# Numerical Study on the Thermal Performance of a Single U-Tube Borehole Heat Exchanger Using Nano-Enhanced Phase Change Materials

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}O

_{3}, TiO

_{2}, SiO

_{2}, multi-wall carbon nanotube, and graphene are added to the Paraffin. Considering the highest melting rate and lowest outlet temperature, the selected nano-enhanced phase change material is evaluated in terms of volume fraction (0.05, 0.10, 0.15, 0.20) and then the shape (sphere, brick, cylinder, platelet, blade) of its nanoparticles. Based on the results, the Paraffin containing Cu and SiO

_{2}nanoparticles are found to be the best and worst ones in thermal performance improvement, respectively. Moreover, it is indicated that the increase in the volume fraction of Cu nanoparticles could enhance markedly the melting rate, being 0.20 the most favorable value which increased up to 55% the thermal conductivity of the nano-enhanced phase change material compared to the pure phase change material. Furthermore, the blade shape is by far the most appropriate shape of the Cu nanoparticles by considering about 85% melting of the nano-enhanced phase change material.

## 1. Introduction

_{2}O

_{3}and Al nanoparticles to a PCM comprised of n-hexadecane and n-tetradecane which were applied in an advanced building for cooling operation. Their results indicated 4.97% and 12.97% reductions in the solidification time when using Al and Al

_{2}O

_{3}nanoparticles, respectively, in comparison with the pure PCM. The impact of adding CuO nanoparticles to RT50 PCM placed inside a shell and tube heat exchanger was carried out numerically by Pahamli et al. [35]. It was concluded that the melting time decreases by 11.6% and 4.56% provided that the volume fractions of the nanoparticles are 4% and 2%, respectively, resulting in superior thermal performance of the heat exchanger. Ramakrishnan et al. [36] added experimentally graphene nanoparticles to a PCM consisted of expanded perlite and RT27 which were used as TES. According to the results, both melting and solidification time decrease by 33% compared to the pure PCM, due to an increase of 49% in the thermal conductivity of the PCM when applying graphene with 1% by weight. An experimental investigation of adding graphene oxide, TiO

_{2}, and CuO nanoparticles to the Paraffin used in a solar still was conducted by Rufuss et al. [37]. The results showed the increments of 101%, 25%, and 29% in the thermal conductivity of the PCM at the presence of graphene oxide, TiO

_{2}, and CuO nanoparticles, respectively, which led to the higher production of freshwater. In another study, the use of NEPCM made of Paraffin wax as PCM and multi-wall carbon nanotube (MWCNT) as nanoparticles in an electronic chipset was examined experimentally by Farzanehnia et al. [38]. The studied NEPCM was found to extend the time of electronic board operation and decrease the time of the cooling process by 6%.

## 2. Computational Fluid Dynamics Model and Simulation Conditions

_{2}O

_{3}, TiO

_{2}, SiO

_{2}, MWCNT, and graphene, are used as nanoparticles in this study to be added to the Paraffin (n-Octadecane) as the base fluid.

^{−3}while the corresponding value for energy was 10

^{−6}(see Table 4).

## 3. Mathematical Formulation

_{NEPCM}) is written as [33]:

_{p})

_{NEPCM}) is given by [33]:

_{NEPCM}) can be expressed as [33]:

_{NEPCM}) is defined as [33]:

_{NEPCM}) can be calculated by means of the Hamilton–Crosser formula [47], in which in addition to including the thermal conductivities of nanoparticles and PCM as well as the nanoparticle volume fraction, the shape of nanoparticles has also been taken into account, which is as follows:

_{sens}and h

_{lat}are the sensible heat enthalpy and latent heat enthalpy, respectively. The total enthalpy is obtained by summation of the enthalpies:

_{mush}is the mushy zone constant fixed at 10

^{5}and ε is a small positive quantity (here 0.001) called computational constant which prevents a division by zero [53,54,55].

## 4. Verification

_{1}, r

_{2}, r

_{3}are 0.03 m, 0.19 m, and 0.27 m, respectively, at a depth of 0.3 m (see Figure 3). The BHE works 10 h a day for cooling operation to release the heat to the ground. In the validation, just a mixed acid PCM used as backfill which consists of decyl acid and lauric acid with a mass proportion of 66:34. The other conditions are the same as stated in part 2 of the present study. As shown in Figure 4, the numerical and experimental results display an excellent agreement with the percent errors of less than 5%.

## 5. Results and Discussion

#### 5.1. Impact of Nano-Enhanced Phase Change Material Type

_{2}nanoparticles with the liquid fraction close to 0.45. At the end of cooling operation, we can observe the small differences between the liquid fractions of NEPCMs with Cu, graphene, MWCNT, and Al

_{2}O

_{3}nanoparticles compared to that for the NEPCMs with CuO, TiO

_{2}and SiO

_{2}nanoparticles. It is worth mentioning that all of the NEPCMs have a significantly higher rate of melting than the pure Paraffin, thanks to the presence of nanoparticles which improve the thermal conductivity of the PCM.

_{2}nanoparticle material shows the smallest melting rate, although the differences between the rest of compounds are not as marked. The compound using Cu nanoparticle shows a better melting rate with a small difference compared to the others after 12 h.

_{2}nanoparticle displays the lower heat transfer rate, and based on Figure 8, the differences between the other models are not significant. To realize better the melting process and heat transfer between different BHE components, 3D contours of temperature distribution and 2D contours of temperature distribution (front view, middle plane) of the BHE are presented in Figure A1. (Appendix A) and Figure A4. (Appendix B), respectively. Based on the abovementioned explanations, the NEPCM containing Cu nanoparticles is chosen for further investigation.

#### 5.2. Impact of Nano-Enhanced Phase Change Material Volume Fraction (ϕ)

#### 5.3. Impact of Nano-Enhanced Phase Change Material Shape Factor (n)

## 6. Conclusions and Future Scope

_{2}O

_{3}, TiO

_{2}, SiO

_{2}, multi-wall carbon nanotube, and graphene nanoparticles to the Paraffin as backfill in the borehole heat exchanger; then, to study the effects of volume fraction of nanoparticles which varies from 0.05 to 0.20 on the thermal performance of the borehole heat exchanger; and finally, to evaluate the role of nanoparticles’ shape such as the sphere, brick, cylinder, platelet, and the blade on the melting rate of nano-enhanced phase change material. The obtained results are as follows:

- The nano-enhanced phase change materials with Cu and SiO
_{2}nanoparticles demonstrated to be the best and worst nanoparticles in improving the thermal performance of the single U-tube borehole heat exchanger, respectively. Therefore, Cu nano-enhanced phase change material was selected for further investigation. - In terms of volume fraction, it was founded that the increase in the volume fraction of Cu nanoparticles enhanced considerably the melting rate of nano-enhanced phase change material, being 0.20 the most suitable volume fraction which increased up to 55% the thermal conductivity of the nano-enhanced phase change material in comparison with the pure phase change material.
- Concerning the shape of nanoparticles, the blade shape was by far the best shape of the Cu nanoparticles which resulted in about 85% melting of the nano-enhanced phase change material.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

C_{p} | Specific heat (J·kg^{−1}·K^{−1}) |

C_{mush} | Mushy zone constant |

$\overrightarrow{g}$ | Gravitational acceleration (m·s^{−2}) |

h | Enthalpy (J·kg^{−1}) |

k | Thermal conductivity (W·m^{−1}·K^{−1}) |

n | Shape factor |

L | Latent heat of nano-enhanced phase change material (J·kg^{−1}) |

P | Pressure (Pa) |

r | Radius (m) |

$\overrightarrow{S}$ | Source term of momentum equation |

t | Time (Second) |

T | Temperature (K) |

$\overrightarrow{V}$ | Velocity vector (m·s^{−1}) |

Greek Symbols | |

β | Thermal expansion coefficient (K^{−1}) |

λ | Liquid fraction |

μ | Dynamic viscosity (Pa·s) |

ρ | Density (kg·m^{−3}) |

ϕ | Volume fraction of nanoparticle |

Subscripts | |

0 | Original |

ref | Reference |

tot | Total |

lat | Latent heat |

sens | Sensible heat |

m | Melting |

Abbreviation | |

GSHP | Ground source heat pump |

GHE | Ground heat exchanger |

BHE | Borehole heat exchanger |

TES | Thermal energy storage |

CFD | Computational fluid dynamics |

PCM | Phase change material |

NEPCM | Nano-enhanced phase change material |

SSPCM | Shape-stabilized PCM |

MWCNT | Multi-wall carbon nanotube |

## Appendix A

**Figure A1.**3D contours of the temperature distribution of the BHE at various hours of operating for different NEPCMs when ϕ = 0.20, n = 3.

**Figure A2.**3D contours of the temperature distribution of the BHE at various hours of operating for NEPCM containing Cu nanoparticles with different volume fractions when n = 3.

**Figure A3.**3D contours of the temperature distribution of the BHE at various hours of operating for NEPCM containing Cu nanoparticles with different shape factors when ϕ = 0.20.

## Appendix B

**Figure A4.**2D contours of the temperature distribution of the BHE at various hours of operating for different NEPCMs when ϕ = 0.20, n = 3 (Front view, middle plane).

**Figure A5.**2D contours of the temperature distribution of the BHE at various hours of operating for NEPCM containing Cu nanoparticles with different volume fractions when n = 3 (Front view, middle plane).

**Figure A6.**2D contours of the temperature distribution of the BHE at various hours of operating for NEPCM containing Cu nanoparticles with different shape factors when ϕ = 0.20 (Front view, middle plane).

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**Figure 4.**Validation of the numerical backfill and soil temperatures at different radiuses to the experimental results of Yang et al. [20].

**Figure 5.**Variation of the liquid fraction with operating time using different NEPCMs at ϕ = 0.20 and n = 3.

**Figure 6.**2D contours of the liquid fraction of different NEPCMs at various hours of operating when ϕ = 0.20 and n = 3 (Top view at Z = 0).

**Figure 7.**Variation of the outlet temperature with operating time when using different NEPCMs at ϕ = 0.20 and n = 3.

**Figure 8.**2D contours of the temperature distribution of the BHE at various hours of operating using different NEPCMs when ϕ = 0.20 and n = 3. (Top view at Z = 0).

**Figure 9.**Variation of the liquid fraction with operating time at various volume fractions of the NEPCM containing Cu nanoparticles when n = 3.

**Figure 10.**2D contours of the liquid fraction of NEPCM containing Cu nanoparticles with different volume fractions at various hours of operating when n = 3 (Top view at Z = 0).

**Figure 11.**Variation of the outlet temperature with operating time at various volume fractions of the NEPCM containing Cu nanoparticles when n = 3.

**Figure 12.**2D contours of the temperature distribution of the BHE at various hours of operating when using NEPCM containing Cu nanoparticles with different volume fractions at n = 3 (Top view at Z = 0).

**Figure 13.**Variation of the liquid fraction with operating time at various shape factors of Cu nanoparticles when ϕ = 0.20.

**Figure 14.**2D contours of the liquid fraction of NEPCM containing Cu nanoparticles with different shape factors at various hours of operating when ϕ = 0.20 (Top view at Z = 0).

**Figure 15.**Variation of the outlet temperature with operating time at various shape factors of Cu nanoparticles when ϕ = 0.20.

**Figure 16.**2D contours of the temperature distribution of the BHE at various hours of operating using NEPCM containing Cu nanoparticles with different shape factors when ϕ = 0.20. (Top view at Z = 0).

Property | Working Fluid | Pipe | Ground |
---|---|---|---|

ρ [kg/m^{3}] | 998.2 | 8978 | 1600 |

C_{p} [J/kg·K] | 4182 | 381 | 1640 |

k [W/m·K] | 0.6 | 387.6 | 0.69 |

μ [Pa·s] | 0.001003 | - | - |

Property | PCM | Nanoparticles | ||||||
---|---|---|---|---|---|---|---|---|

Paraffin (n-Octadecane) [42] | Cu [43] | CuO [43] | Al_{2}O_{3} [43] | TiO_{2} [43] | SiO_{2} [44] | MWCNT [45] | Graphene [46] | |

ρ [kg/m^{3}] | 770 | 8933 | 6510 | 3880 | 4175 | 2200 | 1600 | 2200 |

C_{p} [J/kg·K] | 2196 | 385 | 540 | 792 | 692 | 775 | 796 | 790.1 |

k [W/m·K] | 0.148 | 401 | 18 | 42.34 | 8.4 | 1.38 | 3000 | 5000 |

L [J/kg] | 243500 | - | - | - | - | - | - | - |

μ [Pa·s] | 0.00385 | - | - | - | - | - | - | - |

T_{m} [K] | 301.15 | - | - | - | - | - | - | - |

Elements Numbers | 571,924 | 1,328,873 | 2,244,671 | 3,476,561 |
---|---|---|---|---|

Outlet temperature of working fluid (K) | 307.41 | 307.55 | 307.63 | 307.60 |

Liquid fraction | 0.67 | 0.69 | 0.72 | 0.71 |

Parameters | Value |
---|---|

Calculation domain | 1.2 × 1.2 × 1.2 m^{3} |

U-tube length | 1.1 m |

Borehole depth | 1.2 m |

Borehole diameter | 0.06 m |

Pipe spacing of U-tube (between centers) | 0.0365 m |

Outer diameter of pipe | 0.0065 m |

Inner diameter of pipe | 0.005 m |

Inlet temperature | 308.15 K |

Inlet velocity | 0.6 m/s |

Operating time | 12 h |

NEPCMs | Addition of seven nanoparticles including Cu, CuO, Al_{2}O_{3}, TiO_{2}, SiO_{2}, MWCNT, and graphene to the Paraffin |

Volume concentration of nanoparticles | 0.05, 0.10, 0.15, 0.20 |

Shape of nanoparticles | sphere, brick, cylinder, platelet, blade |

n | Nanoparticle Shape | |
---|---|---|

3 | Sphere | |

3.7 | Brick | |

4.9 | Cylinder | |

5.7 | Platelet | |

8.6 | Blade |

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## Share and Cite

**MDPI and ACS Style**

Javadi, H.; Urchueguia, J.F.; Mousavi Ajarostaghi, S.S.; Badenes, B.
Numerical Study on the Thermal Performance of a Single U-Tube Borehole Heat Exchanger Using Nano-Enhanced Phase Change Materials. *Energies* **2020**, *13*, 5156.
https://doi.org/10.3390/en13195156

**AMA Style**

Javadi H, Urchueguia JF, Mousavi Ajarostaghi SS, Badenes B.
Numerical Study on the Thermal Performance of a Single U-Tube Borehole Heat Exchanger Using Nano-Enhanced Phase Change Materials. *Energies*. 2020; 13(19):5156.
https://doi.org/10.3390/en13195156

**Chicago/Turabian Style**

Javadi, Hossein, Javier F. Urchueguia, Seyed Soheil Mousavi Ajarostaghi, and Borja Badenes.
2020. "Numerical Study on the Thermal Performance of a Single U-Tube Borehole Heat Exchanger Using Nano-Enhanced Phase Change Materials" *Energies* 13, no. 19: 5156.
https://doi.org/10.3390/en13195156