**2.3 Experimental description**

**Figure 4** depicts the layout of the hybrid heating system installation. Because the survey presented that there are not any poultry sheds in JWL which are fit for the installation of the PV/T array. Hence, only the workshop, which is located next to shed 1 as presented in **Figure 4(a)** is fulfilled the requirement of the structural reinforcement. The energy output from the PV/T module is piped down the side of the workshop, under the entrance road and through shed 1 to the plant room as exhibited in **Figure 4(b)**. Moreover, 52 (260Wp) Canadian solar PV panels [27] and four 1 12 m PHE mats are mounted on the roof of the workshop with 15° oriented to the south for enhancing solar energy harvesting. The solar PV inverter is placed on the external wall of the workshop as displayed in **Figure 4(c)**-**(d)**. A 15 kW F1145 NIBE heat pump [28] with R407C refrigerant is designated as it is the biggest capacity the consortium and can afford almost the required thermal energy input from the PV/T and ground copper pipe arrays as given in **Figure 4(e)**. The heat pump system could be employed in reverse to supply cooling in summer if

#### **Figure 4.**

*Hybrid renewable energy heating system installation: (a) workshop and shed 1; (b) trenched under access road to shed 1; (c) PV/T installed on the workshop roof; (d) inverter along with the external wall; (e) NIBE F1145 heat pump; (f) fan coil.*

*Energy, Economic and Environmental (3E) Assessments on Hybrid Renewable Energy... DOI: http://dx.doi.org/10.5772/intechopen.102025*

required. Additionally, the fan coil is mounted vertically on the south internal to provide spacing heating for shed 1 as shown in **Figure 4(f)**. Furthermore, there are fifty ground copper pipes with 15 mm diameter and their dimension size is 2.5 � 5 m (length � deep). The overall surface region of the geothermal pipe array is approximately 10 � 10 m. The vertical copper pipes are connected and run back to the plant room.

#### **3. Numerical model**

#### **3.1 Energy model**

#### *3.1.1 PV/T array*

Thermal energy conversion is classified into two processes including solar radiation conversion into thermal energy and transferring collected thermal energy towards PHE. Hence, this dynamic model is expressed by:

$$\frac{\partial Q\_t}{\partial t} = \mathcal{m}\_{PV/T} \mathcal{C}\_{PV/T} \frac{\partial T\_{PV/T}}{\partial t} = Q\_{abs} - Q\_{PV/T-\text{loss}} - Q\_{ele} \tag{1}$$

where Qt is the overall thermal energy (kW); mPV/T is the mass of PV/T (kg); CPV/T is the heat capacity of PV/T (J/ (kg�K)); TPV/T is the temperature of PV/T (°C); t is the time (s); Qabs is the solar energy absorbed (kW); QPV/T-loss is the overall thermal loss (kW); Qele is the power output (kW).

$$Q\_{abs} = \mathfrak{r}\_c a\_{abs} A\_{\text{eff}} I \tag{2}$$

τ<sup>c</sup> is the transmittance of PV/T; αabs is the absorptivity of PV/T; Aeff is the effective area of PV/T (m<sup>2</sup> ); I is the solar radiation (W/m2 );

$$Q\_{PV/T-loss} = Q\_{conv,c} + Q\_{c,sky} + Q\_{conv,pl,heo} + Q\_{pl,heo} \tag{3}$$

$$Q\_{conv,c} = h\_{cv}(T\_c - T\_a) \tag{4}$$

where hcv is the forced convection coefficient (W/m2 �K), which is written as:

$$h\_{cp} = \text{5.7} + \text{3.8} \cdot V\_{wind} \tag{5}$$

$$T\_c = \mathbf{30} + \mathbf{0.0175} \times (\mathbf{I} - \mathbf{300}) + \mathbf{1.14} \times (\mathbf{T\_a} - \mathbf{25})\tag{6}$$

where Vwind is the wind velocity (m/s); Tc is the PV surface temperature (°C); Ta is the air temperature (°C);

$$Q\_{\varepsilon,ky} = \varepsilon\_{\varepsilon} \cdot \sigma \cdot \left(T\_c^4 - T\_s^4\right) \tag{7}$$

$$T\_s = 0.037536 \cdot T\_a^{1.5} + 0.32 T\_a \tag{8}$$

where ε<sup>c</sup> is the emissivity of PV/T cover layer; σ is the Stefan-Boltzmann's constant, 5.67 � <sup>10</sup>�<sup>8</sup> W/m<sup>2</sup> �K4 ; Ts is the sky temperature (°C).

$$Q\_{conv\_{pl}pl,heo} = h\_{air} \cdot \left(T\_{pl} - T\_{heo}\right) \tag{9}$$

where hair is the convective heat transfer coefficient (W/m<sup>2</sup> �K); Tpl, Theo are the temperature of the EVA layer and PHE wall temperature, respectively (°C).

*Alternative Energies and Efficiency Evaluation*

$$h\_{air} = \frac{N\_u \cdot \lambda\_{air}}{\delta\_{air}}\tag{10}$$

where λair is the air thermal conductivity (W/m K); δair is air gap thickness between the surface cover and PV module (m).

Nu is the Nusselt number as expressed:

$$N\_u = \left[0.06 - 0.017\left(\frac{\beta\_s}{90}\right)\right] \text{Gr}^{1/3} \tag{11}$$

where β<sup>s</sup> is the title–angle of PV panels; Gr is the Grashoff number given as:

$$Gr = \frac{\mathbf{g} \cdot \left(\mathbf{T}\_{pl} - T\_{heo}\right) \cdot \delta\_{air}^3}{\nu\_{air}^2 \cdot T\_{air}} \tag{12}$$

$$Q\_{pl,heo} = \varepsilon\_{pl} \cdot \sigma \cdot \left( T\_{pl}^4 - T\_{heo}^4 \right) \tag{13}$$

where εpl is the emissivity of EVA layer;

$$Q\_{ele} = \eta\_e A\_{g\overline{f}} I \tag{14}$$

where η<sup>e</sup> is the electrical efficiency of PV array (%); Aeff is the effective area of PV array (m<sup>2</sup> ).

The overall heat production is written as:

$$Q\_t = A\_{\text{eff}} \cdot h\_t \cdot (T\_a - T\_w) \tag{15}$$

where ht is the overall heat transfer coefficient between the water and PV module (W/m2 �K); Tw is the water temperature within the PHE (°C).

$$\eta\_t = \frac{Q\_t}{A\_{eff} \cdot I} \tag{16}$$

where η<sup>t</sup> is the thermal efficiency (%).

#### *3.1.2 Ground copper pipe array*

To supply an adequate heat source for the evaporator of the heat pump unit, a low expense geothermal copper pipe array is developed. In lights of the heat transfer fields, it is categorized into solid and fluid regions [29].

#### *3.1.2.1 Solid field*

The solid field contains soil and pipe wall as presented:

$$
\rho\_{\rm soil} c\_{\rm soil} \frac{\partial T\_s}{\partial t} = \frac{\partial}{\partial \mathbf{x}} \left( \lambda\_{\rm soil} \frac{\partial T\_s}{\partial \mathbf{x}} \right) + \frac{\partial}{\partial \mathbf{y}} \left( \lambda\_{\rm soil} \frac{\partial T\_s}{\partial \mathbf{y}} \right) + \frac{\partial}{\partial \mathbf{z}} \left( \lambda\_{\rm soil} \frac{\partial T\_s}{\partial \mathbf{z}} \right) \tag{17}
$$

$$
\rho\_{pip\epsilon}c\_{pip\epsilon}\frac{\partial T\_p}{\partial t} = \frac{\partial}{\partial \mathbf{x}}\left(\lambda\_{pip\epsilon}\frac{\partial T\_p}{\partial \mathbf{x}}\right) + \frac{\partial}{\partial \mathbf{y}}\left(\lambda\_{pip\epsilon}\frac{\partial T\_p}{\partial \mathbf{y}}\right) + \frac{\partial}{\partial \mathbf{z}}\left(\lambda\_{pip\epsilon}\frac{\partial T\_p}{\partial \mathbf{z}}\right) \tag{18}
$$

where ρ is the density (kg/m<sup>3</sup> ); c is the thermal capacity (J/kg�°C); λ is the thermal conductivity (W/m�K).

*Energy, Economic and Environmental (3E) Assessments on Hybrid Renewable Energy... DOI: http://dx.doi.org/10.5772/intechopen.102025*

#### *3.1.2.2 Fluid field*

The energy balance equation of the inlet pipe is given as:

$$\rho\_f \rho\_{fluid} \mathbf{c}\_{fluid} \frac{\partial T\_{inlet}}{\partial \mathbf{t}} + \left(\rho \mathbf{c} \boldsymbol{\nu}\right)\_f \frac{\partial T\_{inlet}}{\partial \mathbf{z}} = \lambda\_{fluid} \frac{\partial^2 T\_{inlet}}{\partial \mathbf{z}^2} + b\_{\text{ig}} \left(T\_{g\text{root}} - T\_{inlet}\right) \tag{19}$$

The energy balance equation of the outlet pipe is expressed as:

$$\rho\_{f\text{fluid}}c\_{f\text{fluid}}\frac{\partial T\_{\text{outlet}}}{\partial \mathbf{t}} + (\rho c \upsilon)\_f \frac{\partial T\_{\text{outlet}}}{\partial \mathbf{z}} = \lambda\_{f\text{fluid}} \frac{\partial^2 T\_{\text{outlet}}}{\partial \mathbf{z}^2} + b\_{\text{og}} \left(T\_{\text{gvout}} - T\_{\text{outlet}}\right) \tag{20}$$

#### *3.1.3 Heat pump*

The heat source of the heat pump is provided by PV/T and geothermal copper pipe to offer a comfortable climate for the shed in the heating season. Hence, a heat pump model is expressed as [30]:

$$m\_r = V\_c \alpha \rho\_{r, \text{suc}} \cdot \left[ \mathbf{1} + \mathbf{C}\_v \left( \mathbf{1} - \frac{\mathbf{P}\_{\text{r,cond}}}{\mathbf{P}\_{\text{r,evup}}} \right)^{\frac{1}{n}} \right] \tag{21}$$

$$
\Delta \xi\_{comp} = \xi\_{r,dis} - \xi\_{r,suc} = \frac{n}{n-1} \cdot \frac{\mathbf{P}\_{\mathbf{r},enup}}{\rho\_{r,suc}} \cdot \left[ \left( \frac{\mathbf{P}\_{\mathbf{r},cond}}{\mathbf{P}\_{\mathbf{r},enup}} \right)^{\frac{n-1}{n}} - 1 \right] \tag{22}
$$

$$Q\_{el} = \frac{m\_r \Delta h\_{comp}}{\eta\_{comp}} \tag{23}$$

where mr is the refrigerant mass flow rate (kg/s); Vc is the compressor swept volume (m<sup>3</sup> ); ω is the compressor rotational speed (rev/s);

The coefficient of performance (COP) is given as:

$$\text{COP}\_h = \frac{\text{Q}\_{heating}}{\text{Q}\_{cl}} \tag{24}$$

#### **3.2 Economic model**

Economic policy has a vital effect on the life cycle cost (LCC) analysis in lights of the hybrid renewable heating system. Hence, the LCC is given as [31, 32]:

$$LCC = E\_{IC} + \sum\_{i=1}^{n} (E\_{SEC} + E\_{ME} + E\_{PC} + E\_{ITS}) \tag{25}$$

where LCC is the system lifetime expense (£); EIC is the original expense (£); ESEC is the system energy cost (£); EME is the maintenance cost (£); EPC is the system periodic cost (£); EITS is the system income tax savings (£).

The payback period (PBP) is employed to determine the time required to recoup the fund expended in an investment [33, 34].

$$PBP = X + \frac{Y}{Z} \tag{26}$$

where X is the number of years of final recovery (£); Y is the balance amount to be recovered (£); Z is the cash inflow (£).
