**1. Introduction**

In modern times, energy storage and conservation solutions are as important as ever due to depletion and climate change challenges. Phase change materials (PCMs) are at the forefront in this domain due to their low cost and availability [1–3].

Due to the continuous development of PCM research, their range of applications has widened: PCMs are now integrated into automotive applications [4], energy storage applications [5], and heat exchangers [6]. Allouhi et al. [7] employed PCMs to optimize an energy storage system for solar water heaters operated by households in rural regions to fulfil their hot water needs at night. Huang et al. [8] used a dual-phase-change material to design a heat sink to minimize its cost and weight. Carmona et al. [9] used a PCM to improve the energy efficiency of a water storage tank for domestic applications. Their numerical model was validated with an experimental study. They found that including 40% of PCM inside the water storage tank increased its efficiency by 16%. PCMs are also used to conserve energy in the building sector as they are integrated into walls [10] and roofs [11], and can be used in indoor applications such as house furniture or decorations [12] to

**Citation:** Ahmed, S.E.;

Abderrahmane, A.; Alotaibi, S.; Younis, O.; Almasri, R.A.; Hussam, W.K. Enhanced Heat Transfer for NePCM-Melting-Based Thermal Energy of Finned Heat Pipe. *Nanomaterials* **2022**, *12*, 129. https:// doi.org/10.3390/nano12010129

Academic Editor: S. M. Sohel Murshed

Received: 7 December 2021 Accepted: 28 December 2021 Published: 31 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

maintain a favorable room temperature. They can also be used in building envelopes as PCM-to-air heat exchangers where air discharges and charges the PCM with energy [13,14]. Padala et al. [15] explored the use of a PCM in a mixture for masonry blocks to determine the ideal mix proportions to attain the best mechanical, durability-related, and thermal characteristics of these mixes. Chen et al. [16] investigated the thermal performance of a thermo-activated PCM mixture integrated into a wall for energy saving purposes during winter. Gholamibozanjani et al. [17] experimentally examined incorporating PCMs to conserve energy inside huts over the seasons of a year. The results proved that the PCM storage units were able to reduce the heating/cooling energy requirements: the accumulative energy-saving varied between 10% and 40% during the year. Tyagi et al. [18] evaluated the performance of a PCM-based energy storage unit comprising panels charged by sunlight during the daytime then used during the night as a heat source for a test room. Violidakis et al. [19] discussed the use of an ultra-high-temperature PCM such as silicon in residential buildings. They possess excellent thermal conductivity and high latent heat thermal energy, achieving greater energy density and capacity. Frazzica et al. [20] produced and characterized mortar PCMs, then they introduced a new experimental setup to evaluate its thermal performance. However, PCMs still face challenges such as long discharging and changing times and low heat transfer rate due to their low thermal conductivity [21]. Thus, new technologies must be developed to improve their thermal properties and heat transfer performance. The most intuitive solution to enhance a PCM's melting process is to extend the contact surface. Dmitruk et al. [22] studied a cylindrical PCM-based heat storage system equipped with a pin-fin structure to improve the heat transfer rate within this system. After multiple charging/discharging cycles, the experimental and numerical results showed the positive effect of the pin-fin structure on PCM performance. Sathe et al. [23] numerically analyzed the thermal-hydraulic performance a PCM melting inside a tilted finned container with a top heating mode. They observed that decreasing the inclination angles and extending the surface and fins increased the melting time for all the PCMs. Nie et al. [24] studied the thermal performance of a PCM as part of a composite containing fumed silica and graphene that was used to enhance the capability of a portable box to maintain cold temperature. According to their results, adding 1 wt% of graphene and 4 wt% of fumed silica enhanced the thermal conductivity of the PCM composite by 55.4% and helped to eliminate the PCM leakage problem. Izgi et al. [25] studied the solidification process of a PCM inside a three-dimensional cylinder. They focused on finding controlling parameters for this phenomenon. From the results, they observed that the diameter of the cylinder influenced the energy discharge and the solidification times. Sweidan et al. [26] performed multiple numerical computations to investigate the effectiveness of various techniques (multiple PCM layers, mingle PCM with highly conductive fins, and PCMsaturated metal foam) in improving PCM performance. Tarigond et al. [27] used iron scrap additives to boost the thermal performance of the PCM inside a thermal energy storage system for hot water. The results demonstrated the positive impact of these additives on the performance of the PCM, as the yield of hot water was improved by 25% compared to the control system. Ahmed et al. [28] proposed a novel design for a cascaded-layered PCM as a cost effective solution for medium-temperature industrial applications. From the results, they indicated the best volume fraction arrangement for thermal energy storage. Selimefendigil et al. [29] used FEM to evaluate the free convection of a copper oxide/water nano-liquid within a square cavity with PCM attached to its vertical wall. They found that by increasing the height of the PCM from 0.2 to 0.8 H, both the local and average Nusselt numbers decreased by 42.14%. Abu-Hamdeh et al. [30] performed a three-dimensional examination of the paraffin wax melting process in an ellipsoidal pipe with a hotter inner pipe. They discovered that the location of the inner pipe and the temperature differential influence the time required for the PCM to melt.

Nowadays, the most effective approaches for improving the thermal performance of PCMs are using a porous medium or metal foam as a support matrix for the PCM and adding high thermal conductivity nanoparticles to the PCM [31]. However, the simplest the most used method involves embedding fins in the PCM containers. Over the years, several studies have been conducted on the influence of fins on heat transfer in various media, including PCMs [32–35].

Jeong et al. [36] reported that the thermal properties of three different shape-stabilized PCM composites were enhanced by adding exfoliated graphite nanoplatelets (xGnP). Nóbrega et al. [37] investigated the influence of adding fins to a tube filled with a nano-PCM mixture. The findings suggested that the fins helped decrease the solidification time by 9.1%, and increasing the concentration of nanoparticles improved the solidification process regardless of the presence of fins. Raj et al. [38] packed a nano-enriched PCM inside a wall-less heat sink used in a thermal management application. The study results revealed that the addition of MWCNTs and GnP nanoparticles to the FS-PCM enhanced its thermal conductivity by 61.73% and 84.48%, respectively, thus improving the heat transfer performance. Jourabian et al. [39] investigated the melting behavior of ice as a PCM within a horizontal elliptical tube filled with nickel-steel porous media. Das et al. [40] addressed the form stability of a PCM subjected to numerous cycles of charging and discharging by producing a novel biocomposite-based PCM. The testing results indicated that using biochar from *Eichornia crassipes* as a supporting matrix mix with a small amount of aluminum metal powder enhanced the thermal conductivity of the PCM 17.27 times and improved its overall stability. Vennapusa et al. [41] tested six lightweight support materials to improve the form stability of a caprylic-acid-based PCM. From the results, they concluded that using expanded perlite as a support matrix for the PCM achieved the highest enthalpy and thermal buffering.

Rathore et al. [42] added expanded vermiculite and expanded graphite to improve the thermophysical properties of a low-cost PCM. The study results revealed that the thermal conductivity increased by 114.4% when the PCM was loaded with 7% of EG. Moreover, the enhanced PCM preserved its thermal properties even after 1000 charging and discharging cycles. Qureshi et al. [43] employed TPMS-based metal foams with a 3D-printed structures as a skeleton for MFPCMs to improve the thermal conductivity of traditional PCMs. According to their results, the thermal conductivity of MFPCMs was strongly affected by the cell type and its unique shape, in addition to the cell porosity. Combining the two approaches, Nada et al. [44] discussed enhancing paraffin wax as a PCM in an energy storage unit by using a carbon foam matrix and MWCNTs additives. Mehryan et al. [45] studied the non-Newtonian behavior in space between two coaxial pipes filled with metal foam. They reported that a 54% reduction in the melting time could be achieved by lowering the power law index from 1 to 0.6.

The literature review revealed that entropy formation during the charging process has been not well-investigated. As a result, in this study, we used GFEM to replicate NEPCM's second-law behavior during melting. The contours of entropy component, temperature, and melt fraction are shown.
