# Analysis of the Possibilities of Using a Heat Pump for Greenhouse Heating in Polish Climatic Conditions—A Case Study

^{*}

## Abstract

**:**

## 1. Introduction

#### Systems for Providing Thermal Comfort in Greenhouses

^{2}greenhouse, located in Australia. The heat pump system has a simple payback period of about six years and reduces LPG consumption by 16%. Tong et al. [20] in Japan investigated system coefficient of performance (COP) for ten household air–air heat pumps. System are used to heat an experimental greenhouse with a floor area of 151.2 m

^{2}at night in winter. The results are compared with a conventional oil heater.

^{2}, and in the case of seasonal crops (March–November) reaches 700 MJ/m

^{2}[27]. The given values are only examples of data which, depending on climatic conditions as well as materials from which a greenhouse was built, may differ from the actual values. For this reason, it is very important to choose the right strategy that enables economical heat management in greenhouse facilities. Therefore, when building or modernizing greenhouses, attention should be paid to the reduction of the energy intensity of the production process, while also ensuring optimal conditions for growing plants.

## 2. Description of the Analyzed Object

## 3. Thermal Balance of the Greenhouse

#### 3.1. Calculation of the Temperature Inside the Greenhouse

- ${x}_{1}$—ambient temperature ${T}_{amb}$ that varies within the range from −12.8 to 22.8 °C;
- ${x}_{2}$—intensity of solar radiation ${I}_{c}$ that covers the range from 0 to 447.3 W/m
^{2}; and - ${x}_{3}$—temperature inside the greenhouse ${T}_{in}$, which can take values from −12.8 to 50 °C.

#### 3.2. The Greenhouse’s Heat Demand

## 4. Selection of the Heating System

#### 4.1. Simulation of the Operation of a Ground Source Heat Pump

#### 4.2. Simulation of the Operation of an Air Source Heat Pump

## 5. Economic Analysis

^{2}, it is equal to €34/m

^{2}. The cost of an air source heat pump is equal to €4952 gross, and when it is calculated per unit of the greenhouse area, it is equal to €12/m

^{2}. The cost of producing a boiler room equipped with a coal-fired boiler with an 18 kW feeder is approximately €1904.5 gross. The total cost of assembly is about €1190, and therefore the total investment cost ${K}_{I,b}$ is estimated to be €3094.5, which, when calculated per unit of the greenhouse area, is equal to €7.4/m

^{2}.

## 6. Emission of Pollution

## 7. Summary and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | area, m^{2} |

$a$ | height of a side wall of the greenhouse, m |

B | amount of fuel, kg (or Mg) |

$b$ | length of the greenhouse, m |

$c$ | width of the greenhouse, m |

${c}_{p,air}$ | specific heat at constant air pressure inside the greenhouse, J/(kg∙K) |

${C}_{w}$ | constant, - |

$d$ | height of the greenhouse, m |

E | emission of substances, kg (or g) |

$g$ | acceleration of gravity, m/s^{2} |

$G{r}_{in}$ | Grashof number for fluid inside an object, - |

$G{r}_{in,g}$ | Grashof number for fluid inside an object at ground level, - |

$h$ | coefficient of heat transfer into the wall, W/(m^{2}∙K) |

${I}_{c}$ | intensity of solar radiation, W/m^{2} |

${K}_{E,hp}$ | heat pump operating costs, €/year |

${K}_{E,b}$ | boiler operation costs, €/year |

${K}_{I}$ | investment costs, € |

${K}_{I,hp}$ | cost of a boiler room with a heat pump, € |

${K}_{I,b}$ | cost of a boiler room with a dust coal-fired boiler, € |

l | roof length, m |

$L$ | payback period, year |

${m}_{air}$ | air mass, kg |

$N$ | electricity consumption by a heat pump, kW |

$Nu$ | Nusselt number, - |

Pr | Prandtl number for air, - |

${Q}_{w}^{r}$ | heating value, MJ/kg |

${\dot{Q}}_{d}$ | heat flux passing through the roof, W |

${\dot{Q}}_{g}$ | heat flux passing into the ground, W |

${\dot{Q}}_{h}$ | heat flux for a greenhouse’s heating demands, W |

${\dot{Q}}_{in}$ | heat flux passing into a wall, W |

${\dot{Q}}_{k}$ | heat flux passing through a partition, W |

${\dot{Q}}_{L}$ | heat flux of ventilation, W |

${\dot{Q}}_{p}$ | heat flux passing through front and back walls, W |

${\dot{Q}}_{rad}$ | heat flux of radiation, W |

${\dot{Q}}_{s}$ | heat flux passing through side walls, W |

${R}_{L}$ | ground resistance, (m^{2}∙K)/W |

$Re$ | Reynolds number, - |

$t$ | time, s (or h) |

${T}_{amb}$ | ambient temperature, °C (or K) |

${T}_{k}$ | final temperature inside the greenhouse, °C (or K) |

${T}_{g}$ | ground temperature, °C (or K) |

${T}_{in}$ | temperature inside the object, °C (or K) |

${T}_{1\dots 4}$ | temperature on the inner/outer wall of the partition, °C (or K) |

$U$ | heat transfer coefficient, W/(m^{2}∙K) |

$V$ | volume of air inside the greenhouse, m^{3} |

W | emission index per unit of spent fuel, g/Mg |

${w}_{h}$ | characteristic linear dimension, m |

$Z$ | profit, € |

Greek symbols | |

$\beta $ | compressibility of fluid, 1/K |

${\beta}_{g}$ | compressibility of fluid next to the ground, 1/K |

${\delta}_{g}$ | equivalent ground thickness, mm |

$\delta $ | layer thickness, mm |

$\eta $ | efficiency of the conversion process, - |

${\eta}_{b}$ | efficiency of the boiler, % |

$\lambda $ | thermal conductivity coefficient, W/(m∙K) |

${\rho}_{air}$ | air density inside the greenhouse, kg/m^{3} |

${\tau}_{1}$ | transparency of glass layer, - |

$v$ | kinetic air viscosity coefficient, m^{2}/s |

Index | |

d | Roof |

g | Ground |

p | front and back walls |

s | side walls |

rad | radiation |

in | Inner |

out | Outer |

1 | Glass |

2 | Air |

3 | cell foil |

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**Figure 4.**The dependence between the final temperature inside the greenhouse, the intensity of radiation and the initial temperature inside the object for the ambient temperature of −12.8 °C.

**Figure 5.**The dependence between the final temperature inside the greenhouse, the intensity of radiation and the initial temperature inside the object for the ambient temperature of 8 °C.

**Figure 6.**The dependence between the final temperature inside the greenhouse, the intensity of radiation and the initial temperature inside the object for the ambient temperature of 22.8 °C.

**Figure 9.**COP of a ground source heat pump as a function of ground temperature for a heating temperature of 35 °C.

**Figure 14.**The COP of the air source heat pump, as a function of ambient temperature, for a heating temperature of 16 °C.

Dimensions of the object | $a$ | 1.84 m |

$b$ | 42.0 m | |

$c$ | 10.0 m | |

$d$ | 4.77 m | |

Roof | ${A}_{d}$ | 483.17 m^{2} |

${l}_{1}$ | 5.752 m | |

${l}_{2}$ | 5.759 m | |

${l}_{3}$ | 5.782 m | |

${l}_{4}$ | 5.795 m | |

${w}_{h,d}$ | 5.772 m | |

$R{e}_{d}$ | 918,117, - | |

Glass layer | ${\delta}_{1}$ | 3 mm |

${\lambda}_{1}$ | 0.800 W/(m∙K) | |

${\tau}_{1}$ | 0.82, - | |

Air layer | ${\delta}_{2}$ | 10 mm |

${\lambda}_{2}$ | 2.44 × 10^{−2}, W/(m∙K) | |

${\tau}_{2}$ | 1.0, - | |

Foil layer | ${\delta}_{3}$ | 6 mm |

${\lambda}_{3}$ | 0.190 W/(m∙K) | |

${\tau}_{3}$ | 0.62, - | |

Walls | ${A}_{s}$ | 154.56 m^{2} |

${A}_{p}$ | 132.2 m^{2} | |

${w}_{h,p}$ | 3.305 m | |

$R{e}_{p}$ | 527,534, - | |

${w}_{h,s}$ | 1.84 m | |

Ground | ${A}_{g}$ | 419.92 m^{2} |

${\lambda}_{\mathrm{g}}$ | 1.49 W/(m∙K) | |

Internal parameters | ${v}_{in}$ | 14.74 × 10^{−6}, m^{2}/s |

$P{r}_{in}$ | 0.704, - | |

${\lambda}_{in}$ | 2.53 × 10^{−2}, W/(m∙K) | |

External parameters | ${v}_{out}$ | 12.53 × 10^{−6}, m^{2}/s |

$P{r}_{out}$ | 0.713, - | |

${\lambda}_{out}$ | 2.302 × 10^{−2}, W/(m∙K) | |

$R{e}_{s}$ | 293,695, - |

No. | ${\mathit{x}}_{\mathbf{1}}$ | ${\mathit{x}}_{\mathbf{2}}$ | ${\mathit{x}}_{\mathbf{3}}$ |
---|---|---|---|

1 | + | + | + |

2 | + | − | − |

3 | − | + | − |

4 | − | − | + |

5 | + | 0 | 0 |

6 | − | 0 | 0 |

7 | 0 | + | 0 |

8 | 0 | − | 0 |

9 | 0 | 0 | + |

10 | 0 | 0 | − |

11 | 0 | 0 | 0 |

−1 | 0 | 1 | |
---|---|---|---|

${\mathit{T}}_{\mathit{a}\mathit{m}\mathit{b}},\xb0\mathrm{C}$ | −12.8 | 5 | 22.8 |

${\mathit{I}}_{\mathit{c}},W/{m}^{2}$ | 0 | 223.65 | 447.3 |

${\mathit{T}}_{\mathit{i}\mathit{n}},\xb0\mathrm{C}$ | −12.8 | 31.4 | 50 |

No. | Regression Coefficient, - | Final Temperature, °C |
---|---|---|

1 | 1.799320052209 | 35.6 |

2 | 1.073490373906 | 22.8 |

3 | 0.000315616715 | −3.3 |

4 | 0.030137100946 | −5.4 |

5 | −0.000001699343 | 29.6 |

6 | 0.134666158924 | −5.8 |

7 | −0.000157275535 | 16.7 |

8 | 0.000125349535 | 6.7 |

9 | −0.005856511074 | 12.5 |

10 | −0.000298081806 | 9.7 |

11 | 0.000010479794 | 11.8 |

Parameter | Unit | Value |
---|---|---|

Heating power at S0/W35 | kW | 21.5 |

Performance factor at S0/W35 | - | 4.66 |

Total mass | kg | 345 |

Sound pressure level | dB(A) | 54.6 |

Refrigerant (R410A) | kg | 6.0 |

Dimensions (width × length × height) | mm | 1242 × 860 × 1154 |

Scope of work (external temp.) | °C | −5–20 |

Fuel | Coal Dust |
---|---|

Fuel consumption | 7670 kg |

Boiler | 18 kW |

Sulfur content in hard coal | 0.83% [34] |

Ash content A’ | 22.4% [34] |

Type of Pollution | Amount, g/Mg | Volume of Emission E, kg | ||
---|---|---|---|---|

1 Season | 5.5 Seasons | 18 Seasons | ||

SO_{x} | 13,280 | 101.8 | 560.2 | 1840.6 |

NO_{x} | 2200 | 16.8 | 92.8 | 304.9 |

CO | 45,000 | 345 | 1898 | 6237 |

CO_{2} | 1,850,000 | 14,189 | 78,042 | 256,404 |

TSP | 22,400 | 171.8 | 944.9 | 3104.6 |

benzo (a) pyrene | 14 | 0.107 | 0.590 | 1.940 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nemś, A.; Nemś, M.; Świder, K.
Analysis of the Possibilities of Using a Heat Pump for Greenhouse Heating in Polish Climatic Conditions—A Case Study. *Sustainability* **2018**, *10*, 3483.
https://doi.org/10.3390/su10103483

**AMA Style**

Nemś A, Nemś M, Świder K.
Analysis of the Possibilities of Using a Heat Pump for Greenhouse Heating in Polish Climatic Conditions—A Case Study. *Sustainability*. 2018; 10(10):3483.
https://doi.org/10.3390/su10103483

**Chicago/Turabian Style**

Nemś, Artur, Magdalena Nemś, and Klaudia Świder.
2018. "Analysis of the Possibilities of Using a Heat Pump for Greenhouse Heating in Polish Climatic Conditions—A Case Study" *Sustainability* 10, no. 10: 3483.
https://doi.org/10.3390/su10103483