# Investigation on an Improved Household Refrigerator for Energy Saving of Residential Buildings

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## Abstract

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## 1. Introduction

## 2. Operating Principle

_{HP}) is raised to the temperature of the heat pipes (T

_{HP}). Thus, the external heat flux (Q

_{out}) decreases, whereas the internal heat flux (Q

_{in}) increases. The heat flux difference between them (Q

_{HP}) is acquired from the fresh food compartment using heat pipe. It should be emphasized that the heat transfer enhancement between the fresh food compartment and freezer (which could also be easily done by reducing its internal thermal isolation) is just a side effect, and the main purpose of adding heat pipes is to decrease the overall heat leakage of the improved refrigerator.

## 3. Measured Conditions of Midea BCD-111 Refrigerator

_{f}) and the fresh food compartment (T

_{fre}) are measured according to the National Standard GB/T 8059-2016. Since the temperatures at the outside surface of side walls of the BCD-111 refrigerator are related to its condensing temperature, the outside surface temperature of side freezer wall (T

_{s,out}) is also measured. Detailed temperature measurement methods can be found in reference [19].

## 4. Mathematical Model

- -
- The temperature fluctuation of air is neglected.
- -
- The walls of refrigerator have the same heat conductive coefficient.
- -
- Rectangular straight fin efficiency is adopted for aluminum plates [20].
- -
- The heat transfer is steady-state and 1D.
- -
- The temperatures at evaporating and condensing sections of heat pipes are considered uniform (T
_{HP}= T_{con}= T_{eva}) since the internal two-phase thermal resistance is far less than the external convective thermal resistance. - -
- The external surface temperature of side freezer walls is given as a boundary condition due to the influence of condenser of the BCD-111 refrigerator.

- Boundary condition 1: the surrounding air temperatures are given for the original freezer walls (or the evaporating sections of heat pipes in fresh food compartment);
- Boundary condition 2: the average outside wall temperatures are given for the improved freezer walls.

_{t}

_{,out}and Q

_{t}

_{,in}are outside and inside heat fluxes, respectively; T

_{amb}, T

_{HP}, and T

_{f}are ambient temperature, heat pipe temperature, and freezer temperature, respectively; α

_{t}

_{,out}and α

_{t}

_{,in}are the convective heat transfer coefficients of ambient and inside air, respectively; δ is the wall thickness; X

_{t}is the ratio of wall thickness inside of heat pipes to the whole topside wall thickness; and A

_{t}is the topside heat transfer area.

_{s}

_{,out}and Q

_{s}

_{,in}are outside and inside heat fluxes, respectively; T

_{s,out}is the outside surface temperature of side freezer wall; α

_{t}

_{,out}and α

_{t}

_{,in}are the convective heat transfer coefficients of ambient and inside air, respectively; X

_{s}is the ratio of wall thickness inside of heat pipes to the whole side wall thickness; and A

_{s}is the side heat transfer area.

_{HP}is the heat flux of heat pipes; Q

_{s,in}and Q

_{s,out}are inside and outside heat flux at each side freezer wall, respectively; and Q

_{t,in}and Q

_{t,out}are inside and outside heat flux at half of the topside freezer wall, respectively.

_{eva,u}and α

_{eva,l}are the convective heat transfer coefficients of upper and lower surfaces of the evaporating sections of heat pipes, respectively; T

_{fre}is the fresh food compartment temperature; and A

_{eva}is the area of the evaporating sections of heat pipes.

_{HP}. Besides, the heat fluxes at the front and the back freezer walls of the improved refrigerator or the freezer walls of the original refrigerator are easily calculated based on the boundary conditions 1 or 2, and thus the energy saving ratios of the freezer of the improved refrigerator are as follows.

_{re,s}, η

_{re,t,}and η

_{re}are the energy saving ratios of the side wall, the topside wall, and the whole freezer of the improved refrigerator, respectively; C, C

_{s}, and C

_{t}are freezer cold loss and cold losses at the side and the topside freezer walls for the improved refrigerator, respectively (C

_{s}= 2 × Q

_{s,out}and C

_{t}= 2 × Q

_{t,out}); and C’

_{s}, C’

_{t}, and C’ are the cold losses of the side wall, the topside wall, and the whole freezer of the original refrigerator, respectively.

## 5. Results and Discussion

#### 5.1. Performances at Different Ambient Temperatures

_{in}(namely X

_{in}= X

_{t,in}= X

_{s,in}), is preliminarily set to 16%. The heat transfer area of the evaporating section of heat pipes (A

_{eva}) is given as its maximum value of 0.146 m

^{2}. In the side and the topside freezer walls of the improved refrigerator, considerable heat is transported to the freezer by heat pipes, which changes the thermal characteristics of the freezer walls. Since the outside surface temperature of side freezer walls is greatly affected by the ambient temperature, the side freezer walls of the original and the modified refrigerators are firstly compared in Figure 5. The convective heat transfer coefficients inside of the side freezer wall (α’

_{s,in}and α

_{s,in}) both increase steadily with ambient temperature, but their difference gradually drops from 0.37 W·m

^{−2}·K

^{−1}to 0.22 W·m

^{−2}·K

^{−1}(the radiative heat flux is relatively low and thus is neglected to simplify the calculation). Correspondingly, the outside surface temperature of the original side freezer wall decreases from −11.5 °C to −13.8 °C, while that of the modified one reduces from −9.0 °C to −12.0 °C, and the gap between them gradually narrows from 2.5 °C to 1.8 °C. The above phenomena show that inside heat transfer of the modified side freezer wall is enhanced due to the existence of heat pipes, and the influence of heat pipes steadily decreases as the heat leakage increases with the ambient temperature.

_{s,in}) is 5.0 W, and the corresponding outside one (C

_{s,out}) is reduced to 2.4 W. Meanwhile, the cold loss at the inside surface of the topside modified freezer wall (C

_{t,in}) is 2.2 W, and the corresponding outside one (C

_{t,out}) drops to 1.0 W. In comparison to the original freezer walls, about 24.7% of the cold loss of side freezer walls and 21.7% of the cold loss of topside freezer wall are recovered by the heat pipes. With a raising ambient temperature, C

_{s,out}increases from 2.1 W to 3.8 W, and C

_{t,out}enlarges from 0.9 W to 1.7 W. The cold loss reduction ratios of side and topside freezer walls (η

_{s,re}and η

_{t,re}, respectively) significantly drops from 28.3% to 15.0% and from 25.3% to 12.8%, respectively. The cold loss recovery behavior of modified side freezer wall remains better than the topside one, and their cold loss recovery capabilities are both considerably restricted by a high ambient temperature.

_{re}) decreases from 16.5% to 8.3%. The results indicate that more cold loss could be recycled by the heat pipes when the refrigerator runs with a lower ambient temperature. In general, the energy saving of the improved refrigerator is reliable when ambient condition varies within a typical range.

#### 5.2. Performances at Different Temperature Gears

_{eva}and X

_{in}, are fixed to 25.0 °C, 0.146 m

^{2}, and 16%, respectively, and the temperature gears are given as A~D, the measured boundary conditions are utilized to further compare the performances of original and improved refrigerators. The representative heat transfer parameters of original and improved side freezer walls are shown in Figure 8. As the temperature gear is adjusted from A to D, the inside convective heat transfer coefficient for the original side wall (α’

_{s}

_{,in}) remains close to 3.34 W·m

^{−2}·K

^{−1}, whereas that for the modified one (α′

_{s}

_{,in}) remains at about 3.59 W·m

^{−2}·K

^{−1}. The inside surface temperature for the modified side wall (T

_{s}

_{,in}) raises from −12.1 °C to −9.6 °C; and the inside surface temperature for the original side wall (T’

_{s}

_{,in}) raises from −13.9 °C to −11.8 °C. When the temperature gear changes from A to D, T

_{s}

_{,in}remains higher than T’

_{s}

_{,in}, and their difference slightly enlarges from 1.8 °C to 2.1 °C. The enhancement on the inside heat transfer of the modified side freezer wall intensifies as the inside temperatures of the refrigerator raise.

_{t}

_{,in}) raises from −10.3 °C to −7.9 °C, and the outside surface temperature for the original topside freezer wall (T’

_{t}

_{,out}) slightly increases from 19.4 °C to 20.3 °C. The inside surface temperature for the original topside freezer wall (T’

_{t}

_{,in}) and the outside surface temperature for the modified topside freezer wall (T

_{t}

_{,out}) remain close to −11.5 °C and 20.8 °C, respectively. Results confirm that the influence of heat pipes intensifies as the inside temperatures of the refrigerator raise.

_{HP}) raises from −2.8 °C to −0.4 °C as the temperature gear is varied from A to D, and the difference between the air temperature at the fresh food compartment and T

_{HP}enlarges from 4.9 °C to 5.4 °C. Correspondingly, the heat transfer capability of heat pipes enhances and its heat flux (Q

_{HP}) increases from 3.0 W to 3.5 W. Heat pipes provide a cold loss recovery function for the freezer, and the heat shunt amount is closely affected by the temperature gear of the refrigerator. Since the temperature of evaporating sections of heat pipes in the fresh food compartment is close to 0 °C and is much higher than the temperature of the original evaporator of the refrigerator, the problem of frosting in the evaporating sections of the heat pipes is less serious.

_{re}) correspondingly increases from 9.7% to 11.6%. On the whole, the improved refrigerator can effectively reduce the cold loss of the freezer even if the temperature gear of the refrigerator changes. The energy saving performance slightly enhances as the cold loss amount decreases with increasing inside temperatures of the refrigerator.

#### 5.3. Performances at Different Heat Pipe Design

_{eva}) is firstly reduced from 0.146 m

^{2}to 0.094 m

^{2}, while the ratio of length to width remains constant. The variations of the average convective heat transfer coefficients of the upper and the lower surfaces of the evaporating sections of heat pipes (α

_{eva}) and the temperature of the heat pipes (T

_{HP}) are shown in Figure 12. As the heat transfer area reduces 9.8%, 19.0%, 27.8%, and 36.0%, α

_{eva}raises gradually from 2.68 W·m

^{−2}·K

^{−1}to 2.83 W·m

^{−2}·K

^{−1}, 2.78 W·m

^{−2}·K

^{−1}, 2.73 W·m

^{−2}·K

^{−1}, and 2.89 W·m

^{−2}·K

^{−1}, respectively. Correspondingly, T

_{HP}decreases from −0.7 °C to −0.9 °C, −1.2 °C, −1.4 °C, and −1.7 °C, respectively. The convective heat transfer capability of the evaporating sections of heat pipes per unit area gradually increases as the temperature gap between the heat pipes and the fresh food compartment enlarges. The heat transfer area of the evaporating sections of heat pipes could considerably affect the internal heat transfer of the improved refrigerator.

_{eva}reduces from 0.146 m

^{2}to 0.094 m

^{2}, the heat flux of the heat pipes (Q

_{HP}) drops from 3.4 W to 2.8 W, and the heat flux decreasing ratio is about 80.4%. Correspondingly, the cold loss reduction ratio (η

_{re}) decreases from 11.2% to 9.3%, and its decreasing ratio is about 82.8%. Results indicate that reduction on the heat transfer area of heat pipes in the fresh food compartment weakens the heat transfer of the heat pipes and thus causes a performance degradation of the improved refrigerator. However, the simulation also proves that a slight sacrifice of heat transfer area for the convenience of design and manufacture of the improved refrigerator is feasible.

_{eva}of 0.146 m

^{2}, the common ratio of wall thickness inside of heat pipes to the whole wall thickness (X

_{in}) is changed from 10% to 25%, and the temperatures of heat pipes and cold reduction ratios of side and topside freezer walls are shown in Figure 14. The temperature of heat pipes (T

_{HP}) raises from −2.1 °C to 1.0 °C with increasing X

_{in}. Correspondingly, the cold loss reduction ratio of the side freezer wall (η

_{s,re}) and that of the topside freezer wall (η

_{t,re}) gradually decrease from 20.7% to 18.1% and from 18.6% to 12.7%, respectively. Given the same location of the heat pipe, the cold loss reduction capability of the modified side freezer wall remains higher than that of the topside one, but the gap between η

_{s,re}and η

_{t,re}significantly enlarges from 2.1% to 5.4%. The temperature of heat pipes is closely related with its installation position in the freezer walls, and the cold loss reduction behavior of the side freezer walls is relatively more stable, even if the location of heat pipes changes. Correspondingly, Figure 15 shows the overall behaviors of the modified freezer with increasing X

_{in}. Cold loss of the modified freezer (C) slightly drops from 7.3 W to 7.6 W, and cold loss reduction ratio (η

_{re}) decreases from 12.1% to 8.9% as X

_{in}increases from 10% to 25%. The overall cold loss recovery amounts of heat pipes at various installation positions remain relatively stable. These results certify the reliability of the energy saving function of the improved refrigerator.

_{s,in}) is varied from 10% to 25%, while that for topside freezer wall (X

_{t,in}) is fixed to 16%, and the calculated results are shown in Figure 16. T

_{HP}raises from −1.8 °C to 0.5 °C, η

_{re}decreases from 11.7% to 9.4%, and their variation ranges are smaller compared with the operating states with changing X

_{s,in}and X

_{t,in}together (shown in Figure 14 and Figure 15). In particular, η

_{s,re}drops from 19.4% to 11.1% whereas η

_{t,re}raises from 16.8% to 24.0%. The temperature distribution at the topside freezer wall is affected by the raising T

_{HP}, and thus its cold loss drops, even if X

_{t,in}is constant. For comparison, the behavior of the improved refrigerator is shown in Figure 17 as X

_{t,in}is varied from 10% to 25% with a fixed X

_{s,in}. Correspondingly, η

_{s,re}increases from 16.0% to 18.2%, η

_{t,re}reduces from 23.7% to 13.6%, T

_{HP}slightly raises from −1.0 °C to −0.3 °C, and η

_{re}decreases from 11.5% to 10.5%. The performance responses to the variation of X

_{t,in}are much weaker than those of X

_{s,in}, which indicates the location of condensing sections of heat pipes at the topside freezer wall plays a more important role. Generally, properly adjusting the location of condensing sections of heat pipes at each freezer can vary the cold loss recovery capability of the improved refrigerator, and the energy saving design is feasible as X

_{s,in}and X

_{t,in}are changed between 10% to 25%.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | heat transfer area [m^{2}] |

amb | ambient air |

C | cold loss [W] |

HP | heat pipes |

Q | heat flux [W] |

R | thermal resistance [K·W^{−1}] |

T | temperature [°C] |

X_{in} | ratio of wall thickness inside of heat pipes to whole wall thickness [%] |

Greek letters | |

α | convective heat transfer coefficient [W·m^{−2}·K^{−1}] |

δ | wall thickness [m] |

ε | iteration error |

λ | heat conductivity coefficient [W·m^{−1}·K^{−1}] |

η | ratio [%] |

Superscripts | |

′ | original refrigerator |

″ | iterative value |

Subscripts | |

1 | boundary condition 1 |

2 | boundary condition 2 |

con | condensing section |

HP | heat pipe |

d | heat conduction |

eva | evaporating section |

f | freezer |

fre | fresh food compartment |

in | inside |

our | outside |

re | recovery |

s | side freezer wall |

t | topside freezer wall |

v | convective heat transfer |

w | freezer wall |

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**Figure 5.**Inside heat transfer characteristics inside of the topside freezer wall at various ambient temperatures.

**Figure 6.**Cold loss comparison between side and topside freezer walls at various ambient temperatures.

**Figure 8.**Inside heat transfer characteristics of the topside freezer wall at various temperature gears.

**Figure 11.**Cold loss recovery behaviors of the improved refrigerator for different temperature gears.

**Figure 14.**Temperatures of heat pipes and cold reduction ratios of side and topside freezer walls at various X

_{in}.

**Table 1.**Boundary conditions under different temperature gears and ambient temperatures [19].

Operating States of the Tested Refrigerator | T_{f} [°C] | T_{fre} [°C] | T_{s,out} [°C] | |
---|---|---|---|---|

Ambient Temperature [°C] | Temperature Gear | |||

25.0 | C | −17.7 | 4.7 | 27.0 |

17.0 | C | −16.0 | 5.2 | 18.1 |

20.0 | C | −16.5 | 5.0 | 21.3 |

31.0 | C | −20.2 | 2.9 | 32.6 |

25.0 | A | −19.6 | 2.1 | 27.0 |

25.0 | B | −19.3 | 2.6 | 27.0 |

25.0 | D | −17.2 | 5.0 | 26.7 |

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## Share and Cite

**MDPI and ACS Style**

Cao, J.; Wang, Q.; Hu, M.; Ren, X.; Liu, W.; Su, Y.; Pei, G.
Investigation on an Improved Household Refrigerator for Energy Saving of Residential Buildings. *Appl. Sci.* **2020**, *10*, 4246.
https://doi.org/10.3390/app10124246

**AMA Style**

Cao J, Wang Q, Hu M, Ren X, Liu W, Su Y, Pei G.
Investigation on an Improved Household Refrigerator for Energy Saving of Residential Buildings. *Applied Sciences*. 2020; 10(12):4246.
https://doi.org/10.3390/app10124246

**Chicago/Turabian Style**

Cao, Jingyu, Qiliang Wang, Mingke Hu, Xiao Ren, Weixin Liu, Yuehong Su, and Gang Pei.
2020. "Investigation on an Improved Household Refrigerator for Energy Saving of Residential Buildings" *Applied Sciences* 10, no. 12: 4246.
https://doi.org/10.3390/app10124246