**2. Materials and Methods**

In this research area, previous works were devoted to simulations of the heat storage cells thermal state of the ETS unit [29] and calculation of the ETS unit thermal characteristics [30,31]. The results of experimental studies of the thermal state of heat-storage cells in both heat-charging and heat-emission modes of ETS unit have been reported [32,33]. Also, an energy-saving infrared heater (IR) for calves was developed for preventive maintenance premises of cattle-breeding farm with an adjustable heat flux depending on the position of the animal and an evaluation of the parameters of its operation was carried out [34].

The heat supply system for the preventive maintenance of an 8 m long, 4 m wide and 4 m high premises, for housing calves, was chosen as the subject of research. The recommended air temperature value in the premises was 17 ◦C, while the maximum permissible relative humidity (ARH) of the air was 75% [20].

In our research, the air heating combined type ETS unit [31] designed for operation under the electric energy time of use price plan was chosen. A ceiling fan of the type MR-1 [35] was applied for temperature equalization and uniform air flow distribution in the premises.

As part of this work, field studies of the thermal and humidity parameters of the air were carried out in two similar preventive maintenance premises of cattle-breeding farm. Two variants of the operation of the heat supply system were investigated. In the first room, air heating is carried out from the combined ETS unit without the use of ceiling fans, and in the second, with their use. Experimental studies of the proposed heat supply system were carried out in winter from mid-December to the end of March. The temperature and ARH were measured along the height of the preventive maintenance premises at several characteristic control points.

During the experimental studies, the consumption of electrical energy for heat supply of the preventive maintenance premises was recorded for two variants of the system operation.

The results of measurements of the thermal and humidity parameters of the air in the preventive maintenance were processed using the probabilistic-statistical method. A calculation method was also used to justify the parameters and selection of the ceiling fan.

#### **3. Calculating and Selecting the Ceiling Fan Parameters**

At the present time, the most commonly applied air heating systems in cattle-breeding farms are those with heated air distribution into the upper area of premises. In this case, the air temperature becomes uniform, in the upper zone, within a short period of time (there is no sensible temperature gradient) owing to the intensive turbulent air mixing. At the same, air flows do not practically reach the lower ('sluggish') zone. It happens because the temperature of air exhausted from the outlet into an unlimited area differs from that of the ambient air in premises with anisothermal air jets. Therefore, air jet parameters, as well as their trajectory, depend on not only inertial forces but also on those of gravity [33].

The following factors have an essential effect on the circulation of air flows produced by the ceiling fans: the height of the premises, the length of suspension, the number fans and their installation points, etc.

The reasonable length of fan suspension *h*<sup>f</sup> (see Figure 1) insuring the maximum air flow rate in the operating area, can be defined from the following equation:

$$\mathbf{h}\_{\mathbf{f}} = \frac{H\_{\mathbf{P}} - L}{4},\tag{1}$$

where *H*p is distance between the floor and the ceiling (m), *L* is that between the floor and the animal shoulder (m).

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

In this case, fan blades diameter (*D* = 2*R*) shall not exceed 1/3 of the premises width [3]. As applied to up-to-date premises designed for calves housing, fans must be mounted along the longer premises axis.

The number of fans *N*<sup>f</sup> 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]:

$$N\_{\rm f} = c\_{\rm f} P^{2.91} H\_{\rm P}^{-2.14} \omega\_{\rm av}^{4.43} \,\prime \,\,\,\tag{2}$$

where *P* is room perimeter (m), *ω*av is average air flow rate, in operation area, i.e., standing or rest zone, (m/s); *c*<sup>f</sup> is coefficient depending on the ceiling fan design and its operation conditions.

Since the air velocity field has practically uniform profile, we can assume *ω*ave = 0.5 *ω*<sup>0</sup> where *ω*<sup>0</sup> is initial value of air velocity (m/s).

It has been found out that coefficient *c*<sup>f</sup> = 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*<sup>f</sup> = 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**

Combined type ETS unit comprises two independently operating heaters, i.e., heat storage core and convector heater (see Figure 2). The heat storage core is designed to be charged with thermal energy during the lower electric power price rate period in order to supply heat during periods of higher electric power price rates. The electric convector-type heater serves as a direct heating energy source supplying heat mainly during the period when the heat storage core is being charged. Technical parameters of the installation are presented in Table 1.

**Figure 2.** Electric thermal storage unit.

**Table 1.** Technical characteristics of ETS unit.


The required volume of ETS unit heat storage core can be calculated using the following expression:

$$V\_{\rm HSC} = \frac{3600 Q\_{\rm ch,ave} \tau\_{\rm hc}}{\rho\_{\rm HSM} c\_{\rm HSM} \left( T\_{\rm HSC,max} - T\_{\rm HSC,min} \right)} \tag{3}$$

where *Q*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/m3); *<sup>c</sup>*HSM is heat capacity ratio of the core material (kJ·kg−1·K−1); *<sup>T</sup>*HSC,max and *<sup>T</sup>*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].

The maximum temperature of the casing outer surface, by the end moment of the ETS unit charging mode is *T*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].

In view of the fact that there is, practically, no heat loss, in the beginning of the core charging period, the average value of thermal energy *Q*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:

$$Q\_{\rm loss} = k\_{\rm rad} \alpha\_{\rm sh\\_nve} F\_{\rm ETS} (T\_{\rm sh} - T\_{\rm ap}) \, , \tag{4}$$

where *α*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<sup>−</sup>1); *T*ap is ambient air temperature in premises (◦C); *F*ETS is surface area of the ETS casing (m2); *k*rad is coefficient taking into account the heat loss by radiation from the surface of the ETS casing (value is 1.25).

When calculating thickness *δ*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:

$$\delta\_{\rm ins} = \frac{\lambda\_{\rm ins} F\_{\rm zve} \left( T\_{\rm ins, int} - T\_{\rm sh, max} \right)}{Q\_{\rm loss}},\tag{5}$$

where *<sup>λ</sup>*ins is thermal-conductivity coefficient of the thermal insulation material (W·m−1· ◦K<sup>−</sup>1); *T*ins,int is temperature of the thermal insulation internal layer, by the end of the charging period (◦C).

$$F\_{\text{ave}} = \frac{F\_{\text{irrs}} + F\_{\text{ETH}}}{2},\tag{6}$$

where *F*ins is surface area of the thermal insulation (m2).

Electric heater capacity *W*unit of ETS unit is defined from the following equation:

$$\mathcal{W}\_{\text{unit}} = k\_{\text{r}} Q\_{\text{ch\\_ave}} \frac{\eta\_{\text{hc}}}{\eta\_{\text{ch}}} + Q\_{\text{loss}} \tag{7}$$

where *τ*ch is duration of ETS unit charging period (h); *k*<sup>r</sup> is power reserve coefficient that takes into account the aging of electric heating elements and changes in the supply voltage (value is 1.2).

Quantity of the accumulated heat can be calculated from the following expression:

$$Q\_{\rm st} = Q\_{\rm ins} + Q\_{\rm HSM} = \text{ }\tag{8}$$

$$\mathbf{I} = c\_{\rm ins} \rho\_{\rm ins} V\_{\rm ins} \left( T\_{\rm ins,max} - T\_{\rm ins,min} \right) + c\_{\rm HSM} \rho\_{\rm HSM} V\_{\rm HSM} \left( T\_{\rm HSC,max} - T\_{\rm HSC,min} \right)$$

where *<sup>c</sup>*ins is heat capacity ratio of the thermal insulation (kJ·kg−1· ◦K<sup>−</sup>1); *ρ*ins is its volumetric density (kg/m3); *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.

Quantity of heat *Q*st accumulated in ETS unit makes it possible to define time period *τ*warm required for its heating to temperature value *T*HSC,max:

$$\pi\_{\text{warm}} = \frac{Q\_{\text{st}}}{3600(0.8W\_{\text{unit}}?\, -Q\_{\text{loss,max}})} \,\text{}\,\text{}\tag{9}$$

where *Q*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).

In paper by [31] the method of the thermal and aerodynamic calculation of the basic thermal characteristics has been described, for dynamic type ETS unit.

When calculating the average value of heat-exchange coefficient *α*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]:

$$\text{Gr} = \frac{\beta h^3 g (T\_{\text{sh}} - T\_{\text{ap}})}{v^2},\tag{10}$$

where *<sup>β</sup>* <sup>=</sup> <sup>1</sup> <sup>273</sup>+*T*ap (K−1); *<sup>h</sup>*—is ETS unit height (m); *<sup>g</sup>* is gravity factor (m/s2); *<sup>ν</sup>* is air kinematic viscosity (m2/s).

$$
\overline{\rm N\u{u}} = 0.695 Gr\_{dlig}^{0.25}.\tag{11}
$$

In order to define the average value of the heat-exchange coefficient *α*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 [38–40]:

$$\overline{\text{Nu}} = 0.023 \text{Pr}^{0.4} \text{Re}^{0.8} \left( \frac{T\_{\text{wch}}}{T\_{\text{air\\_wch}}} \right)^{-0.55}.\tag{12}$$

Thermal-physical properties of solid heat storage materials (HSM) have been analyzed. Formulas for calculating temperature dependent values of the thermal-conductivity coefficient and heat capacity ratio are presented in Table 2 [41].


**Table 2.** Thermal-physical properties of solid-state HSM.

Figures 3 and 4 shows the change of the thermal-conductivity coefficient and heat capacity ratio, in temperature range from 50 ◦C to 650 ◦C. These are the minimum and the maximum temperatures of the heat storage elements, in ETS unit heat emission and charging modes, respectively.

Analysis of the obtained results provides the reason to conclude that chamotte, corundum and dinas feature linear temperature dependence of the thermal-conductivity coefficient (see Figure 3). Magnesium oxide has the highest values of the thermal-conductivity coefficient and heat capacity ratio in the course of heating and cooling processes, compared to other materials in the study (see Figures 3 and 4). It should also be noted that the thermal-conductivity coefficient of magnesium oxide is inversely proportional to the temperature [42].

**Figure 3.** Dependence of thermal-conductivity coefficient on temperature *T*HSM.

**Figure 4.** Dependence of heat capacity ratio on temperature *T*HSM.

#### **5. Discussion**

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 in this study. An initial evaluation of the energy efficiency for the system with ceiling fans was also carried out.

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

Two system operation modes applied to preventive maintenance premises were studied. One of these operation modes involves inflow ventilation with heating internal air from electric thermal storage units thus implementing the combined air heating method (without the use of ceiling fans). In this case, there exists a temperature drop in the lower areas and under the cage, i.e., directly under the slatted floor, and 'no flow areas' occur. Besides, minimum required air temperature of 17 ◦C is not achieved in areas where animals are located (area under the cage [20]). This means that either a heating installation of higher capacity should be used during or the period of its operation should be extended.

In the other operation mode, air flows driven with the use of the ceiling fans circulate with permissible velocity limited in accordance with the recommendations for technological production design (not exceeding 0.3 m/s) [20]. Avoiding forming a heat cushion directly under the ceiling helps to inject a certain amount of heat into the work area, thus maintaining a required temperature environment. It also contributes to reduce the heat loss through the enclosing structures, first of all through the ceiling.

Recommendations for technological production design [20] stipulate the optimal air temperature for housing calves that must be maintained within the cage and under the slatted floor.

Temperature conditions and the aggregate thermal energy consumption for heating depend essentially on the temperature distribution over the space of the premises.

Figure 5 shows vertical air temperature profile, in preventive maintenance premises for calves.

It should be noted that operating ceiling fans ensure ARH reduction by up to 5% in areas where animals are located because of the warmer air supplied into these areas (see Figure 6).

**Figure 5.** Air temperature distribution, in preventive maintenance premises for calves.

**Figure 6.** ARH distribution, in preventive maintenance premises for calves.
