2.1. Mathematical Modeling of PV/T Module
The structure of one PV/T module is shown in
Figure 2. (a), which consists of glass cover plate, EVA adhesive, photovoltaic panel, EVA adhesive, collector channel, and insulation back plate from top to bottom. EVA is copolymerized from ethylene and acetic acid, which is widely used as a photovoltaic material. It plays multiple roles in bonding the inside PV/T photovoltaic thermal module, fixing the internal structure of the collector, and insulating to protect the photovoltaic panel.
The purpose of simulation is to obtain the energy transfer process inside PV/T photovoltaic thermal module. Therefore, the following assumptions are made to simplify the model and reduce computational complexity:
1. The temperature of each layer of PV/T photovoltaic thermal module is uniform, and there is no temperature gradient within the same horizontal layer;
2. The heat transfer process only occurs in the direction perpendicular to the PV/T module;
3. The contact between different layers inside the module is good, without thermal conductivity or contact resistance;
4. Neglecting the absorption and transmittance of EVA adhesive to solar radiation;
5. The thermal properties of each layer of material are stable and do not change with temperature;
6. The insulation material has good insulation performance, without the heat dissipation of the frame and back panel.
The energy conservation of PV/T photovoltaic thermal module is shown in the
Figure 2. (
b). For the entire PV/T photovoltaic thermal module, its energy conservation equation can be written as:
In the formula:
- Solar radiation energy absorbed by PV/T photovoltaic thermal module per unit area, W·m-2;
- Power generation of photovoltaic cells per unit area, W·m-2;
- The heat absorbed by the cooling working fluid per unit heat exchange area in the collector, W·m-2;
- Average density of collector [
10], kg·m-3;
- Specific heat capacity of the collector, J·kg-1·K-1;
- Thickness of PV/T module, m;
- Convective heat transfer of air per unit area of glass cover plate, W·m-2;
- Radiant heat transfer per unit area of glass cover plate to the sky, W·m-2.
In the formula:
- Heat transfer coefficient between glass and air, W·m-2·K-1;
,
- Glass cover plate and ambient temperature, K.
In the formula:
- The emissivity of the glass cover plate;
-Stefan Boltzmann constant, 5.67 × 10-8, W·m-2·K-4;
- Sky background temperature.
There is an energy conservation equation for the glass cover plate:
In the formula:
- The absorption rate of solar radiation by the glass cover plate;
- The solar radiation intensity projected onto the surface of PV/T photovoltaic thermal module, W·m-2;
- Heat transfer coefficient between the upper EVA adhesive and the glass cover plate, W·m-2·K-1;
- Temperature of the upper EVA adhesive, K.
For the upper EVA adhesive, the energy conservation equation is:
In the formula:
- Heat transfer coefficient between photovoltaic panel and upper EVA adhesive, W·m-2·K-1;
- The temperature of the photovoltaic panel, K.
For photovoltaic panel, the energy conservation equation is:
In the formula:
- The transmittance of the glass cover plate to solar radiation;
- Heat transfer coefficient between photovoltaic panel and lower EVA adhesive, W·m-2·K-1;
- The temperature of the lower EVA adhesive, K.
For the lower EVA adhesive, the energy conservation equation is:
In the formula:
- The heat transfer coefficient between the lower EVA adhesive and the collector aluminum plate, W·m-2·K-1;
- Temperature of the collector aluminum plate, K.
For collector aluminum plates, there is an energy conservation equation:
In the formula:
- Heat transfer coefficient between the collector aluminum plate and the cooling medium, W·m-2·K-1;
- The temperature of the cooling working fluid inside the PV/T photovoltaic thermal module, K.
For the cooling medium inside the collector, there is an energy conservation equation:
In the formula:
- Mass of cooling working fluid inside the collector, kg;
,- The temperature of the cooling medium enters and exits the collector, K;
- Area of collector aluminum plate, m2;
- The average heat transfer temperature difference between the collector aluminum plate and the cooling working fluid of the collector, K;
- Mass flow rate of cooling working fluid inside PV/T photovoltaic thermal module, kg·s-1.