# A Numerical Investigation of a Melting Rate Enhancement inside a Thermal Energy Storage System of Finned Heat Pipe with Nano-Enhanced Phase Change Material

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## Abstract

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## 1. Introduction

_{2}O

_{3}), and copper oxide (CuO), are dispersed in PCM to create hybrid NePCMs. The NePCM composed of 75% GNPs and 25% MWCNTs exhibits the greatest thermal conductivity increase. Sivashankar et al. [44] studied CPV cells employing graphene nanoplatelets integrated into PCM. They reported that the efficiency and output power of the CPV cells improved when NePCM is added to the system, and the optimal volumetric fraction of nanoparticles was determined to be 0.5%. Faraji et al. [45] used numerical analysis to explore the NePCM melting in an inclined rectangular cage. They demonstrated that the particle concentration in PCM has an impact on heat transmission performance. Mhiri et al. [46] developed a unique kind of stable PCM for TES systems comprised of nanocomposites containing a paraffin/graphite combination embedded in carbon foam. The findings indicated that adding graphite and carbon foam to paraffin wax improved its thermal qualities and prevented melted paraffin from escaping, hence preserving its steady thermal performance. Shirazi et al. [47] examined the viability of employing PCM nanocomposites to regulate the heat generated by a Li-ion battery package effectively. According to simulation findings, encapsulating the batteries inside a paraffin nanocomposite reduced temperature variance and increased thermal conductivity. Bondareva et al. [48] explored the thermal properties of a finned heat sink loaded with NePCM. They discovered that the addition of the nanopowders improved the first melting process due to heat conduction between the liquid PCM and the solid. Ghalambaz et al. [49] used the Taguchi optimization technique to optimize the melting process of the NePCM in a shell/tube TES configuration. The findings indicated a 23.3% increase in stored thermal energy (Cu) and a 22.5% increase in stored thermal energy (GO) were attained.

## 2. Problem Description

#### 2.1. Mathematical Model

- The flow of liquid NePCM is regarded to be incompressible and laminar.
- Overlooking the volumetric impact of viscous dissipation and heat source.
- The shell wall is assumed to maintain a constant temperature, ignoring the heat transfer resistance of the container wall and the convective heat transfer process inside the tube.
- There is no heat transfer between the shell and its surroundings.

#### 2.2. Validation and Mesh Independence Study

## 3. Results and Discussion

_{avg}), average Bejan number (Be

_{avg}), the average liquid fraction (B), and the average temperature in the TES unit are interpreted for various nanoparticle concentrations and wavenumbers.

#### 3.1. Time Needed for Melting NePCM

#### 3.2. Nanoparticle’s Concentration Effect on the Acceleration of the Melting Process

_{avg}), average Bejan number (Be

_{avg}), the average liquid fraction (B), and the average temperature in the TES unit are shown in Figure 6. As a reference, the findings of pure PCM are also presented.

_{avg}and Be

_{avg}values decreased, which could be attributed to the fact that introducing nanoparticles to the PCM bolstered its thermal properties, increasing heat transfer and melting rate, implying that the temperature in NEPCM samples became uniform faster as time passed (leading to a smaller temperature gradient, as seen in Figure 6 bottom right). As a result, the heat transmission intensity reduces, and Nu

_{avg}and Be

_{avg}fall quicker in NEPCM than in pure PCM.

#### 3.3. Influence of Waves Number on the Melting Process

_{avg}), average Bejan number (Be

_{avg}), the average liquid fraction (B), and the average temperature in the TES unit are shown in Figure 8.

_{avg}, Be

_{avg}, the average liquid fraction (B), and T

_{avg}as a function of time. Figure 8 illuminates that heat transfer for N = 6 and N = 8 is superior to N = 4 after the first 45 min, which is a critical period in melting propagation, especially for the bottom region. N = 8 design minimizes the distance between the fins and the external surface, which minimizes the thermal resistance of NEPCM. The full body of the PCM takes 227, 180, and 155 min to melt for N = 4, N = 6, and N = 8, respectively. This indicates that using the N = 8 design rather than the N = 4 design reduces the melting time by 31%. The Be

_{avg}is high for the first 25 min in all circumstances owing to elevated heat transfer rates, then it subsequently drops as the temperature gradient progressively diminishes, which is indicated by the T

_{avg}plot in Figure 8.

## 4. Conclusions

- Owing to the presence of natural convection, the melting rate seen in the upper section of the analyzed annulus is significantly higher than that observed at its bottom portion;
- Depending on the volume fraction of nano-additive used, the melting time could be reduced from 3% to 14% with 2% and 4% nanoparticle concentrations, respectively;
- The phase transition process may be greatly accelerated by increasing the wave number N. When the wave number was increased from four to eight, the overall melting time decreased by 31%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**A**) Three-dimensional model of the shell and tube TEs with embedded fins; (

**B**) A two-dimensional illustration of the studied model with boundary conditions; (

**C**) A mesh sample; (

**D**) fins dimensions.

**Figure 4.**Effect of time on temperature, liquid fraction, and Bejan number during the PCM melting process.

**Figure 5.**Impact of Cu nanoparticle concentration on temperature, liquid fraction, and Bejan number during the PCM melting process after 10 min.

**Figure 6.**Influence of Copper nanoparticles concentration on average Nusselt number, the average liquid fraction (B), Bejan number, and average temperature during the NePCM melting process.

**Figure 7.**Effect of wave number N on temperature, liquid fraction, and Bejan number during the PCM melting process after 10 min.

**Figure 8.**Influence of wave number on average Nusselt number, the average liquid fraction (B), Bejan number, and average temperature during the NePCM melting process.

Properties of the Materials | PCM | Inner-Tube Wall | Nanoparticle | |
---|---|---|---|---|

(paraffin wax) | Copper | Copper | ||

Solid | Liquid | |||

Thermal conductivity, k, (W/mK) | 0.39 | 0.157 | 401 | 401 |

Density, ρ, (kg/m^{3}) | 775 | 833.6 | 8900 | 8954 |

Kinematic viscosity (m^{2}/s) | 8.31 × 10^{−5} | |||

Thermal expansion coefficient, β, (1/K) | - | 7.14 × 10^{−3} | 1.67 × 10^{−5} | |

Specific heat, c_{p}, (kJ/kgK) | 2.44 | 2.384 | 0.385 | 0.385 |

The melting point (°C) | 54.32 | |||

Latent heat of fusion (kJ/kg) | 184.48 | |||

The reference temperature (°C) | 50 |

Mesh | G1 | G2 | G3 |
---|---|---|---|

Number of elements | 25,096 | 66,982 | 100,384 |

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**MDPI and ACS Style**

Jirawattanapanit, A.; Abderrahmane, A.; Mourad, A.; Guedri, K.; Younis, O.; Bouallegue, B.; Subkrajang, K.; Rajchakit, G.; Shah, N.A. A Numerical Investigation of a Melting Rate Enhancement inside a Thermal Energy Storage System of Finned Heat Pipe with Nano-Enhanced Phase Change Material. *Nanomaterials* **2022**, *12*, 2519.
https://doi.org/10.3390/nano12152519

**AMA Style**

Jirawattanapanit A, Abderrahmane A, Mourad A, Guedri K, Younis O, Bouallegue B, Subkrajang K, Rajchakit G, Shah NA. A Numerical Investigation of a Melting Rate Enhancement inside a Thermal Energy Storage System of Finned Heat Pipe with Nano-Enhanced Phase Change Material. *Nanomaterials*. 2022; 12(15):2519.
https://doi.org/10.3390/nano12152519

**Chicago/Turabian Style**

Jirawattanapanit, Anuwat, Aissa Abderrahmane, Abe Mourad, Kamel Guedri, Obai Younis, Belgacem Bouallegue, Khanyaluck Subkrajang, Grienggrai Rajchakit, and Nehad Ali Shah. 2022. "A Numerical Investigation of a Melting Rate Enhancement inside a Thermal Energy Storage System of Finned Heat Pipe with Nano-Enhanced Phase Change Material" *Nanomaterials* 12, no. 15: 2519.
https://doi.org/10.3390/nano12152519