# Parametric Study of Panel PCM–Air Heat Exchanger Designs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}·6H

_{2}O) + sodium chloride (NaCl) + strontium chloride (SrCl

_{2}·6H

_{2}O), 93% + 5% + 2% by mass. In the numerical analyses, we used PCM latent enthalpy values obtained by differential scanning calorimeter (DSC) measurements, as depicted in Figure 2 and in thermal cycles data in Table 1. The PCM formulation considered in this study exhibited a melting point of 26.2 °C, peak temperature of 29.6 °C, and phase-change enthalpy of around 180 J/g.

## 2. Materials and Methods

^{3}kg/m

^{3}and the specific heat at constant pressure was 1.6 kJ/kg/K; values for the liquid phase were 1.56 × 10

^{3}kg/m

^{3}and 1.9 kJ/kg/K, respectively. Other assumptions used in the computational model included:

- Air flow was incompressible due to the small variations of density for the considered inlet velocities.
- Material properties were constant for the liquid and solid phases of the PCM.
- Natural (free) convection within the encapsulated PCM was considered negligible, hence the pouches experienced heat conduction-dominated phase change.

**u**, p,

**τ**, c

_{p}, T,

**q**are mass density, velocity, pressure, stress tensor, specific heat at constant pressure, temperature, and heat flux, respectively. The stress tensor in the case of Newtonian fluid is given by:

_{p}and thermal conductivity κ are (nonlinear) functions of temperature T. To describe phase change within the PCM pouches, we use the apparent heat capacity formulation. This formulation assumes that specific heat is equal to the phase-fraction-averaged specific heats plus the latent heat of melting multiplied by the temperature derivative of the mass fraction, namely:

^{®}software [15], specifically its Heat Transfer module. COMSOL is widely used for the computational modeling of various coupled physics problems, including conjugate heat transfer and phase change. There are numerous studies that verify and validate COMSOL’s Heat Transfer module for these purposes. Kylili et al. [16] used it to characterize the thermal performance of PCM-enhanced building elements, validating their results with experiments. Kant et al. [17] used and validated COMSOL for the prediction of melting–solidification of five different fatty acids in an aluminum container. Moreover, COMSOL has been validated with PCM heat transfer problems similar to the present study [18,19,20]. COMSOL employs the finite element method (FEM) for solving the set of partial differential equations comprising the model. COMSOL’s capability of coupling and modeling different multiphysics makes it a convenient and highly flexible CFD tool. Because coupled 3D simulations are computationally intensive to speed-up simulations, the client-server capability of COMSOL to run computations on a remote high-performance cluster was used. Simulations were run for 10 h of simulation time using 15 cores and took several hours of wall-clock time on average.

## 3. Results

#### 3.1. Steady-State Isothermal Pressure Drop Analysis

_{inlet}= 2 m/s and h = 12.19 mm. The results in Figure 6a show that air flow accelerated through the channels formed by neighboring PCM pyramids until being obstructed by the pouch in the next row, and subsequently flowed around it. Similar flow patterns were observed for each row of PCM pouches. The results in Figure 6b show that the largest decrease in pressure was experienced between the inlet plane and the first row of pyramids, and the decrease in pressure was significantly lower through the next rows, with the lowest pressure values found in the vicinity of the outlet plane. The results also showed very small pressure variations along each given row of pyramidical pouches.

#### 3.2. Transient Phase Change Analysis

_{pouch}is the volume of the pouch.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Representative stack of four layers of PCM–air heat exchanger: (

**a**) isometric view, (

**b**) side view of the assembly.

**Figure 2.**Differential scanning calorimeter (DSC) test-generated enthalpy curve for the mixture of calcium chloride hexahydrate (CaCl

_{2}·6H

_{2}O) + sodium chloride (NaCl) + strontium chloride (SrCl

_{2}·6H

_{2}O) (93% + 5% + 2%) for different thermal cycles. The average phase-change enthalpy for cycles 5–25 was approximately 180 J/g.

**Figure 3.**Designs of PCM panels for the pyramidical (PY) configuration with different frustrum heights: (

**a**) h = 15.24 mm, (

**b**) h = 6.35 mm.

**Figure 4.**PCM–air heat exchanger designs: PY—pyramidical, PYO—pyramidical with offset, PYR—pyramidical rotated, CY—cylindrical, and CYO—cylindrical with offset. All dimensions are in mm.

**Figure 5.**Boundary conditions for the PCM–air heat exchanger model: (

**a**) steady-state incompressible flow for the assessment of pressure drop across, (

**b**) coupled transient conjugate heat transfer and incompressible flow for assessment of thermal performance. The numbers identify individual pouches in order to track the evolution of the PCM within a given pouch.

**Figure 6.**Air flow through a PCM–air heat exchanger panel: (

**a**) steady-state air velocity magnitude and (

**b**) pressure distributions for the PYO design, for u

_{inlet}= 2 m/s and h = 12.19 mm.

**Figure 7.**Pressure drops across PCM–air heat exchanger panels. Total pressure drop for varying pouch heights and inlet velocities for (

**a**) PY, (

**b**) PYO, (

**c**) PYR, (

**d**) CY, and (

**e**) CYO designs.

**Figure 8.**Evolution of solid phase fractions with time during the charging of PCM pouches for (

**a**) PY, (

**b**) PYO, (

**c**) PYR, (

**d**) CY, and (

**e**) CYO designs. The phase change process ends when the phase fraction reaches zero. Delays in phase transitions were observed for each subsequent row of PCM pouches in all the investigated designs.

**Figure 9.**Temperature change with time during charging of the PCM panels for (

**a**) PY, (

**b**) PYO, (

**c**) PYR, (

**d**) CY, and (

**e**) CYO designs. Arrows indicate completion of phase transition.

**Figure 10.**PCM panel volume-averaged (

**a**) phase fraction and (

**b**) temperature versus time during discharging. The phase-change process is considered complete when the phase fraction flattens.

Heating Cycle | Onset Temperature, °C | Peak Temperature, °C | Latent Heat, J/g |
---|---|---|---|

2 | 22.4 | 25.1 | 128 |

5 | 24.4 | 26.7 | 178 |

10 | 25.1 | 28.4 | 196 |

15 | 26.6 | 30.8 | 181 |

20 | 26.2 | 29.7 | 170 |

25 | 26.3 | 29.3 | 169 |

PCM Volume, mm^{3}/Surface Area Exposed to Air, mm^{2} = Volume-to-Surface Ratio, mm | ||||
---|---|---|---|---|

Height, mm | Pyramidical (PY)/Pyramidical rotated (PYR) | Pyramidical with offset (PYO) | Cylindrical (CY) | Cylindrical with offset (CYO) |

6.35 | 103784/18248 = 5.69 | 90811/15967 = 5.69 | 115701/12155 = 9.52 | 101239/10635 = 9.52 |

10.16 | 132494/25693 = 5.16 | 115933/22481 = 5.16 | 185125/19448 = 9.52 | 161986/17017 = 9.52 |

11.18 | 137070/27235 = 5.03 | 119936/23831 = 5.03 | 203642/21392 = 9.52 | 178193/18718 = 9.52 |

12.19 | 140603/28589 = 4.92 | 123027/25016 = 4.92 | 222143/23337 = 9.52 | 194383/20420 = 9.52 |

13.21 | 143229/29757 = 4.81 | 125326/26037 = 4.81 | 240660/25282 = 9.52 | 210574/22122 = 9.52 |

14.22 | 145086/30739 = 4.72 | 126950/26986 = 4.72 | 259178/27227 = 9.52 | 226781/23823 = 9.52 |

15.24 | 146304/31532 = 4.64 | 128016/27591 = 4.64 | 277679/29172 = 9.52 | 242971/25525 = 9.52 |

17.78 | 147439/32700 = 4.51 | 129009/28612 = 4.51 | 323956/340333 = 9.52 | 283463/29779 = 9.52 |

Property | Units | Solid | Liquid |
---|---|---|---|

density | kg m^{−3} | 1.71 × 10^{3} [11] | 1.56 × 10^{3} [12] |

thermal conductivity | W m^{−1}K^{−1} | 1.08 [13] | 0.56 [13] |

specific heat at constant pressure | J kg^{−1}K^{−1} | 1.6 × 10^{3} [14] | 1.9 × 10^{3} [14] |

melting temperature | K | 300 | |

melting temperature range | K | 296–304 | |

latent heat of fusion | kJ kg^{−1} | 180 |

Boundary | Inlet | Outlet | Walls | PCM-Air Interface | |
---|---|---|---|---|---|

Field | |||||

T | T_{inlet} | $\frac{\partial \mathrm{T}}{\partial n}=0$ | $\frac{\partial \mathrm{T}}{\partial n}=0$ | T_{air} = T_{PCM} | |

u | u_{inlet} | $\frac{\partial \mathsf{u}}{\partial n}=0$ | u_{wall} | u_{wall} | |

p | $\frac{\partial p}{\partial n}=0$ | p_{outlet} | $\frac{\partial p}{\partial n}=0$ | $\frac{\partial p}{\partial n}=0$ |

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**MDPI and ACS Style**

Kamidollayev, T.; Trelles, J.P.; Thakkar, J.; Kosny, J.
Parametric Study of Panel PCM–Air Heat Exchanger Designs. *Energies* **2022**, *15*, 5552.
https://doi.org/10.3390/en15155552

**AMA Style**

Kamidollayev T, Trelles JP, Thakkar J, Kosny J.
Parametric Study of Panel PCM–Air Heat Exchanger Designs. *Energies*. 2022; 15(15):5552.
https://doi.org/10.3390/en15155552

**Chicago/Turabian Style**

Kamidollayev, Tlegen, Juan Pablo Trelles, Jay Thakkar, and Jan Kosny.
2022. "Parametric Study of Panel PCM–Air Heat Exchanger Designs" *Energies* 15, no. 15: 5552.
https://doi.org/10.3390/en15155552