2.3.3. Thermal Conduction

The isolation layer consists of fiberglass felt and perlite coated. The thermal conduction *φ*cond between the internal hot air and the external ambient environment is given by the Fourier's law of heat conduction in (8) [23].

$$\phi\_{\rm cond} = \frac{T\_{\rm int} - T\_{\rm ext}}{\delta\_f / \lambda\_f + \delta\_p / \lambda\_p} A\_{\rm iso} = \frac{(T\_{\rm fin} - T\_{\rm ind}) / 2 - 50}{\delta\_f / \lambda\_f + \delta\_p / \lambda\_p} A\_{\rm iso} \tag{8}$$

where *δ<sup>f</sup> δ<sup>p</sup>* and *λ<sup>f</sup> λ<sup>p</sup>* are the respective thickness, and thermal conductivity of fiberglass and perlite, and *A*iso is the isolation layer area.

The prediction of average power consumption *Q*¯ sto can be obtained by Equations (6)–(8) as shown in Equation (9).

$$\begin{split} Q\_{\text{sto}} &= \phi\_{\text{conv}} + \phi\_{\text{rad}} + \phi\_{\text{cond}} \\ &= 0.27 R\_{\text{c}}^{0.63} P\_{r\_{\text{g}}}^{0.36} P\_{r\_{\text{c}}} \frac{\lambda}{D} \left( T\_{\text{fin}} - T\_{\text{ini}} \right) A\_{\text{c}\text{la}} + \varepsilon \sigma \left( \left( T\_{\text{fin}} + 273 \right)^{4} - \left( T\_{\text{ini}} + 273 \right)^{4} \right) A\_{\text{bri}} \\ &+ \frac{\left( T\_{\text{fin}} - T\_{\text{ini}} \right) / 2 - 50}{\delta\_{f} / \lambda\_{f} + \delta\_{p} / \lambda\_{p}} A\_{\text{isoo}} \end{split} \tag{9}$$

where *T*fin is unknown which can be obtained in Section 2.4 (Thermal Bricks Energy Release).

#### *2.4. Thermal Bricks Energy Release*

Thermal bricks energy release includes heat transfer and customers' heating.

#### 2.4.1. Heat Transfer

When the SETS releases thermal energy, the inlet hot air temperature of the heat exchanger is regulated by the circulating wind speed of the fan. In the heat exchanger, according to the conservation of energy, the thermal energy released *Q*a by the inlet hot air is equal to the thermal energy absorbed *Q*<sup>w</sup> by the outlet circulating water. Therefore, the relationship between the inlet hot air temperature and the outlet circulating water temperature is given in (10) [25].

$$\begin{cases} \ Q\_{\rm a} = \dot{m}\_{\rm a} c\_{\rm a} \left( T\_{\rm a,in} - T\_{\rm a,o} \right) \\ \ Q\_{\rm W} = \dot{m}\_{\rm W} c\_{\rm W} \left( T\_{\rm w,o} - T\_{\rm w,in} \right) \end{cases} \tag{10}$$

where, *m*˙ <sup>a</sup> and *m*˙ <sup>w</sup> are the flow rate of hot air and water through the heat exchanger, respectively. *c*<sup>a</sup> and *c*<sup>w</sup> are the specific heat of hot air and water through the heat exchanger, respectively. Since *Q*<sup>a</sup> = *Q*w, *T*a,i can be deduced as shown in Equation (11). Ignoring the heat loss from the hot air at the outlet of the SETS to the heat exchanger inlet, and assuming that *T*a,i ≈ *T*fin, then, taking this into Equation (9), the average power consumption *Q*¯ sto can be obtained.

$$T\_{\rm a,in} = T\_{\rm a,o} + \frac{\dot{m}\_{\rm W}c\_{\rm W} \left(T\_{\rm W,o} - T\_{\rm w,in}\right)}{\dot{m}\_{\rm s}c\_{\rm s}}\,\tag{11}$$

where, *T*w,o − *T*w,in is determined by the Section 2.4.2 (Customers Heating).
