# Electric Heating System with Thermal Storage Units and Ceiling Fans for Cattle-Breeding Farms

^{*}

## Abstract

**:**

## 1. Introduction

_{2}[18,19].

## 2. Materials and Methods

## 3. Calculating and Selecting the Ceiling Fan Parameters

_{f}(see Figure 1) insuring the maximum air flow rate in the operating area, can be defined from the following equation:

_{p}is distance between the floor and the ceiling (m), L is that between the floor and the animal shoulder (m).

_{f}capable to ensure the required values of air velocity and flow rate, for reasonable fan suspension length, can be found from the following expression deduced using experimental methods [3]:

_{av}is average air flow rate, in operation area, i.e., standing or rest zone, (m/s); c

_{f}is coefficient depending on the ceiling fan design and its operation conditions.

_{ave}= 0.5 ω

_{0}where ω

_{0}is initial value of air velocity (m/s).

_{f}= 0.07, for premises having 4 × 8 m, in plain view, and 4 m in height, for ceiling fans type MR-1. By substituting the variables in formula (2) with their known values we obtained N

_{f}= 1.3. One 60 W fan unit type MR-1 with controlled air flow performance rate was chosen, having three 620 mm long blades [35].

## 4. Calculating Basic Thermal Characteristics of the Electric Thermal Storage Unit

_{ch_ave}is average heat capacity of ETS unit (W); τ

_{he}is duration of ETS unit heat emission period (h); ρ

_{HSM}is volumetric density of the heat storage core material (kg/m

^{3}); c

_{HSM}is heat capacity ratio of the core material (kJ·kg

^{−1}·K

^{−1}); T

_{HSC,max}and T

_{HSC,min}are temperature values of ETS unit heat storage core, in the initial (600 °C to 650 °C) and the final (50 °C to 100 °C) moments of the heat charging period, respectively [36,37].

_{sh,max}= 60 °C to 70 °C, while at the end moment of the heat emission period it is in the range of T

_{sh,min}= 25 °C to 30 °C which is in the reasonable compliance with the requirements for ETS unit casing outer surface temperature specified in [36].

_{loss}emitted from the surface of the ETS unit casing into surrounding space, in the course of charging, should be calculated for the casing surface temperature value T

_{sh}= (T

_{sh,min}+ T

_{sh,max})/2, using the following formula:

_{sh_ave}is average value of the coefficient of heat-exchange between the electric thermal storage outer surface and ambient air (premises), (W·m

^{−2}·°K

^{−1}); T

_{ap}is ambient air temperature in premises (°C); F

_{ETS}is surface area of the ETS casing (m

^{2}); k

_{rad}is coefficient taking into account the heat loss by radiation from the surface of the ETS casing (value is 1.25).

_{ins}of the thermal insulation layer, it should be considered as a single-layer plain wall. The required thickness of ETS unit thermal insulation layer insuring compliance of the heat loss from the thermal storage unit with the specified Q

_{loss}value can be defined from the following equation:

_{ins}is thermal-conductivity coefficient of the thermal insulation material (W·m

^{−1}·°K

^{−1}); T

_{ins,int}is temperature of the thermal insulation internal layer, by the end of the charging period (°C).

_{ins}is surface area of the thermal insulation (m

^{2}).

_{unit}of ETS unit is defined from the following equation:

_{ch}is duration of ETS unit charging period (h);

**k**

_{r}is power reserve coefficient that takes into account the aging of electric heating elements and changes in the supply voltage (value is 1.2).

_{ins}is heat capacity ratio of the thermal insulation (kJ·kg

^{−1}·°K

^{−1}); ρ

_{ins}is its volumetric density (kg/m

^{3}); T

_{ins,max}and T

_{ins,min}are temperature values of the thermal insulation in the end moments of ETS unit charging and heat emission periods, respectively.

_{st}accumulated in ETS unit makes it possible to define time period τ

_{warm}required for its heating to temperature value T

_{HSC,max}:

_{loss,max}is heat loss, for the maximum temperature of the casing surface T

_{sh,max}of ETS unit, at the end moment of the heat charging period (W).

_{sh_ave}, for the outer ETS unit casing surface, similarity criterion Gr should be defined from Formula (10), following which similarity criterion Nu is calculated in accordance with expression (11). After that, α

_{sh_ave}value can be determined [30]:

^{−1}); h—is ETS unit height (m); g is gravity factor (m/s

^{2}); ν is air kinematic viscosity (m

^{2}/s).

_{ch_ave}, in air channels of ETS unit heat storage cells, similarity criterion Nu has to be calculated using Equation (12), with the account of the temperature difference θ

_{ch}= T

_{wch}/T

_{air_ch}[38,39,40]:

## 5. Discussion

#### 5.1. Experimental Studies of Thermal and Humidity Parameters of Air

#### 5.2. Evaluation of the Energy Efficiency of the Combined Heat Supply System

_{air}is air heat capacity ratio (kJ·kg

^{−1}·°K

^{−1}), G is mass of air (kg), ΔT is specified air temperature control interval in work zone (°C), Q

_{p}is thermal energy production by the heating installation (W).

_{p2}within which air gets heated to a specified temperature will be equal to:

_{te}is coefficient that takes account of additional thermal energy incoming as a result of the ceiling fans operation.

_{f}fall into the interval between 1.2 and 1.25.

_{p2}= 0.8τ

_{p1}.

_{es}is heat-exchange coefficient of the enclosing structure internal surface (W·m

^{−2·}°K

^{−1}), T

_{ap}is ambient air temperature in premises (°C), T

_{es}and F

_{es}are, respectively, temperature (°C) and area (m

^{2}) of the enclosing structure internal surface, Q

_{air}is thermal energy loss with exhausted air (W).

_{con}and radiant α

_{rad}energy components:

_{rad}= const since it does not depend on the air flow velocity and it can be assigned a value in the range of 4 W·m

^{−2}·K

^{−1}to 4.5 W·m

^{−2}·K

^{−1}, for animal-housing premises [44].

_{o2}and without ceiling fans τ

_{o1}(in the assumption that Q

_{air}= 0):

_{o2}= 0.95τ

_{o1}.

_{1}> n

_{2}. Consequently, the average heat energy income, for Q

_{p1}= Q

_{pn1}, exceeds that, for Q

_{p2}= Q

_{pn2}. It means that the thermal energy consumption is greater, in the first case.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Diagram for optimal ceiling fan installation: 1—ceiling fan; 2—cages for calves; 3—slatted floor of the cage.

Input voltage (V) | 380/220 |

Heat storage capacity (kW) | 4.8 |

Electric convector heater capacity (kW) | 2.4 |

Minimum heat charging period (h) | 4 |

Heat emission period (h) | 48 |

Weight (kg) | 200 |

Material | c (kJ·kg^{−1}·°K^{−1}) | λ (W·m^{−1}·°K^{−1}) | ρ_{ave} (kg/m^{3}) |
---|---|---|---|

Magnesium oxide | 1.05 + 0.29·10^{−3} T_{HSM} | 4.7–1.7·10^{−3} T_{HSM} | 3000 |

Chamotte | 0.88 + 0.23·10^{−3} T_{HSM} | 0.84 + 0.58·10^{−3} T_{HSM} | 2200 |

Corundum | 0.79 + 0.42·10^{−3} T_{HSM} | 2,1 + 1.9·10^{−3} T_{HSM} | 3300 |

Dinas | 0.837 + 0.25·10^{−3} T_{HSM} | 0.93 + 0.69·10^{−3} T_{HSM} | 2200 |

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**MDPI and ACS Style**

Khimenko, A.; Tikhomirov, D.; Trunov, S.; Kuzmichev, A.; Bolshev, V.; Shepovalova, O. Electric Heating System with Thermal Storage Units and Ceiling Fans for Cattle-Breeding Farms. *Agriculture* **2022**, *12*, 1753.
https://doi.org/10.3390/agriculture12111753

**AMA Style**

Khimenko A, Tikhomirov D, Trunov S, Kuzmichev A, Bolshev V, Shepovalova O. Electric Heating System with Thermal Storage Units and Ceiling Fans for Cattle-Breeding Farms. *Agriculture*. 2022; 12(11):1753.
https://doi.org/10.3390/agriculture12111753

**Chicago/Turabian Style**

Khimenko, Aleksei, Dmitry Tikhomirov, Stanislav Trunov, Aleksey Kuzmichev, Vadim Bolshev, and Olga Shepovalova. 2022. "Electric Heating System with Thermal Storage Units and Ceiling Fans for Cattle-Breeding Farms" *Agriculture* 12, no. 11: 1753.
https://doi.org/10.3390/agriculture12111753