# Evaluation of Melting Mechanism and Natural Convection Effect in a Triplex Tube Heat Storage System with a Novel Fin Arrangement

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## Abstract

**:**

## 1. Introduction

## 2. System Description

^{3}/s, respectively.

## 3. Mathematical Modeling

- Consider incompressible and Newtonian fluid molten PCM.
- Consider ignorable viscous dissipation.
- Consider variable density while the other physical properties of PCM are constant.
- Apply Boussinesq approximation for density variation in the liquid PCM.

_{p}dT), and latent heat (ML

_{f}) of the PCM. ${t}_{m}$ is the melting time.

## 4. Numerical Analysis

^{−4}, 10

^{−4}, and 10

^{−6}, respectively.

#### 4.1. Spatial and Temporal Discretization

#### 4.2. Model Validation

## 5. Results and Discussion

#### 5.1. Effects of Using Triangular Fins on the Charging Phenomenon

^{2}for each fin) in all the cases.

#### 5.2. Effects of Using Reverse Triangular Fins on the Charging Process

#### 5.3. Summary of Selecting the Best Configuration

#### 5.4. Comparing the Thermal Performance of Reverse Triangular Fins with That of No-Fin and Uniform-Fin Cases

#### 5.5. Investigating the Effects of the Fin Added at the Bottom of the Heat Exchanger on the Charging Process of the PCM

## 6. Conclusions

- The slope of the sides of the triangular fins has a determinant role in the circulation of the PCM inside the heat storage unit.
- The case with the lowest slope (case with the highest fins height) provided a better barrier to keep the PCM inside the zone between two pairs of neighbor fins, while the case with the shortest fin height accelerated the PCM circulation through the zones.
- The case with the highest height of the fins, and thus the lowest base, experienced the fastest phase change process due to having the largest surface area of the fin.
- The reverse triangular fin provided a strong barrier against transferring the molten PCM through the zone, which slightly accelerated the melting process and improved the thermal storage rate.
- The case with reverse triangular fins and the highest height showed higher performance compared with the other cases, since 98.8% of the entire zone was melted, except the region at the bottom of the unit.
- Adding a rectangular fin to the bottom of the heat exchange with reverse triangular fins and the highest height was selected as the best model, resulting in the lowest melting time (1978 s) and the highest heat storage rate (81.5 W).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${A}_{m}$ | Mushy zone constant | Greek symbols | |

${C}_{p}$ (J kg^{−1} K^{−1}) | Specific heat | $\lambda $ | Liquid fraction |

E (J) | Heat storage | $\beta $ (K^{−1}) | Thermal expansion |

$g$(m s^{−2}) | Gravity | $\rho $ (kg m^{−3}) | PCM Density |

$k$ (W m^{−1} K^{−1}) | Effective thermal conductivity | $\Delta H$ (J kg^{−1}) | PCM Latent heat |

${L}_{f}$ (J kg^{−1}) | Latent heat of fusion | $\mu $ (m^{2}·s^{−1}) | Viscosity |

P (kg m^{−1} s^{−2}) | Pressure | Abbreviation | |

$\overrightarrow{S}$ (kg m^{−1} s^{−2}) | Source term | TES | Thermal energy storage |

$t$ (s) | Time | PCM | Phase change materials |

$T$ (°C) | Temperature | LHS | Latent heat storage |

${T}_{f}$(°C) | Air temperature | HTF | Heat transfer fluid |

${T}_{s}$(°C) | Solid temperature | LHTES | Latent heat thermal energy storage |

${T}_{Liquidus}$(°C) | Liquidus temperature | TTHX | Triple tube heat exchanger |

${T}_{Solidus}$(°C) | Solidus temperature | ||

$\overrightarrow{V}$ (m/s) | Velocity |

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**Figure 1.**The schematic of the proposed systems, including the no-fin case, uniform-fin case, triangular finned (TF) case, reverse triangular finned (RTF) case, and RTF case with added fin.

**Figure 3.**Comparing the numerical results of the present study, including the overall temperature and liquid fraction values of the PCM, with those of [62].

**Figure 6.**(

**a**) melting fraction and (

**b**) mean temperature of the PCM for different base dimensions of the fins (cases 4 to 7) (considering the best positions and the fixed cross-section of 10 mm

^{2}).

**Figure 10.**(

**a**) melting fraction and (

**b**) mean temperature of the PCM for different dimensions of the fins (Cases 8 to 11) (considering the best positions and the fixed cross-section of 10 mm

^{2}).

**Figure 12.**(

**a**) melting fraction and (

**b**) mean temperature for different cases (Cases 1, 2, and 8) (considering the fixed cross-section of 10 mm

^{2}and the best positions for the fins).

**Figure 15.**(

**a**) melting fraction and (

**b**) mean temperature of the PCM for various cases (cases 3, 12, and 13) (considering the fixed cross-section of 10 mm

^{2}and the best positions for the fins).

**Table 1.**Fins dimensions of the studied cases including the no-fin, uniform-fin, triangular finned (TF), reverse triangular finned (RTF) cases, and RTF case with an added fin to the bottom of the heat exchanger.

Cases | Description | Triangle Base/Uniform Fins Width (mm) | Triangle Height/Uniform Fins Height (mm) | Added Fin Dimensions (mm) |
---|---|---|---|---|

1 | no-fin | - | - | - |

2 | uniform-fin | 2 | 5 | - |

3 | uniform-fin + added fin | 1.6 | 5 | 1 × 20 |

4 | TF-base 2.5 | 2.5 | 8 | - |

5 | TF-base 3.0 | 3.0 | 6.65 | - |

6 | TF-base 3.5 | 3.5 | 5.7 | - |

7 | TF-base 4.0 | 4.0 | 5 | - |

8 | RTF-base 2.5 | 2.5 | 8 | - |

9 | RTF-base 3.0 | 3.0 | 6.65 | - |

10 | RTF-base 3.5 | 3.5 | 5.7 | - |

11 | RTF-base 4.0 | 4.0 | 5 | - |

12 | RTF-base 2.5 + added fin (constant base) | 2.5 | 6.4 | 1 × 20 |

13 | RTF-base 2.5 + added fin (constant height) | 2 | 8 | 1 × 20 |

**Table 2.**Thermodynamic properties of the PCM used [34].

Properties | $\mathit{\rho}\mathit{l}$ [kg/m ^{3}] | $\mathit{\rho}\mathit{s}$ [kg/m ^{3}]
| Lf [kJ/kg] | Cp [kJ/kg·K] | K [W/m·K] | µ [N·s/m ^{2}] | TL [°C] | TS [°C] | β [J/K] |
---|---|---|---|---|---|---|---|---|---|

Values | 770 | 860 | 170 | 2 | 0.2 | 0.023 | 36 | 29 | 0.0006 |

Number of cells | 43,000 | ||

Value of Time step size (s) | 0.1 | 0.2 | 0.4 |

Melting duration | 4733 | 4727 | 4701 |

**Table 4.**Melting time and heat storage rate for various cases of triangular fins (cases 4–7), and reverse triangular fins (cases 8–11).

Case | Case 4 | Case 5 | Case 6 | Case 7 | Case 8 | Case 9 | Case 10 | Case 11 |
---|---|---|---|---|---|---|---|---|

TF-base 2.5 | TF-base 3.0 | TF-base 3.5 | TF-base 4.0 | RTF-base 2.5 | RTF-base 3.0 | RTF-base 3.5 | RTF-base 4.0 | |

Melting time (s) | 3060 | 3118 | 3176 | 3212 | 2997 | 3149 | 3180 | 3209 |

Heat storage rate (W) | 55.01 | 53.9 | 52.99 | 52.39 | 56.05 | 53.38 | 52.85 | 52.36 |

Case | Case 1 (No-Fin) | Case 2 (Uniform-Fin) | Case 8 (RTF-Base 2.5) |
---|---|---|---|

Melting time (s) | 4654 | 3056 | 2997 |

Heat storage rate (W) | 36.2 | 55.1 | 56.1 |

Case | Case 3 (Uniform-Fin + Added Fin) | Case 12 (RTF-Base 2.5 + Added Fin (Base Constant)) | Case 13 (RTF-Base 2.5 + Added Fin (Height Constant)) |
---|---|---|---|

Melting time (s) | 2057 | 2178 | 1978 |

Heat storage rate (W) | 77.9 | 74.5 | 81.5 |

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Najim, F.T.; Kaplan, S.; Mohammed, H.I.; Dulaimi, A.; Abed, A.M.; Ibrahem, R.K.; Al-Qrimli, F.A.; Mahmoud, M.Z.; Awrejcewicz, J.; Pawłowski, W.
Evaluation of Melting Mechanism and Natural Convection Effect in a Triplex Tube Heat Storage System with a Novel Fin Arrangement. *Sustainability* **2022**, *14*, 10982.
https://doi.org/10.3390/su141710982

**AMA Style**

Najim FT, Kaplan S, Mohammed HI, Dulaimi A, Abed AM, Ibrahem RK, Al-Qrimli FA, Mahmoud MZ, Awrejcewicz J, Pawłowski W.
Evaluation of Melting Mechanism and Natural Convection Effect in a Triplex Tube Heat Storage System with a Novel Fin Arrangement. *Sustainability*. 2022; 14(17):10982.
https://doi.org/10.3390/su141710982

**Chicago/Turabian Style**

Najim, Farqad T., Sami Kaplan, Hayder I. Mohammed, Anmar Dulaimi, Azher M. Abed, Raed Khalid Ibrahem, Fadhil Abbas Al-Qrimli, Mustafa Z. Mahmoud, Jan Awrejcewicz, and Witold Pawłowski.
2022. "Evaluation of Melting Mechanism and Natural Convection Effect in a Triplex Tube Heat Storage System with a Novel Fin Arrangement" *Sustainability* 14, no. 17: 10982.
https://doi.org/10.3390/su141710982