: CPCM1 (1vol%), CPCM2 (3vol%) and CPCM3 (5vol%). This

presents unique challenges, such as understanding the impact of orientations 0o, 30o and 60o on natural convection and optimising design parameters for scalability and cost-effectiveness, highlighting the need for further research. Boundary conditions and solution: The selection of appropriate boundary conditions in numerical simulations of 2D nano PCMs enclosures is vital for accurately predicting heat transfer and phase change behaviour. In the present work, the Curved- quadrilateral outer wall is subjected to 1000 W/m2, and the remaining walls are considered adiabatic. The PCM’s characteristics remain stable across varying temperatures and during natural convection in its liquid phase. The analysis employs the Boussinesq approximation, which simplifies the study by ignoring infinites- imal differential volumes during the melting or charging phases of the PCM. The liquid PCM is identified as a Newtonian and incompressible fluid exhibiting laminar flow within the enclosure. The governing equations Eq(1) to (6) are solved using FLUENT-vesrion19 software. ∂ρ ∂t +∇. ( ρ− →V ) = 0 (1) ρ∂− →V ∂t +ρ (− →V .∇ )− →V =−∇p +µ∇2− →V +ρ− →g (T−T0) +− →S (2) S represents the momentum source term, which is relevant solely within the PCM domain. The momentum source term is, − →S = (1−δ)2 δ3 + 0.001Amushy − →V (3) Amushy represents the mushy zone constant; it is taken as 107 kg/m3s in the present work.δ represents the liquid fraction. Additionally, understanding the total enthalpy encompasses both sensible and latent enthalpy. Energy equation, ∂ ∂t (ρΗ) +∇. ( ρ− →V H ) =∇. (k∇T ) (4) Tr represents the reference temperature. H =Hr + ∫ T Tr CpdT +δL (5) Liquid fraction is defined as, δ = ΔΗ englishL{ & 0,ifT <T s & T −Ts Tl−Ts ,ifT s <T T l δ = ∆H L ={ 6 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. 0, if &T <Ts T −Ts Tl−Ts , if T s <T Tl (6) The PCM for the present thermal energy storage system is RT28HC, and its thermophysical properties are presented in Table 1, along with nanoparticles. The thermophysical properties of CuO based PCM with concentrations 1wt% (CPCM1), 3wt% (CPCM2) and 5wt% (CPCM3) are calculated using correlation (Al-Jethelah et al. 2018). Table 1: Material properties of PCM and nanoparticles Property RT28HC (Soares et al. 2015) CuO nanoparticles (Al-Jethelah et al. 2018) Density (Solid phase) (kg/m 3) 880 6500 Specific heat (J/kg K) 2000 0.54 Thermal conductivity (W/m K) 0.2 18 Dynamic viscosity (Pa.s) 0.00272 - Latent heat (kJ/kg) 245 - Melting temperature ( oC) 27 – 29 - Expansion coefficient (1/K) 0.0006 8.5 ×10-6 A detailed mesh configuration is essential to accurately model fluid behaviour, particularly near walls. To solve the governing equations for incompressible flow, which is often encountered in studies involving phase change materials. The SIMPLE algorithm is crucial for maintaining a proper relationship between pressure and velocity fields, ensuring that the continuity equation is satisfied through systematic adjustments. The QUICK scheme is implemented to discretise the momentum and energy equations, with specific control settings of 0.35 for pressure, 0.6 for momentum, and 0.9 for liquid fraction. Additionally, the PRESTO scheme enhances the accuracy of pressure-velocity predictions. This approach is combined with a staggered grid. The study emphasises the importance of grid density in achieving solution independence, concluding that 12,700 grids are adequate. A finer grid distribution in the radial direction permits longer time steps, which is crucial for accurately measuring the time required for complete melting. The analysis of simulations with varying time steps (0.05s, 0.1s and 0.5s) led to the decision to set the integration time step at 0.05s, highlighting its significance in the overall accuracy of the results.

and Discussion Validation studies The numerical model must be validated against experimental data, especially in battery thermal manage- ment, where passive cooling systems using PCM are employed to maintain accuracy and dependability. This validation procedure helps detect disparities, refine model assumptions, and improve boundary conditions, enhancing model predictiveness. The research may minimize experimental trials and help to develop thermal management strategy optimization by assuring numerical techniques accurately. Experimental studies on practical applications with PCM demonstrate the model’s accuracy, as evidenced by the close alignment of experimental data and numerical results. This high fidelity validates the model’s assumptions, while any dis- crepancies highlight areas for potential improvement, underscoring the importance of continuous refinement in modelling techniques for the design of effective TES. Studying melting phase change materials (PCMs) under constant heat flux is crucial for applications like battery thermal cooling. [CHART][CHART] (a) (b) Figure 2: Validation of TES for (a) Electronics cooling (Dhaidan et al. 2013) (b) PV system 7 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. (Huang et al. 2011) The research (Dhaidan et al. 2013) Focused on the melting behaviour of nano-PCM in a square enclosure with one heated wall and adiabatic sides. PCM thermal performance by measuring temperatures at various points using thermocouples and tracking the solid-liquid interface has been valida- ted using the present numerical model. This research is significant for improving the efficiency of thermal management systems, and the results are agreed with minimal error of ±2.34% as presented in Figure 2 (a). Similarly, experimental results of PCM’s front-line local temperature (Huang et al. 2011) agreed with a mistake of ±4.1%. Effect of CuO nanoparticle concentration The analysis of the local temperature distribution in nano-phase change materials (nano-PCM) reveals the significant impact of CuO nanoparticle concentration on thermal performance. As illustrated in Figure 3, three configurations (CPCM1, CPCM2, CPCM3) show that increasing CuO concentration (1%, 3%, and 5%) enhances thermal conductivity, leading to a more rapid and uniform temperature increase across va- rious sensor locations. The local temperature curves highlight the improved heat transfer dynamics, with higher concentrations resulting in quicker thermal responses and shorter phase transition durations. This information is crucial for understanding the heat storage and dissipation characteristics of nano-enhanced PCMs, emphasising the importance of nanoparticle concentration in optimising thermal management sys- tems. Figure 3: Variation of local temperature distribution of nano-PCM for 0 o orientation (a) CPCM1 (b) CPCM2 (c) CPCM3 The temperature changes over time are illustrated for various senor locations (T 1–T6) within the computa- tional domain, demonstrating the thermal response of each CPCM under heating conditions. It depicts the effect of CuO nanoparticle concentration on the thermal performance of the phase change material (PCM). As the CuO content rises from 1% to 5%, there is a notable increase in temperature across various sensor lo- cations, suggesting improved thermal conductivity. The duration of the phase change process also decreases with higher CuO concentrations, indicating that the PCM melts more quickly. Furthermore, while sensor temperature variations are more pronounced at lower CuO concentrations, a more uniform temperature dis- 8 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. tribution is observed at higher concentrations, particularly in the 5% CuO sample. This uniformity suggests better heat distribution and absorption, leading to the highest final temperature recorded in the 5% CuO sample. Effect of orientation The impact of TES orientation (0 °, 30 °, and 60 °) on the liquidfraction and temperature distribution in a nano-phase change material (PCM) system has been presented in Figure 4. It is observed that an increase in inclination, specifically at angles of 30 ° and 60°, results in a more rapid melting process when compared to the horizontal orientation (0 °), which maintains solid phase change material for an extended duration. The observed acceleration can be attributed to improved natural convection at inclined angles, leading to more efficient heat transfer and expedited phase transitions. The temperature distribution exhibits greater uniformity and achieves elevated peak temperatures at steeper inclinations. The 60 ° orientation is identified as the most efficient for heat transfer, characterised by pronounced temperature gradients and enhanced thermal uniformity. In contrast, the 0° orientation predominantly depends on conduction, leading to a slower melting process and reduced efficiency. The results indicate that the inclination angle of TES plays a crucial role in its thermal performance, particularly in temperature distribution and liquidfraction. As illustrated in Figure 4(a), at the simulation time of 10 min, almost all orientations have shown similar liquidfraction. As simulation time increases, i.e., at t=80 min, 80% of the PCM is converted by absorbing heat from the source in the case of 0 o orientation. It has been noted that 60% and 45% of liquidfraction for other orientations, i.e., 30 oand 60o, respectively. At simulation time t=150 min, it is observed that PCM in 0 o orientation almost converted into liquid, whereas in the other two cases is observed as 90% and 85%, respectively. Temperature readings further illustrate this trend in Figure 4(b), with maximum temperatures rising from 305 K at 0 ° to over 312 K at 60 °, marking a notable increase in thermal efficiency. 9 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. 10 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. (a) (b) Figure 4: Performance comparison variation of RT28HC filled Curved-quadrilateral enclosure (a) Liquid fraction (b) Temperature The analysis of a CPCM3-filled curved-quadrilateral enclosure at 0 ° orientation highlights the significance of liquid fraction evolution and temperature distribution in understanding heat transfer dynamics. The pro- gressive melting of the phase change material (PCM) is visually represented, showing a transition from solid to liquid, primarily driven by conduction and natural convection. The initial melting occurs near the heat source, with the molten area expanding over time, indicating the importance of the enclosure’s geometry in optimising thermal energy storage. This understanding is vital for improving PCM-based thermal ma- nagement systems, particularly in energy storage and passive cooling applications, underscoring the study’s relevance in enhancing performance in these technologies. The performance of the CPCM3-filled curved- quadrilateral enclosure exhibits considerable variation across distinct time intervals, indicating the dynamics of heat transfer and phase change. In the early stage (10 min to 50 min), the liquid fraction shows rapid growth, with a performance improvement of 150%, as the CPCM3 begins melting near the heat source. In the intermediate stage, spanning from 50 to 100 minutes, the impact of natural convection enhances the 11 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. melting process, leading to a 140% increase in the liquid fraction. In the late stage, as most of the CPCM3 has transitioned to a liquid state, the performance improvement stabilises at 50%. The observed variation in performance underscores the necessity of optimising heat input and enclosure design to improve the efficiency of PCM-based thermal energy storage systems. Similarly, supplementary material has been provided for the Performance of CPCM3-filled Curved-quadrilateral enclosure for 30 o and 60o orientations. Figure 5: Performance variation of CPCM3 filled Curved-quadrilateral enclosure for 0 o orien- tation Variation of liquidfraction The variation in liquid fraction across different orientations (0 °, 30°, and 60°) demonstrates the considerable influence of enclosure inclination on the melting performance of PCM and composite phase change materials (CPCMs), as shown in Figure 6. At an orientation of 0 °, the melting process occurs at the highest rate, with CPCM3 demonstrating the most significant increase in liquid fraction attributed to its enhanced thermal conductivity. When the enclosure is tilted to 30 °, there is a slight decrease in the melting rate, which can be attributed to changes in natural convection patterns that influence heat transfer efficiency. At an orientation of 60 °, the phase change exhibits a significant speed reduction, suggesting a diminished contribution from convective heat transfer in this configuration. CPCM3 consistently demonstrates superior performance com- pared to PCM, CPCM1, and CPCM2 across all orientations, highlighting the effectiveness of its enhanced thermal properties. The results underscore the significance of optimising enclosure orientation to enhance phase change efficiency, with an orientation of 0 ° yielding the most effective heat transfer conditions for accelerated melting. It is demonstrated that the orientation of enclosures significantly influences the melting times of phase change materials, with a clear trend showing that lower inclinations enhance heat transfer. The 0° orientation allows for the fastest phase transition, particularly for CPCM3, which outperforms other materials. As the angle increases to 30 ° and 60 °, melting times increase substantially due to diminished natural convection, highlighting the importance of orientation in optimising thermal performance. Overall, this analysis underscores the necessity of considering enclosure inclination to maximise energy absorption and storage capabilities in phase change applications. 12 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. Figure 6: Variation of liquid fraction in PCM, CPCM1, CPCM2 and CPCM3 (a) 0o (b) 30o(c) 60o

The sector-based curved quadrilateral design for encapsulating phase change material (PCM) has been cho- sen to enhance battery thermal management through its optimised geometry. The study emphasises the importance of understanding local temperature variations within phase change materials for optimising their performance in thermal energy storage and passive cooling applications. The analysis of PCM encapsula- tion shape and orientation, particularly with CuO-based PCM at varying concentrations, reveals challenges related to natural convection and the need for optimised design parameters. The validation of numeri- cal models against experimental data is essential for ensuring their reliability in TES applications. The close alignment between experimental results and numerical predictions demonstrates the model’s accuracy and validates its assumptions. It is observed that the research on melting phase change materials under constant heat flux is particularly relevant for applications such as battery thermal cooling. The study of nano-PCMs in a controlled environment has shown promising results, with minimal errors in temperature measurements, indicating the model’s effectiveness in enhancing thermal management systems. Overall, the findings underscore the importance of accurate modelling in optimising TES designs. It is perceived that increasing CuO concentration from 1% to 5% enhances thermal conductivity, resulting in quicker and more uniform temperature increases across various sensor locations. The findings demonstrate that higher CuO concentrations improve heat transfer, shorter phase transition durations, and a more uniform temperature distribution, particularly at 5% concentration. This suggests that optimising nanoparticle concentration is crucial for enhancing the thermal management capabilities of phase change materials. Overall, the study underscores the importance of CuO concentration in improving the efficiency of heat storage and dissipation in nano-enhanced PCMs.

Al-Jethelah M, Ebadi S, Venkateshwar K, et al (2019) Charging nanoparticle enhanced bio-based 13 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. PCM in open cell metallic foams: An experimental investigation. Appl Therm Eng 148:1029–1042. https://doi.org/10.1016/j.applthermaleng.2018.11.121Al-Jethelah M, Tasnim SH, Mahmud S, Dutta A (2018) Nano-PCM filled energy storage system for solar-thermal applications. Renew Energy 126:137–155. https://doi.org/10.1016/j.renene.2018.02.119Bondareva NS, Sheremet MA (2017) Flow and heat transfer evolution of PCM due to natural convection melting in a square cavity with a local heater. Int J Mech Sci 134:610–619. https://doi.org/10.1016/j.ijmecsci.2017.10.031Dhaidan NS, Khalaf AF (2020) Experimental evaluation of the melting behaviours of paraffin within a hemicylindrical storage cell. Int Commun Heat Mass Transf 111:104476. https://doi.org/10.1016/j.icheatmasstransfer.2020.104476Dhaidan NS, Khodadadi JM, Al-Hattab TA, Al-Mashat SM (2013) Experimental and numerical investigation of melting of phase change material/nanoparticle suspensions in a square container subjected to a constant heat flux. Int J Heat Mass Transf 66:672–683. https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.057Dora N, Ramsai C, Srini- vasa Rahul C (2021) Design and Numerical Simulation of PCM-Based Energy Storage Device for Helmet CoolingEl Omari K, Kousksou T, Le Guer Y (2011) Impact of shape of container on natural convection and melting inside enclosures used for passive cooling of electronic devices. Appl Therm Eng 31:3022– 3035. https://doi.org/10.1016/j.applthermaleng.2011.05.036Gharbi S, Harmand S, Jabrallah S Ben (2015) Experimental comparison between different configurations of PCM based heat sinks for cooling electronic components. Appl Therm Eng 87:454–462. https://doi.org/10.1016/j.applthermaleng.2015.05.024Hadiya JP, Shukla AKN (2016) Experimental thermal behavior response of paraffin wax as storage unit. J Therm Anal Calorim 124:1511–1518. https://doi.org/10.1007/s10973-016-5276-2Huang MJ, Eames PC, Norton B, Hewitt NJ (2011) Natural convection in an internally finned phase change material heat sink for the thermal management of photovoltaics. Sol Energy Mater Sol Cells 95:1598–1603. https://doi.org/10.1016/j.solmat.2011.01.008Jindal P, Sharma P, Kundu M, et al (2022) Computational Fluid Dynamics (CFD) analysis of Graphene Nanoplatelets for the cooling of a multiple tier Li-ion battery pack. Therm Sci Eng Prog 31:101282. https://doi.org/10.1016/j.tsep.2022.101282Kalbasi R, Salimpour MR (2015) Constructal design of phase change material enclosures used for cooling electronic devices. Appl Therm Eng 84:339–349. https://doi.org/10.1016/j.applthermaleng.2015.03.031Kandasamy R, Wang XQ, Mujumdar AS (2008) Transient cooling of electronics using phase change material (PCM)-based heat sinks. Appl Therm Eng 28:1047–1057. https://doi.org/10.1016/j.applthermaleng.2007.06.010Khan RJ, Bhuiyan MZH, Ahmed DH (2020) Investigation of heat transfer of a building wall in the presence of phase change

(PCM). Energy Built Environ 1:199–206. https://doi.org/10.1016/j.enbenv.2020.01.002Kousksou T, Mahdaoui M, Ahmed A, Msaad AA (2014) Melting over a wavy surface in a rectangular cavity heated from below. Energy 64:212–219. https://doi.org/10.1016/j.energy.2013.11.033Kumar R, Alam MT, Gupta AK (2024) Delineating effects of cell arrangements, wall shapes, flow configurations, and phase change mate- rial on airflow-based lithium-ion battery thermal management. Int Commun Heat Mass Transf 159:108271. https://doi.org/10.1016/j.icheatmasstransfer.2024.108271Li ZW, Lv LC, Li J (2016) Combination of heat storage and thermal spreading for high power portable electronics cooling. Int J Heat Mass Transf 98:550– 557. https://doi.org/10.1016/j.ijheatmasstransfer.2016.03.068Mosaffa AH, Talati F, Basirat Tabrizi H, Rosen MA (2012) Analytical modeling of PCM solidification in a shell and tube finned thermal storage for air conditioning systems. Energy Build 49:356–361. https://doi.org/10.1016/j.enbuild.2012.02.053Nagaraju D, Preetham MVSMV, Mohammad AR, et al (2022) Influence of phase change material encapsulation shape on performance of energy-efficient roof design. Energy Storage 4:e321. https://doi.org/10.1002/EST2.321Roe C, Feng X, White G, et al (2022) Immersion cooling for lithium-ion batteries – A review. J Power Sources 525:231094. https://doi.org/10.1016/j.jpowsour.2022.231094Ruˇ cevskis S, Akishin P, Korjakins A (2020) Parametric analysis and design optimisation of PCM thermal energy storage system for space cooling of buildings. Energy Build 224:. https://doi.org/10.1016/j.enbuild.2020.110288Santhosh Reddy V, Venkatachalapathy S, Nanda Kishore PVR (2024) Study on thermal performance and flow behavior of myristyl alcohol phase change material microencapsulated with hybrid shell in minichannels. Appl Therm Eng 257:124138. https://doi.org/10.1016/j.applthermaleng.2024.124138Sciacovelli A, Gagliardi F, Verda V (2015) Maximization of performance of a PCM latent heat storage system with inno- vative fins. Appl Energy 137:707–715. https://doi.org/10.1016/j.apenergy.2014.07.015Seddegh S, Joy- bari MM, Wang X, Haghighat F (2017) Experimental and numerical characterization of natural con- 14 Posted on 31 Mar 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.174340277.79562610/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. vection in a vertical shell-and-tube latent thermal energy storage system. Sustain Cities Soc 35:13–24. https://doi.org/10.1016/j.scs.2017.07.024Seddegh S, Wang X, Henderson AD (2015) Numerical investiga- tion of heat transfer mechanism in a vertical shell and tube latent heat energy storage system. Appl Therm Eng 87:698–706. https://doi.org/10.1016/j.applthermaleng.2015.05.067Shmueli H, Ziskind G, Letan R (2010) Melting in a vertical cylindrical tube: Numerical investigation and comparison with experiments. Int J Heat Mass Transf 53:4082–4091. https://doi.org/10.1016/j.ijheatmasstransfer.2010.05.028Singh LK, Kumar R, Gupta AK (2023) A novel strategy of enhanced thermal performance in air cooled lithium-ion battery by wavy walls. Therm Sci Eng Prog 43:101964. https://doi.org/10.1016/j.tsep.2023.101964Soares N, Gaspar AR, Santos P, Costa JJ (2015) Experimental study of the heat transfer through a ver- tical stack of rectangular cavities filled with phase change materials. Appl Energy 142:192–205. https://doi.org/10.1016/j.apenergy.2014.12.034Srivastava G, Nandan R, Das MK (2022) Thermal runaway management of Li ion battery using PCM: A parametric study. Energy Convers Manag X 16:100306. https://doi.org/10.1016/j.ecmx.2022.100306Sunku Prasad J, Anandalakshmi R, Muthukumar P (2021) Nu- merical investigation on conventional and PCM heat sinks under constant and variable heat flux conditions. Clean Technol Environ Policy 23:1105–1120. https://doi.org/10.1007/s10098-020-01829-8Yang X, Lu Z, Bai Q, et al (2017) Thermal performance of a shell-and-tube latent heat thermal energy storage unit: Role of annular fins. Appl Energy 202:558–570. https://doi.org/10.1016/j.apenergy.2017.05.007Zennouhi H, Beno- mar W, Kousksou T, et al (2017) Effect of inclination angle on the melting process of phase change material. Case Stud Therm Eng 9:47–54. https://doi.org/10.1016/j.csite.2016.11.004Zhao L, Xing Y, Wang Z, Liu X (2017) The passive thermal management system for electronic device using low-melting-point alloy as phase change material. Appl Therm Eng 125:317–327. https://doi.org/10.1016/j.applthermaleng.2017.07.004 15