Computational assessment of cold thermal energy storage improvement using hybrid nanofluid cooling and metal foam media

Abstract

This article conducts an in-depth numerical investigation of an advanced cold thermal energy storage system based on an annular enclosure incorporating dual cold boundaries and radial fin elements to promote faster solidification. The system performance is improved through the combined application of several heat transfer enhancement techniques, namely porous metallic foam, hybrid nanoparticle-based working fluids, and the inclusion of radiative heat transfer effects. The porous foam matrix enhances overall thermal conduction by facilitating efficient heat transport across the storage region, whereas the hybrid nanomaterials intensify heat transfer at the microscale. The formulated mathematical model captures transient phase-change behavior while simultaneously accounting for conductive and radiative heat transfer mechanisms. A Galerkin finite element approach with an implicit time-stepping scheme and adaptive mesh refinement is adopted to precisely track the moving solid–liquid interface. Validation against established results from the literature demonstrates strong agreement. The results indicate that incorporating thermal radiation reduces the freezing time by approximately 22.95%, underscoring its importance in low-temperature energy storage applications. The most pronounced enhancement is achieved through porous foam implementation, which decreases the solidification duration by nearly 79.19%, while replacing water with a hybrid nanofluid provides an additional reduction of about 5.81%.

Introduction

Energy storage systems have become essential in a wide range of applications, such as air-conditioning technologies, refrigeration, and sustainable energy storage solutions^1–3. The efficient management of time during the solidification and freezing processes is essential for optimizing energy consumption and ensuring the effective performance of these systems^4–6. As the demand for energy-efficient technologies grows, the enhancement of cold storage systems has become a significant area of research^7–9. To improve the performance of these systems, various approaches can be employed, such as the incorporation of porous foam to accelerate heat transfer, the inclusion of hybrid nanoparticles to boost conduction, and the application of radiation cooling to manage thermal losses^10–13. These techniques, when combined, have the potential to significantly reduce freezing time and increase overall system efficiency, offering promising solutions^14–16. In recent years, there has been growing research interest in examining the performance and behavior of phase change materials (PCM) across various energy units^17–19. To analyze and predict system performance, researchers have employed various numerical and experimental approaches to better understand heat transfer characteristics and phase-change dynamics under different operating conditions^20–22. Improving system performance has become one of the key objectives for researchers over the past decade^23–25. Yu et al.²⁶ demonstrated that a flipping strategy can enhance heat storage performance by applying a 180° rotation of the thermal storage unit, which improves heat transfer and overall energy utilization. Their study showed that this single rotation enhanced the melting rate. Sheikholeslami and Hussein²⁷ proposed a novel solar still configuration incorporating PCM at the beneath of floor. They proved that integrating tree-shaped fins within the PCM region significantly improves heat transfer, causing melting period to reduce about 15%. Memon et al.²⁸ scrutinized the free convection melting process around a heated cylinder within a tank filled with paraffin. Their findings indicated that adjusting the placement of the cylinder enhanced the charging.

Wang et al.²⁹ examined two different porous media configurations, namely closed and open cells structures, in a PCM-based thermal system. They indicated that the closed-cell porous structure yields a higher liquid fraction compared with the open-cell configuration. In addition, they reported that utilizing closed option reduces melting time by 55%. Peiro et al.³⁰ conducted experimental investigations on single PCM storages to examine their thermal behavior. Their findings showed that the CLHS demonstrated 19.36% better effectiveness compared to the other storage systems tested. Sheikholeslami and Alturaihi³¹ proposed an improved solar panel cooling configuration considering dust accumulation effects under the climatic conditions of Najaf city. Their study showed that integrating a hybrid cooling approach, combining PCM with a water-based duct system, can significantly enhance the electrical efficiency around 16.22%. Afaynou et al.³² scrutinized the optimization of an energy storage system incorporating hybrid PCM. Their results indicated that when the entire container is filled with PCM, the device temperature can be reduced by approximately 38%, while the melting duration of the PCM is reported to be about 1163 s. Kurnia et al.³³ conducted a modeling to evaluate the efficacy of improved heat transfer in rotating Phase Change Heat Storage (PCHS) devices. Their results revealed that rotation improved performance about 25% during charging. Wang and Mobedi³⁴ scrutinized the impact of incorporating metal foam in PCM-based systems. They applied both the pore-scale and volume-averaged modeling approaches and demonstrated that the results obtained from the two methods show good agreement. Huang et al.³⁵ reported that fins markedly enhance thermal performance by mitigating hysteresis effects. These fins effectively enhanced both solidification and melting rates. Sheikholeslami and Mustafa³⁶ proposed the use of PCM combined with porous foam as a passive cooling strategy for solar panel. Their findings demonstrated that integrating this cooling configuration effectively improves thermal regulation of the panel, leading to an enhancement in electrical power output of approximately 5.02%. Fang and Chen³⁷ conducted a numerical investigation into the phase transition temperature differences between consecutive phase change materials (PCMs) within a unit, ensuring that the average melting temperature remained consistent across each unit. Their findings highlighted that PCMs with larger ∆T between consecutive stages exhibit more effective sensible heating and a greater capacity. Hanchi et al.³⁸ explored a finned enclosure combined with PCM and exposed to two heated boundaries. They showed that introducing inclined fins at an angle of 15° causes melting periode to decline about 2.45%. Li et al.³⁹ examined the melting and freezing characteristics of a system under flipped conditions. Their findings revealed that flipping acceleration notably influences the process when the solid fraction remains below 50% during freezing.

Recent advancements in cold thermal energy storage systems have focused on enhancing the solidification process to improve energy efficiency and thermal performance. However, many previous studies primarily relied on individual enhancement methods, such as finned structures, porous media, or nanomaterials, without integrating these techniques into a comprehensive system. The novelty of current research stems from the integrated application of multiple enhancement techniques—radial fins, hybrid nanomaterials, and metal foam—coupled with the consideration of radiation heat transfer effects, a factor frequently overlooked in previous studies. This combined approach not only expedites the solidification but also boost cold energy storage capacity and ensures greater temperature uniformity. Furthermore, the implement of an adaptive grid technique in the numerical model significantly improves the accuracy of the solidification front prediction, addressing a critical gap in the existing literature. Unlike conventional models that simplify boundary conditions or exclude radiation effects, the current article provides a more realistic simulation of the freezing process under complex thermal conditions. These innovations contribute to a more efficient energy system, making this study a valuable step forward in developing high-performance thermal storage technologies for various industrial and residential applications.

Storing cold energy within enclosure

This study offers a numerical model of the solidification process through a porous annular tank fitted with radial fins. The configuration features two cold walls, each equipped with fins to enhance heat transfer, as portrayed in Fig. 1. The porous region is infused with a hybrid nanomaterial to boost the unit’s thermal performance. The combination of these enhancement strategies meaningfully boosts the freezing rate, while the inclusion of radiative heat transfer effects ensures a more comprehensive and realistic analysis. The numerical modeling employs an implicit solution approach, along with an adaptive mesh approach, to solve the two governing equations of the present model. These governing equations are formulated by assuming that the influence of gravitational forces is sufficiently small to be ignored, simplifying the system and focusing on thermal conduction and phase change phenomena. Several case studies have been simulated to scrutinize the impact of various parameters on the solidification rate, providing insight into the effectiveness of the design and materials. The model explores how different configurations and conditions influence the overall productivity, with a particular focus on optimizing the solidification process^40,41.

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Fig. 1.

Container with two cold side in presence of porous foam.

In calculating the effective properties in Eq. (3), the features of PCM must be measured. The below formulation, as proposed in⁴¹, has been applied to derive these properties:

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5

6

The present work employs the coupling of the Galerkin method, a method previously suggested by Sheikholeslami^40,41. He proposed various shapes for cold storage systems and demonstrated that the accuracy of the model was consistent with experimental data. In this study, the effect of hybrid nanomaterials is incorporated using the formulation outlined earlier. The use of a single-phase model, which has been adjusted for the present work, is appropriate due to the low concentration of each component (0.02), ensuring the accuracy and applicability of the model for this specific scenario.

Results and discussion

This article illustrates a detailed numerical investigation of the freezing through a porous annular tank equipped with radial fins, offering a new technique to boost efficiency of energy storage unit. Two cold walls—horizontal and vertical—are strategically applied to the enclosure, with radial fins attached to both surfaces to rise the heat transfer area. The hybrid nanomaterial, consisting of suspended metallic nanoparticles within the PCM, is embedded in the porous medium to further boost the effective thermal conductivity. A notable phase of this article is the incorporation of thermal radiation into the governing equations, a factor often neglected in previous research despite its significant influence on heat transfer in cold storage systems. The mathematical model employs the Galerkin finite element method with an implicit time-stepping approach. The analysis explores the effects of critical factors such as the thermal conductivity of hybrid nanomaterials, the integration of porous media, radiative heat transfer, and fin configurations. Findings indicate that the simultaneous application of hybrid nanoparticles, porous structures, and fins markedly enhances the solidification rate.

The verification test was accompanied by comparing the outputs with data from previous studies⁴⁰. The outputs, presented in Fig. 2, demonstrate a strong agreement, confirming that the current numerical model is suitable for the current study. The correctness of the modeling is further enhanced by the use of an adaptive grid, as shown in the sample configuration in Fig. 3. This technique improves the prediction of scalar values, particularly in regions with high gradients, leading to more precise results.

Fig. 2.

Denser mesh near the high gradeint region.

Fig. 3.

The report of good accuracy against output of Ref⁴⁰.

The distribution of scalar fields over time for various parameter levels is shown in Figs. 4, 5 and 6, and 7. The presence of two cold sides accelerates the freezing process, particularly when fins are applied to both sides. The initial temperature is 274 K, and due to the lower temperature of the cold walls, cold energy gradually penetrates the domain as time progresses. This results in the isotherms aligning with the shape of the container, reflecting the dominance of these boundary conditions. As the porosity of the domain decreases, the solidification rate increases, with full solidification occurring at 336.27 s. In the absence of foam and in the presence of water alone, the time for complete freezing is 1715.51 s. When nanoparticles are introduced into the water, the overall temperature of the domain is further reduced, while a slight increase in the solid fraction is observed, which contributes to an improvement in the solidification process.

Fig. 4.

Contours plots for various time levels at .

Fig. 5.

The case with and distribution of scalars.

Fig. 6.

The case with and distribution of scalars.

Fig. 7.

The case with and distribution of scalars.

The progression of the freezing front, illustrated in Fig. 8, reveals that increasing the radiation parameter (Rd) accelerates solidification, while the incorporation of porous foam further intensifies this effect. A reduction in foam porosity significantly shortens the freezing time, decreasing it from 1615.88 s to 336.27 s. Figures 9, 10 and 11 present the temporal evolution of the average values of three distinct functions under varying parameter settings. Introducing nanoparticles into the water enhances conductive heat transfer, promoting a larger solid phase fraction, lowering the domain temperature, and reducing the system’s total energy. In the energy analysis, both latent and sensible heat release are accounted for. Higher values of Rd and nanoparticle volume fraction (ϕ) lead to shorter times to achieve a complete solid fraction. As the process continues, the system temperature drops, with a more pronounced decrease observed in cases utilizing porous foam.

Fig. 8.

The augment of speed of freezing with change of Rd and γ.

Fig. 9.

Amounts of variables with alter of time and γ.

Fig. 10.

Amounts of variables with alter of time and ϕ.

Fig. 11.

Amounts of variables with alter time and Rd.

Figure 12 presents the impact of various active factors on freezing time. The incorporation of porous foam markedly improves the freezing process, as its solid matrix enhances heat conduction, leading to a 79.19% reduction in freezing time. Increasing the radiation parameter (Rd) further shortens freezing time by 22.95%, while dispersing hybrid nanoparticles in water results in an additional 5.81% decrease. Among these factors, porous foam proves to be the most effective, achieving a reduction in freezing time that is approximately 13.63 times greater than that obtained by altering the nanoparticle volume fraction (ϕ) and 3.45 times greater than that achieved by increasing Rd. These findings clearly highlight the dominant role of porous foam in expediting the freezing process compared to other enhancement techniques.

Fig. 12.

Time management of process.

Conclusion

This study offers a detailed numerical analysis of the freezing process in a porous annular container equipped with radial fins. The design integrates hybrid nanoparticles, porous metal foam, and extended surfaces to accelerate solidification. The synergy between radial fins and hybrid nanoparticles improves thermal conductivity within the phase change material (PCM) and facilitates more efficient heat dissipation. Radiative heat transfer, often neglected in prior studies, is incorporated into the model, showing a notable impact on the freezing rate. Results reveal that porous foam delivers the most significant enhancement, decreasing freezing time by 79.19% compared to the foam-free case—about 13.63 times the improvement achieved by nanoparticles alone and 3.45 times that of radiation effects. Radiation shortens solidification by 22.95%, while hybrid nanoparticles in water-based PCM reduce it by 5.81%. The porous foam acts as a conductive matrix, substantially boosting both solidification rate and overall energy storage capacity. The analysis further shows that higher radiation parameters (Rd) and nanoparticle volume fractions (ϕ) accelerate the attainment of full solid fraction. Temperature decline across the domain is more pronounced with porous foam, and lower foam porosity leads to faster freezing. The shortest complete solidification time, 336.27 s, is achieved with the foam structure, compared to 1715.51 s without foam. These outputs underscore the dominant role of metal foam, supported by nanoparticles and radiation, in advancing cold energy storage efficiency.

Author contributions

“N.H.A., A.B., and H.A.Z.A. wrote the main manuscript text and A.B.K prepared figures. All authors reviewed the manuscript.”

Funding

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, under grant no. (IPP: 32-135-2025).

Data availability

All relevant data from this study are included in this article.

Declarations

Competing interests

The authors declare no competing interests.