# Experimental Analysis of the Function of a Window with a Phase Change Heat Accumulator

^{*}

## Abstract

**:**

## 1. Introduction

- Incorrect selection of PCMs used in the application location in question;
- Unsealing forms moulds with PCMs applied;
- Change of physicochemical properties of PCMs after many phase transformation cycles;
- Insufficient ability of solid-state PCMs to conduct heat.

## 2. Materials and Methods

#### 2.1. Materials

- 2 mm thick aluminum sheet, covered with matt black paint.

#### 2.2. Apparatus

- Almemo 2890-9 recorder, company Ahlborn, Ilmenau, Germany;
- Pt1000 temperature sensor, company Salus, Kobielice, Poland;
- Heat flux density sensor: FQA020C, company Ahlborn, Ilmenau, Germany;
- LT 019008 thermocouple, company Ahlborn, Ilmenau, Germany;
- Almemo FLA 613 GS pyranometer, company Ahlborn, Ilmenau, Germany.

#### 2.3. Resarch Method

#### 2.4. Experimental Tests

#### 2.5. Mathematical Model

_{w2}is the specific heat of the material at point 2, ϱ

_{2}is the density at point 2, R

_{1-2}is the heat resistance between points 1 and 2, and T

^{t}

_{1}is the temperature at point 1 during t.

_{C.PCM}is the specific heat of the PCM, ϱ

_{PCM}is the density PCM, and R

_{1,2-2,2}are the heat-resistant PCM values between points 1,2 and 2,2.

_{i}is the density at point I, and λ

_{i}is the heat transfer coefficient i.

_{Z1}), and between the PCM accumulator and the internal glazing (R

_{Z2}). These complex heat resistances are temperature functions that take into account heat transfer by convection q

_{k}and radiation q

_{r}. The above thermophysical phenomena were considered in accordance with the relationships described in [61].

_{z}is the heat flux density transmitted by radiation and convection, q

_{k}is the heat flux density transmitted by convection, and q

_{r}is the flux density transmitted by radiation.

_{0}is the black body radiation factor, ε

_{1-2}is the replacement emissivity, and φ

_{1-2}is the angle radiation factor (so-called configuration factor).

_{1}and glazing surface F

_{2}, the equivalent emissivity ${\epsilon}_{1-2}$ and the angular radiation factor φ

_{1-2}were determined in accordance with Equations (15) and (16):

_{PCM}phase transformation over time were developed using the calorimetric thermogram obtained and described by the author [27]. The above approach is analogous to solving Stefan’s problem [6,59], except that it concerns compounds with blurred melting and solidification. For the needs of this model, a discrete accumulator grid from PCM was selected with a width of dx = dy = 5 mm. Therefore, the cross-section of the accumulator in question consisted of 200 elements (grid dimensions: 50 mm × 100 mm). In addition, the extreme nodes of the discussed cross-section were modelled as the aluminium side of the accumulator, taking into account the resistance and heat capacity of the aluminium alloy used in the field tests.

## 3. Results

#### 3.1. Experimental Results

#### 3.2. Results of the Mathematical Simulation

#### 3.3. Statistical Analysis

_{d}(t), obtained from the mathematical calculations T

_{s}(t).

_{t}is the actual value of y at t $,{\widehat{y}}_{t}$ is the theoretical value of the explanatory variable, and $\overline{y}$ is the arithmetic mean of the values of the explanatory variable.

^{2}determination close to unity. There was also no significance in the expression of free linear regression equations in the cases considered.

#### 3.4. Simulations of the Operation of a Composite Window with a Phase Change Heat Accumulator for Data of a Typical Meteorological Year in Rzeszów

## 4. Discussion

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Photograph of the isothermal field testing chamber. (

**b**) Diagram of the field testing chamber: (1) heat accumulator; (2) heat meter with thermocouple; (3) temperature sensor; (4) thermoregulator; (5) energy consumption meter; (6) recorder; (7) oil heater.

**Figure 2.**(

**a**) Graphical diagram of the mathematical model of a composite window with a phase change heat accumulator. (

**b**) Analogous electric diagram of the mathematical model of a composite window with a phase change heat accumulator.

**Figure 3.**Thermal functioning of the window with an external triple glazing unit and an internal single glazing unit. (

**a**) Graph of the heat flux density values recorded on the inner surface of the glazing unit with the PCM and the reference window. (

**b**) Graph of temperature values recorded on the inner surface of the PCM glazing unit and the reference window.

**Figure 4.**Thermal functioning of the window with an external triple glazing unit and an internal double glazing unit. (

**a**) Graph of heat flux density values recorded on the inner surface of the glazing unit with the PCM and the reference window. (

**b**) Graph of temperature values recorded on the inner surface of the PCM glazing unit part and the reference window.

**Figure 5.**Thermal functioning of the window with an external triple glazing unit and internal triple glazing unit. (

**a**) Graph of heat flux density values recorded on the inner surface of the glazing unit with the PCM and the reference window. (

**b**) Graph of temperature values recorded on the inner surface of the PCM glazing unit and the reference window.

**Figure 6.**Thermal functioning of the window with an external double glazing unit and an internal single glazing unit. (

**a**) Graph of heat flux density values recorded on the inner surface of the glazing unit with the PCM and the reference window. (

**b**) Graph of temperature values recorded on the inner surface of the PCM glazing unit and the reference window.

**Figure 7.**Thermal functioning of the window with an external double glazing unit and an Internal double glazing unit. (

**a**) Graph of heat flux density values recorded on the inner surface of the glazing unit with the PCM and the reference window. (

**b**) Graph of temperature values recorded on the inner surface of the PCM glazing unit and the reference window.

**Figure 8.**Thermal functioning of the window with an external double glazing unit and an internal triple glazing unit. (

**a**) Graph of heat flux density values recorded on the inner surface of the glazing unit with the PCM and the reference window. (

**b**) Graph of temperature values recorded on the inner surface of the PCM glazing unit and the reference window.

**Figure 9.**Results of the mathematical simulation. (

**a**) Accumulator temperature field with PCM during charging. (

**b**) PCM accumulator temperature field during discharging.

**Figure 10.**Results for the external triple glazing unit and internal single glazing unit. (

**a**) Comparison of heat flux density values recorded and obtained from the model in the PCM part. (

**b**) Comparison of the density values of heat fluxes registered and obtained from the model in the reference part.

**Figure 11.**Results for the external triple glazing unit and internal double glazing unit. (

**a**) Comparison of heat flux density values recorded and obtained from the model in the PCM part. (

**b**) Comparison of the density values of heat fluxes registered and obtained from the model in the reference part.

**Figure 12.**Results for the external triple glazing unit and internal triple glazing unit. (

**a**) Comparison of heat flux density values recorded and obtained from the model in the PCM part. (

**b**) Comparison of the density values of heat fluxes registered and obtained from the model in the reference part.

**Figure 13.**Results for the external double glazing unit and internal single glazing unit. (

**a**) Comparison of heat flux density values recorded and obtained from the model in the PCM part. (

**b**) Comparison of the density values of heat fluxes registered and obtained from the model in the reference part.

**Figure 14.**Results for the external double glazing unit and internal double glazing unit. (

**a**) Comparison of heat flux density values recorded and obtained from the model in the PCM part. (

**b**) Comparison of the density values of heat fluxes registered and obtained from the model in the reference part.

**Figure 15.**Results for the external double glazing unit and internal triple glazing unit. (

**a**) Comparison of heat flux density values recorded and obtained from the model in the PCM part. (

**b**) Comparison of the density values of heat fluxes registered and obtained from the model in the reference part.

**Figure 16.**(

**a**) Adjustment of the temperature value of the internal pane, measured relative to those calculated in the PCM accumulator part, with an external triple-pane window and an internal single-pane window. (

**b**) Adjustment of the temperature values of the internal pane, measured relative to those calculated in the reference part, with an external triple-pane window and an internal single-pane window.

**Figure 17.**(

**a**) Adjustment of the internal temperature value of the pane, measured relative to those calculated in the PCM accumulator part, with an external triple-pane window and an internal double-pane window. (

**b**) Adjustment of the temperature value of the internal pane, measured relative to those calculated in the reference part, with an external triple-pane window and an internal double-pane window.

**Figure 18.**(

**a**) Adjustment of the internal temperature value of the pane, measured relative to those calculated in the PCM accumulator part, with an external triple-pane window and an internal triple-pane window. (

**b**) Adjustment of the temperature value of the internal pane, measured relative to those calculated in the reference part, with an external triple-pane window and an internal triple-pane window.

**Figure 19.**(

**a**) Adjustment of the internal temperature value of the pane, measured relative to those calculated in the PCM accumulator part, with an external double-pane window and an internal triple-pane window. (

**b**) Adjustment of the temperature value of the internal pane, measured relative to those calculated in the reference part, with an external double-pane window and an internal triple-pane window.

**Figure 20.**Graph of heat loss of a composite window with a phase change cushion according to data for a typical meteorological year in Rzeszów.

**Figure 21.**Graph of the heat gain of a composite window with a phase change cushion according to data for a typical meteorological year in Rzeszów.

**Figure 22.**Graph of heat balance results for a composite window with a phase change cushion according to typical data for a meteorological year in Rzeszów.

Parameter | Single Glazing | Double Glazing Unit | Triple Glazing Unit |
---|---|---|---|

Heat transfer coefficient (W/m^{2}·K) | 5 | 1.1 | 0.7 |

Transmittance (-) | 0.82 | 0.75 | 0.5 |

Light permeability (-) | 0.89 | 0.78 | 0.6 |

Construction of glazing unit (mm) | /4/ | /4/16 Ar/4/ | /4/16Ar/4/16 Ar/4/ |

Sets of Glazing Units | Quotient of Variance for PCM Part | Critical Value | Quotient of Variance for the Reference Part | Critical Value |
---|---|---|---|---|

F_{PCM (α,f1,f2)} | F_{kr} | F_{Ref (α,f1,f2)} | F_{kr} | |

3–1 | 1.0485 | 1.1100 | 1.0306 | 1.1100 |

3–2 | 1.1021 | 1.1100 | 1.0213 | 1.1100 |

3–3 | 1.1027 | 1.1100 | 1.0900 | 1.1100 |

2–1 | 1.2242 | 1.1100 | 1.0337 | 1.1100 |

2–2 | 1.2241 | 1.1100 | 1.1000 | 1.1100 |

2–3 | 1.0943 | 1.1100 | 1.0155 | 1.1100 |

**Table 3.**Heat balance of the tested combinations of windows, according to the data for a typical meteorological year in Rzeszów.

Exterior Window | Triple Glazing Unit | Double Glazing Unit | ||||||
---|---|---|---|---|---|---|---|---|

Inner Window | Single Glazing | Double Glazing Unit | Triple Glazing Unit | Triple Glazing Unit | ||||

Window with PCM | Reference Window | Window with PCM | Reference Window | Window with PCM | Reference Window | Window with PCM | Reference Window | |

Month | (kWh) | |||||||

X | 13.06 | 6.82 | 14.73 | 9.03 | 11.71 | 8.510 | 7.49 | 9.13 |

XI | −21.57 | −11.04 | −18.13 | −9.14 | −18.74 | −9.254 | −27.29 | −8.70 |

XII | −35.81 | −18.91 | −30.39 | −17.03 | −29.56 | −17.008 | −40.21 | −16.20 |

I | −24.39 | −11.63 | −18.38 | −8.78 | −18.05 | −8.472 | −31.44 | −7.82 |

II | −14.37 | −6.87 | 0.46 | 0.47 | −9.11 | −4.524 | −19.15 | −3.40 |

III | 22.71 | 15.85 | 23.99 | 17.44 | 19.29 | 15.970 | 15.47 | 16.67 |

IV | 32.36 | 21.72 | 31.26 | 22.26 | 25.02 | 20.073 | 25.17 | 20.67 |

Sum | −19.45 | 5.30 | 3.55 | 14.25 | −−19.45 | 5.295 | −69.97 | 10.36 |

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**MDPI and ACS Style**

Lichołai, L.; Musiał, M.
Experimental Analysis of the Function of a Window with a Phase Change Heat Accumulator. *Materials* **2020**, *13*, 3647.
https://doi.org/10.3390/ma13163647

**AMA Style**

Lichołai L, Musiał M.
Experimental Analysis of the Function of a Window with a Phase Change Heat Accumulator. *Materials*. 2020; 13(16):3647.
https://doi.org/10.3390/ma13163647

**Chicago/Turabian Style**

Lichołai, Lech, and Michał Musiał.
2020. "Experimental Analysis of the Function of a Window with a Phase Change Heat Accumulator" *Materials* 13, no. 16: 3647.
https://doi.org/10.3390/ma13163647