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

Normally, internal air temperature is kept within a specified range with the use of the on-off action control.

In case that heating-ventilation system is not equipped with ceiling fans the time period within which air gets heated to a specified temperature equals to [43]:

$$
\pi\_{\rm p1} = \frac{c\_{\rm air} G \Delta T}{Q\_{\rm P}},
\tag{13}
$$

where *<sup>c</sup>*air is air heat capacity ratio (kJ·kg−1· ◦K<sup>−</sup>1), *G* is mass of air (kg), Δ*T* is specified air temperature control interval in work zone (◦C), *Q*<sup>p</sup> is thermal energy production by the heating installation (W).

In case of the ceiling fans application, time period *τ*p2 within which air gets heated to a specified temperature will be equal to:

$$
\pi\_{\rm p2} = \frac{c\_{\rm air} G \Delta T}{k\_{\rm te} Q\_{\rm P}},
\tag{14}
$$

where *k*te is coefficient that takes account of additional thermal energy incoming as a result of the ceiling fans operation.

It was experimentally found out that the values of *k*<sup>f</sup> fall into the interval between 1.2 and 1.25.

Then it is follows from Expressions (13) and (14) that *τ*p2 = 0.8*τ*p1.

Let us consider the effect of the ceiling fans operation on the air-cooling rate in premises. Evidently, air cooling time period is defined by the heat dissipation rate:

$$Q\_{\rm out} = \alpha\_{\rm es} \left( T\_{\rm ap} - T\_{\rm es} \right) F\_{\rm es} + Q\_{\rm air} \tag{15}$$

where *<sup>α</sup>*es is heat-exchange coefficient of the enclosing structure internal surface (W·m−2·◦K<sup>−</sup>1), *T*ap is ambient air temperature in premises (◦C), *T*es and *F*es are, respectively, temperature ( ◦C) and area (m2) of the enclosing structure internal surface, *Q*air is thermal energy loss with exhausted air (W).

Heat-exchange coefficient αfen comprises both convective *α*con and radiant *α*rad energy components:

$$
\alpha\_{\text{es}} = \alpha\_{\text{con}} + \alpha\_{\text{rad}\prime} \tag{16}
$$

where the surfaces of the premises are blown by air flows there the forced and combined convection operation mode takes place in which case the following expression is valid, with regard to [44]:

$$\alpha\_{\rm con} = 3.38 \left( \frac{\omega}{l} \right)^{-0.5} \text{ \AA} \tag{17}$$

where *ω* is air flow velocity (m/s), *l* is distance between the floor and arbitrary cross-section (m).

Studies carried out in [3] have shown that, in case of ceiling fans application, velocity of air flows blowing onto the surfaces increases by the average rate from 0.15 m/s to 0.18 m/s, i.e., increases by a factor of 1.2. If we assume *l* = 1 m (area where animals are located), then the coefficient of heat convective exchange is 1.1 times higher, for ceiling fans active state, compared to their idle status. Coefficient *α*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−<sup>1</sup> to 4.5 W·m−2·K<sup>−</sup>1, for animal-housing premises [44].

Having performed the relevant transformations, we can deduce the relationship between the time of air cooling, in premises, in case of ceiling fans application *τ*o2 and without ceiling fans *τ*o1 (in the assumption that *Q*air = 0):

$$
\pi\_{\rm o2} = \pi\_{\rm o1} \frac{\alpha\_{\rm con} + \alpha\_{\rm rad}}{1.1 \alpha\_{\rm con} + \alpha\_{\rm rad}}.\tag{18}
$$

With the account of optic and thermal-technical parameters of standard buildings [44] designed for young stock housing, Expression (18) can be reduced to the following form *τ*o2 = 0.95*τ*o1.

Therefore, in the case when no ceiling fan is applied, the period of self-sustained oscillating process of maintaining a required air temperature in areas where animals are kept is equal to:

$$T\_1 = \tau\_{p1} + \tau\_{o1}.\tag{19}$$

With operating ceiling fans, this parameter can be calculated as follows:

$$T\_2 = 0.8\tau\_{p1} + 0.95\tau\_{01} \,\text{.}\tag{20}$$

The relative switching frequency of heaters without ceiling fans defined from Expressions (19) and (20) equals to:

$$m\_1 = \frac{x\_{p1}}{x\_{p1} + x\_{o1}}.\tag{21}$$

The same parameter defined for the case when ceiling fans are applied has the following form:

$$m\_2 = \frac{0.8r\_{\rm p1}}{0.8r\_{\rm p1} + 0.95r\_{\rm o1}}.\tag{22}$$

It is clear from Formulas (21) and (22) that *n*<sup>1</sup> > *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.

Electric power consumption by ceiling fans is insignificant (its maximum input power is just 0.06 kW). Besides, thermal energy dissipated by the electric motor remains in premises thus contributing to the positive component of the thermal balance.

Results of a number of tests and initial technical-economic evaluation of the newly designed heat supply system of preventive maintenance premises for calves have shown that electric power consumption is 1760 kWh for a month-long heating period without ceiling fans, while in case of ceiling fans application it is 1520 kWh. Therefore, electricity consumption can be reduced by 14%.

#### **6. Conclusions**

The combined energy–saving heat supply system, which includes a combined ETS unit and a ceiling fan, allows the provision of normative air parameters in the livestock premises: air temperature and ARH.

Experimental studies of the heating–ventilation system carried out for preventive maintenance premises of cattle-breeding farmin the winter period have shown that the application of ceiling fans makes it possible to reduce the heating and cooling times of air in the premises. At the same time, there was a decrease in the consumption of electric energy for the heat supply system by up to 14%. The electric capacity of the ETS unit or the overall time of its operation can be also reduced. The energy-saving effect is achieved by using the heat of the air that accumulates in upper zone of the premises, when it is supplied by a ceiling fan, to the locations of the animals.

Based on the results of tests, a comparative analysis of temperature and ARH distribution with height of the preventive maintenance premises was made for the ceiling fan switching on and off operation modes. An initial evaluation of the energy efficiency for the system with ceiling fans was performed.

Application of combined type ETS unit for air heating makes it possible to reduce the current end user's annual expenditures on electricity by up to 30%, provided that the time of use price plan for electricity is adhered to.

Moreover, it ensures more uniform daily electric power load schedules in power networks, reduction of the equipment installed capacity, as well as that of nighttime electric energy loss. Besides, a mass-scale implementation of ETS units in farming will not require putting into operation considerable additional power-generating capacities.

**Author Contributions:** Conceptualization, D.T. and A.K. (Aleksei Khimenko); methodology, S.T. and A.K. (Aleksei Khimenko); validation, D.T., S.T. and A.K. (Aleksey Kuzmichev); formal analysis, A.K. (Aleksei Khimenko), A.K. (Aleksey Kuzmichev) and V.B.; investigation, S.T. and D.T.; resources, A.K. (Aleksei Khimenko); data curation, D.T. and A.K. (Aleksei Khimenko); writing—original draft preparation, D.T., S.T. and A.K. (Aleksei Khimenko); writing—review and editing, A.K. (Aleksei Khimenko) and V.B.; visualization, A.K. (Aleksei Khimenko) and D.T.; supervision, D.T. and O.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
