# A Novel Molecular PCM Wall with Inorganic Composite: Dynamic Thermal Analysis and Optimization in Charge–Discharge Cycles

^{*}

## Abstract

**:**

^{2}can maintain the average surface temperature within a comfort range for 12.1 h, about half the time of a 24 h charge–discharge cycling periodicity. Furthermore, placing the heating film in the unit center is preferable for improving overall heat efficiency and shortening the time to reach the thermal comfort temperature range. This work can provide guidance for practical thermal design optimization of building envelopes integrated with PCM for thermal insulation and energy storage.

## 1. Introduction

#### 1.1. Background

_{2}emissions by 2060, Chinese cities have been striving to optimize building energy systems in terms of changes from a combustion-fuel-based structure to a safe and reliable electricity-based system, integrating renewable energy exploitation and energy storage technologies [6].

#### 1.2. Literature Review

#### 1.3. Objective and Focus

## 2. Methods

#### 2.1. Molecular PCM Wall unit with Sodium Acetate–Urea Composite

#### 2.2. Dynamic Heat Transfer Modeling

- The motion of melted PCM is considered a Newtonian incompressible laminar flow;
- Thermophysical properties of the PCM are independent of temperature;
- Boussinesq approximation is invoked to model buoyancy-induced natural convection;
- All materials are regarded as homogeneous and isotropic in all directions;
- PCM volume change during the phase transition is negligible;
- Contact surfaces are closely fitted, the contact thermal resistance of the interface is zero, and the temperature and heat flow are continuous;
- The thickness of the electric heating film is zero.

^{3}); μ is the dynamic viscosity of the PCM (Pa·s); β is the coefficient of thermal expansion of the PCM (1/K); T

_{m}is the average value of the temperature of the phase change material (K); and the acceleration due to gravity (g) is assumed to be −9.8 m/s

^{2}. In Equations (1) and (2), S is the source term related to the liquid fraction of PCM in the pore volume, and S

_{x}and S

_{y}are the components of the source term in the x and y directions, respectively, which are defined as follows:

_{mush}is the mushy zone constant related to the morphology of the mushy region, the value of which is in the range of 10

^{4}~10

^{7}kg/(m

^{3}·s). As discussed in Section 2.1, A

_{mush}is 10

^{5}kg/(m

^{3}·s); σ is a small value to avoid errors arising from division by zero and is set as 10

^{−3}; and γ is a liquid fraction, which can be calculated according to the following equation:

_{s}and T

_{l}are the solidus and liquid temperature (K), respectively. The enthalpy method is used to derive the energy balance equation of the PCM layer:

_{p}is the specific heat capacity (J/kg·K), k is the thermal conductivity (W/m·K), h

_{ref}is the reference enthalpy (J/kg), T

_{ref}is the reference temperature (K), h

_{sf}is the latent heat (J/kg), and ∆H equals 0 when the PCM is solid and h

_{sf}when the PCM is liquid. The governing equation for the other wall layers is as follows:

## 3. Results and Discussion

#### 3.1. PCM Thermophysical Property Testing

#### 3.2. Numerical Case Analysis

_{mush}was set to 1 × 10

^{5}, the transient term was discretized in second-order fully implicit format, the momentum and energy terms were discretized in second-order windward differential format, the pressure term was discretized using the PRESTO algorithm, and the coupling of the pressure and velocity was discretized using the SIMPLE algorithm. The pressure relaxation factor was set to 0.3, the momentum equation relaxation factor was set to 0.7, and the energy equation relaxation factor was set to 1. The residuals were set to 10

^{−3}, 10

^{−3}, and 10

^{−6}for the continuity equation, momentum equation, and energy equation, respectively.

_{charge}represents the heating time, whereas t

_{discharge}represents the duration of heating stoppage. According to the ASHRAE standard (ASHRAE 55-2020 [34]), when using low-temperature radiant floor heating, the average temperature of the ground under areas of frequent human activity should be 25~27 °C and not exceed 29 °C, whereas that of the ground under areas of occasional human activity should not exceed 32 °C [7]. The efficiency of a PCM wall in 24 h can be calculated using Equation (11), where q is the heat flow of the heat transfer to the room, q

_{r}is the surface heating flow, and all input power of the heating film is converted into heat.

#### 3.3. Dynamic Phase Change Simulation

^{2}, with a maximal liquid fraction of 0.57 at 8 h during a 24 h cycling periodicity. The heating power is approximately 1.67 and 1.25 times higher, and the maximal liquid fraction is 1.84 and 1.15 times higher than the other two cases, respectively. A heating power of 250 W/m

^{2}releases the largest amount of stored heat in 24 h.

^{2}, 200 W/m

^{2}, and 150 W/m

^{2}, respectively. Therefore, during a 24 h cycle, increased heating power may contribute a reduction in overall heating efficiency. However, 150 W/m

^{2}is not necessarily an optimal choice, as the heating of the next day starts at the end of the previous day’s cycle, and 200 W/m

^{2}and 250 W/m

^{2}are preferrable starting temperatures for the next day. The heat release curves of starting temperatures of 200 W/m

^{2}and 250 W/m

^{2}are similar, although 200 W/m

^{2}is associated with lower energy consumption, so it follows that in the current situation, 200 W/m

^{2}heating power is preferred over 250 W/m

^{2}. Furthermore, the power is 150 W/m

^{2}at 12.1 h, with a temperature range of 25–27 °C, which is 1.71 and 1.21 times longer than the other two cases, respectively, despite being associated with the longest preheating time.

^{2}, 67.2 W/m

^{2}and 73.5 W/m

^{2}, with heating efficiencies of 99.5%, 84.8%, and 72.1%, respectively. The maximal values of the average surface temperature of the proposed PCM wall for the three cases are assessed to be 28.1 °C, 28.7 °C, and 30.1 °C, respectively, which are all acceptable for indoor thermal comfort requirements. The lengths of time in the temperature range of 25 °C to 27 °C are 11.1 h, 7.1 h, and 3.7 h for the three cases, respectively. Therefore, 6 h of heating is preferrable to a 24 h charge–discharge cycle.

## 4. Conclusions and Prospects

- (1)
- An increased urea fraction leads to a reduction in melting temperature. For 30% urea composite, the melting temperature ranges from 28 to 30 °C, approaching the indoor thermal comfort level, with enhanced thermal stability during cycles;
- (2)
- With decreasing PCM layer thickness, the melting time is reduced, and released heat capacity increases. However, reducing the PCM layer thickness may also increase overheating risk, leading to considerable fluctuation of the heat flow and surface temperature;
- (3)
- Increased heating power contributes to increased PCM melting speed. For the studied case, a 20 mm thick PCM layer with 150 W/m
^{2}heating power can maintain the surface temperature within the comfort range for approximately half the time in a charge–discharge cycle; - (4)
- Placing the heating film in the middle of the PCM wall unit can improve the overall heat efficiency and PCM melting uniformity, shortening the time required to reach the thermal comfort temperature range.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**T-history method for thermal property testing of sodium acetate–urea composite [17].

**Figure 6.**Temperature variation curves for sodium acetate–urea PCM determined using the T-history method.

**Figure 7.**Repetitive temperature tests in PCM composite charge–discharge cycles (red circle: thermal stability comparison during phase transition).

**Figure 10.**Numerical simulation results among 4 groups and 12 case scenarios: Group A, PCM layer thickness; Group B, heating power capacity; Group C, PCM layer location with respect to the heating film; Group D, time ratio of the PCM charge-to-discharge process.

**Figure 11.**Contours of liquid fraction variations during phase transition processes with different (

**a**) PCM layer thicknesses, (

**b**) heating powers, and (

**c**) PCM layer locations with respect to the heating film (L, left; M, middle; R, right).

PCM | Melting Temperature T _{m} (°C) | Enthalpy H _{m} (kJ/kg) | |
---|---|---|---|

Organic | Paraffin | 25–30 | 150 |

Butyl stearate CH_{3}(CH_{2})_{16}COO(CH_{2})_{3}CH_{3} | 18–23 | 140 | |

N-octadecane CH_{3}(CH_{2})_{16}CH_{3} | 22.5–26.2 | 205 | |

Dodecanol CH_{3}(CH_{2})_{11}OH | 17.5–23.3 | 188 | |

Inorganic | Potassium fluoride KF·4H_{2}O | 18.5–19 | 231 |

Calcium chloride CaCl_{2}· | 29.7 | 171 | |

Sodium sulphite Na_{2}S_{2}O_{3}· | 40 | 210 | |

Sodium acetate CH_{3}COONa | 45–55 | 240 |

**Table 2.**Structure and main thermophysical properties of the proposed modular PCM wall unit [3].

Layer | Decoration | PCM | Frame | Insulation |
---|---|---|---|---|

Material | Wood fiber | Sodium acetate–urea | Nanomontmorillonite fiber composites | Extruded polystyrene |

Thickness (mm) | 8 | 20 | 3 | 20 |

Solid/liquid density, ρ (kg/m^{3}) | 1000 | 1460/1480 | 2000 | 35 |

Thermal solid/liquid conductivity, k (W/m·K) | 0.34 | 1.2/0.56 | 2002.5 | 1380 |

Specific solid/liquid heat capacity, c_{p} (J/kg·K) | 2510 | 2410/2720 | 0.45 | 0.03 |

Thermal expansion coefficient, β (1/K) | 0.00044 | |||

Dynamic viscosity, μ (Pa·s) | 0.00324 | |||

Melting point, T_{m} (K) | 301.15–305.15 | |||

Latent heat, h_{sf} (kJ/kg) | 200 |

Group | Case | d (mm) | q (W/m^{2}) | Position | t_{charge}/t_{discharge} |
---|---|---|---|---|---|

A | 1 | 10 | 200 | R | 8/16 |

2 | 20 | 200 | R | 8/16 | |

3 | 30 | 200 | R | 8/16 | |

B | 4 | 20 | 150 | R | 8/16 |

5 | 20 | 200 | R | 8/16 | |

6 | 20 | 250 | R | 8/16 | |

C | 7 | 20 | 200 | L | 8/16 |

8 | 20 | 200 | M | 8/16 | |

9 | 20 | 200 | R | 8/16 | |

D | 10 | 20 | 200 | L | 6/18 |

11 | 20 | 200 | M | 8/16 | |

12 | 20 | 200 | R | 10/14 |

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## Share and Cite

**MDPI and ACS Style**

Yang, Q.; Xiong, J.; Mao, G.; Zhang, Y.
A Novel Molecular PCM Wall with Inorganic Composite: Dynamic Thermal Analysis and Optimization in Charge–Discharge Cycles. *Materials* **2023**, *16*, 5955.
https://doi.org/10.3390/ma16175955

**AMA Style**

Yang Q, Xiong J, Mao G, Zhang Y.
A Novel Molecular PCM Wall with Inorganic Composite: Dynamic Thermal Analysis and Optimization in Charge–Discharge Cycles. *Materials*. 2023; 16(17):5955.
https://doi.org/10.3390/ma16175955

**Chicago/Turabian Style**

Yang, Qianru, Jianwu Xiong, Gang Mao, and Yin Zhang.
2023. "A Novel Molecular PCM Wall with Inorganic Composite: Dynamic Thermal Analysis and Optimization in Charge–Discharge Cycles" *Materials* 16, no. 17: 5955.
https://doi.org/10.3390/ma16175955