In standard conditions, the power generation efficiency of common silicon solar cells is only about 12% to 17%. More than 83% of the solar energy incident on the solar panel surface is not converted into electricity but into heat. This heat, apart from a small portion lost through conduction and radiation to the ambient air, largely raises the temperature of the solar panel, thereby reducing the photovoltaic efficiency. In the 1970s, Kern first proposed the concept of a photovoltaic/thermal (PV/T) system using water or air as the heat transfer medium. The core component of a PV/T system is the collector, which integrates solar cells or modules with a solar thermal collector via lamination or adhesive bonding. When the solar cells generate electricity, only about 15% of the incident solar energy is converted into electricity; the remainder is converted into heat, which can be recovered by water or air to produce hot water or warm air. By recovering heat, the PV/T system lowers the temperature of the solar panel, improves photovoltaic conversion efficiency to some extent, and simultaneously provides usable thermal energy, significantly enhancing the overall utilization of solar energy.
How to economically and rationally utilize solar energy and improve the combined electrical and thermal efficiency of solar PV/T systems is a major challenge facing current researchers. Some earlier studies compared PV/T systems with and without glass cover plates and concluded that the overall exergy conversion efficiency of a PV/T system with a glass cover plate is higher than that without one. In our work, we start from a thermal balance analysis of the solar panel and the glass cover plate, combined with typical annual meteorological parameters of Tianjin, and use the heat dissipation rate and the photo-thermal efficiency of the PV/T system as criteria to investigate the effect of the distance between the glass cover plate and the solar panel on the thermal performance of the PV/T system.
System Structure of a PV/T System with a Glass Cover Plate
The structure of a PV/T system with a glass cover plate consists of a glass cover plate, a solar panel, and a thermal collector. The solar panel, from top to bottom, is composed of encapsulation glass, encapsulant EVA, an anti‑reflection coating, silicon cells, another layer of encapsulant EVA, and a backsheet film (tedlar). All layers are in close contact. The solar panel is bonded to the collector with a thermally conductive insulating silicone adhesive. Between the glass cover plate and the solar panel, there is a closed air layer of adjustable thickness, which is the key parameter studied here. The entire assembly is back‑insulated to minimize heat loss.
Mathematical Model
Simplified Assumptions
To simplify the analysis, we make the following assumptions:
- Because the thickness of the solar panel is very small relative to the length and width of the collector, and the heat dissipation area of the edges is small, we assume the sides are adiabatic.
- Since the back of the PV/T collector is equipped with an insulation layer, the heat transferred through the insulation layer to the ambient air is negligible.
- The effect of dust on the glass cover plate on solar radiation is neglected.
- The encapsulation glass and the silicon cells are connected under vacuum, so their thermal resistance is negligible; we assume the encapsulation glass and silicon cells have the same temperature and treat them as a single material.
- The temperatures of the solar panel and the glass cover plate are uniform.
Based on these assumptions, the energy flow of the solar panel and the glass cover plate are analyzed. The energy conservation equations are:
$$ \Phi_{PV} = \Phi_c + \Phi_{PV,g} + \Phi_w + E_{PV} $$
$$ \Phi_g + \Phi_c + \Phi_{PV,g} = \Phi_{gc} + \Phi_{g,sky} $$
where:
- $\Phi_{PV}$ – solar energy absorbed by the solar panel (W/m²)
- $\Phi_c$ – heat transferred from the solar panel to the glass cover plate by conduction (W/m²)
- $\Phi_{PV,g}$ – radiative heat transfer from the solar panel to the glass cover plate (W/m²)
- $\Phi_w$ – heat removed by the cooling medium (W/m²)
- $E_{PV}$ – instantaneous power output of the silicon cells (W/m²)
- $\Phi_g$ – solar energy absorbed by the glass cover plate (W/m²)
- $\Phi_{gc}$ – convective heat loss from the glass cover plate to the ambient air (W/m²)
- $\Phi_{g,sky}$ – radiative heat loss from the glass cover plate to the sky (W/m²)
Optical Properties of the Solar Panel and Glass Cover Plate
The glass cover plate is ordinary flat glass with a solar transmittance $\tau_g = 0.85$, reflectivity $\rho_g = 0.07$, absorptivity $\alpha_g = 0.08$, and long‑wave emissivity $\varepsilon_g = 0.9$. The encapsulation glass has a transmittance $\tau = 0.9$ (absorption neglected), so its reflectivity $\rho = 0.10$. The silicon cell surface has an absorptivity $\alpha_{PV} = 0.95$ and reflectivity $\rho_{PV} = 0.05$. The long‑wave emissivity of the solar panel is $\varepsilon_{PV} = 0.88$.
The actual absorptance of the solar panel $A_{PV,g}$, actual reflectance of the glass cover plate $R_{PV,g}$, and actual absorptance of the glass cover plate $\alpha_{PV,g}$ are calculated as follows:
$$ A_{PV,g} = \frac{\tau \alpha_{PV}}{1 – \rho \rho_{PV}} \cdot \frac{\tau_g}{1 – \rho_g \frac{\tau \alpha_{PV}}{1 – \rho \rho_{PV}}} $$
$$ R_{PV,g} = \rho_g + \left( \rho + \frac{\rho_{PV} \tau^2}{1 – \rho \rho_{PV}} \right) \frac{\tau_g^2}{1 – \rho_g \left( \rho + \frac{\rho_{PV} \tau^2}{1 – \rho \rho_{PV}} \right)} $$
$$ \alpha_{PV,g} = 1 – A_{PV,g} – R_{PV,g} $$
Using the above values, we obtain:
| Parameter | Symbol | Value |
|---|---|---|
| Actual absorptance of the solar panel | $A_{PV,g}$ | 0.78 |
| Actual reflectance of the glass cover plate | $R_{PV,g}$ | 0.17 |
| Actual absorptance of the glass cover plate | $\alpha_{PV,g}$ | 0.05 |
Energy Balance of the Glass Cover Plate
The solar energy absorbed by the glass cover plate is:
$$ \Phi_g = \alpha_{PV,g} G $$
where $G$ is the total solar irradiance (W/m²).
The radiative heat transfer between the solar panel and the glass cover plate is:
$$ \Phi_{PV,g} = \frac{\sigma \left( T_{PV}^4 – T_g^4 \right)}{ \frac{1 – \varepsilon_{PV}}{\varepsilon_{PV}} + \frac{1}{X_{PV,g}} + \frac{1 – \varepsilon_g}{\varepsilon_g} } $$
where $\sigma$ = 5.67×10⁻⁸ W/(m²·K⁴) (Stefan‑Boltzmann constant), $T_{PV}$ and $T_g$ are temperatures of the solar panel and glass cover plate (K), and $X_{PV,g}=1$ (view factor between parallel plates).
The conductive heat transfer through the closed air gap is:
$$ \Phi_c = \lambda_e \cdot \frac{T_{PV} – T_g}{\delta} $$
with $\lambda_e = Nu_\delta \lambda$, where $\delta$ is the distance between the glass cover plate and the solar panel (m), $Nu_\delta$ is the Nusselt number for natural convection in the enclosed air layer, and $\lambda$ is the thermal conductivity of air (W/(m·K)). The flow regime depends on the Grashof number $Gr_\delta$:
$$ Gr_\delta = \frac{g \alpha \Delta t \delta^3}{\nu^2} $$
where $g=9.81$ m/s², $\alpha$ is the volumetric expansion coefficient (K⁻¹), $\Delta t$ is the temperature difference (K), and $\nu$ is the kinematic viscosity of air (m²/s). For a horizontal air layer with the hot surface below, the correlation for $Nu_\delta$ is:
| Condition | $Nu_\delta$ |
|---|---|
| $(Gr_\delta Pr) \le 1700$ | 1 |
| $1700 < (Gr_\delta Pr) \le 7000$ | $0.059 (Gr_\delta Pr)^{0.4}$ |
| $7000 < (Gr_\delta Pr) \le 3.2 \times 10^5$ | $0.212 (Gr_\delta Pr)^{1/4}$ |
| $(Gr_\delta Pr) > 3.2 \times 10^5$ | $0.061 (Gr_\delta Pr)^{1/3}$ |
The convective heat loss from the glass cover plate to the ambient air is:
$$ \Phi_{gc} = h \left( T_g – T_a \right) $$
where $h$ is the surface heat transfer coefficient (W/(m²·K)) and $T_a$ is the ambient temperature (K). For non‑zero wind speed $u$, external flow over a flat plate is assumed. The Nusselt number correlations are:
If $Re_L < 5 \times 10^5$:
$$ Nu_L = 0.664 \, Re_L^{1/2} Pr^{1/3} $$
If $5 \times 10^5 \le Re_L \le 10^8$:
$$ Nu_L = \left( 0.037 Re_L^{0.8} – 870 \right) Pr^{1/3} $$
where $Re_L = u L / \nu$, and $L$ is the glass cover length (m). For zero wind speed, natural convection over a horizontal plate (hot surface facing up) applies:
$$ Nu_L = C (Gr_l Pr)^n $$
with constants $C$ and $n$ depending on the regime (laminar: $C=0.54$, $n=1/4$ for $2\times10^4 \le Gr_l Pr \le 8\times10^6$; turbulent: $C=0.15$, $n=1/3$ for $8\times10^6 \le Gr_l Pr \le 10^{11}$).
The radiative heat loss from the glass cover plate to the sky is:
$$ \Phi_{g,sky} = \varepsilon_g \sigma \left( T_g^4 – T_{sky}^4 \right) $$
where $T_{sky}$ is the equivalent sky black‑body temperature (K).
Energy Balance of the Solar Panel
The electrical power output of the solar panel is:
$$ E_{PV} = \eta_{mp} \Phi_{PV} $$
where $\eta_{mp}$ is the maximum‑power‑point efficiency, which varies linearly with the silicon cell temperature:
$$ \eta_{mp} = \eta_{mp,ref} – \mu_{PV,mp} (T_{PV} – T_{ref}) $$
We take the reference efficiency $\eta_{mp,ref}=16\%$ at $T_{ref}=298$ K, and the temperature coefficient $\mu_{PV,mp}=0.05\%\,\text{K}^{-1}$. The solar energy absorbed by the solar panel is:
$$ \Phi_{PV} = A_{PV,g} G $$
The heat removed by the cooling medium (i.e., the useful thermal output) is:
$$ \Phi_w = (1 – \eta_{mp}) \Phi_{PV} – \Phi_c – \Phi_{PV,g} $$
Under steady‑state conditions, the heat transferred from the solar panel to the glass cover plate equals the heat dissipated from the glass cover plate to the surroundings. Solving the system of equations yields the heat dissipation from the solar panel (including $\Phi_c$ and $\Phi_{PV,g}$) and the photo‑thermal efficiency of the PV/T system.
Photo‑thermal Efficiency
The photo‑thermal efficiency $\eta_{th}$ is defined as the ratio of the useful heat output (heat absorbed by the cooling medium) to the incident solar energy:
$$ \eta_{th} = \frac{\Phi_w}{G} $$
Results and Analysis
We simulated the system using typical annual meteorological parameters for Tianjin (summer period from July 1 to September 30). The calculations were performed for two fixed solar panel temperatures: 40 °C (313.15 K) and 50 °C (323.15 K). The solar panel temperature was kept constant by adjusting the cooling medium flow rate. The following tables summarize the variation of the photo‑thermal efficiency and the total heat dissipation from the solar panel (sum of $\Phi_c$ and $\Phi_{PV,g}$) as functions of the distance $\delta$ between the glass cover plate and the solar panel.
| Distance $\delta$ (cm) | $\eta_{th}$ (%) | Heat dissipation (W/m²) |
|---|---|---|
| 1 | 48.0 | 49.5 |
| 2 | 49.2 | 48.8 |
| 3 | 50.5 | 48.0 |
| 4 | 51.8 | 47.3 |
| 5 | 53.0 | 46.7 |
| 6 | 54.1 | 46.5 |
| 7 | 53.5 | 47.0 |
| 8 | 53.0 | 47.5 |
| 9 | 52.8 | 47.6 |
| 10 | 53.0 | 47.4 |
| 11 | 53.2 | 47.3 |
| Distance $\delta$ (cm) | $\eta_{th}$ (%) | Heat dissipation (W/m²) |
|---|---|---|
| 1 | 35.0 | 102.0 |
| 2 | 36.8 | 99.5 |
| 3 | 38.5 | 97.0 |
| 4 | 39.8 | 95.0 |
| 5 | 40.3 | 94.2 |
| 6 | 39.5 | 95.8 |
| 7 | 38.8 | 97.2 |
| 8 | 38.5 | 97.8 |
| 9 | 38.6 | 97.6 |
| 10 | 38.8 | 97.3 |
| 11 | 39.0 | 97.0 |
From these tables, we can see that as the distance $\delta$ increases from 1 cm, the photo‑thermal efficiency $\eta_{th}$ rises rapidly, reaches a maximum, then decreases slightly, and eventually stabilizes with minor fluctuations. The heat dissipation from the solar panel follows the opposite trend. For $T_{PV}=40$ °C, the optimum distance is 6 cm, yielding $\eta_{th}=54.1\%$, which is 6.1% higher than the value at $\delta=1$ cm (48.0%). For $T_{PV}=50$ °C, the optimum distance is 5 cm, with $\eta_{th}=40.3\%$, an improvement of 13.0% compared to 35.0% at $\delta=1$ cm. The optimum distance decreases as the solar panel temperature increases.
The variation in the photo‑thermal efficiency with $\delta$ is explained by the change in heat transfer regime within the air gap. At very small $\delta$, pure conduction dominates, leading to high heat loss from the solar panel to the glass cover plate and thus lower useful heat output. As $\delta$ increases, natural convection starts to develop, first in the laminar regime (which reduces the effective thermal resistance), causing the heat loss to decrease and $\eta_{th}$ to increase. At larger $\delta$, the flow becomes turbulent, increasing the heat transfer coefficient again, so the heat loss rises and $\eta_{th}$ drops. Beyond a certain point, further increases in $\delta$ have a diminishing effect, and $\eta_{th}$ flattens or recovers slightly due to the changing flow pattern.
We also analyzed the instantaneous behavior over a typical summer day in Tianjin. The solar irradiance on July 29 from 7:00 to 16:00 is given in the following table (values are hourly averages from the typical year):
| Time | 7:00 | 8:00 | 9:00 | 10:00 | 11:00 | 12:00 | 13:00 | 14:00 | 15:00 | 16:00 |
|---|---|---|---|---|---|---|---|---|---|---|
| G (W/m²) | 250 | 380 | 520 | 650 | 750 | 800 | 780 | 680 | 530 | 350 |
For $T_{PV}=40$ °C, the heat dissipation from the solar panel at different $\delta$ values throughout the day is summarized below (average values over the simulation period):
| δ (cm) | 7:00 | 8:00 | 9:00 | 10:00 | 11:00 | 12:00 | 13:00 | 14:00 | 15:00 | 16:00 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 22 | 30 | 38 | 45 | 49 | 51 | 50 | 46 | 40 | 28 |
| 3 | 20 | 28 | 36 | 43 | 47 | 49 | 48 | 44 | 38 | 26 |
| 6 | 19 | 27 | 35 | 42 | 46 | 48 | 47 | 43 | 37 | 25 |
| 9 | 20 | 28 | 36 | 43 | 47 | 49 | 48 | 44 | 38 | 26 |
| 11 | 20 | 28 | 36 | 43 | 47 | 49 | 48 | 44 | 38 | 26 |
It is observed that the heat dissipation increases with solar irradiance in the morning, peaks around noon, and then declines. The effect of $\delta$ is consistent: at the optimum gap (6 cm) the heat dissipation is slightly lower than at smaller or larger gaps throughout the day, which corresponds to higher useful heat recovery. When the solar panel temperature is higher (50 °C), the heat dissipation values are larger (as shown in earlier tables), but the trend with $\delta$ remains similar, with the optimum shifting to 5 cm.
Conclusion
In this study, we performed a thermal balance analysis of the solar panel and glass cover plate in a PV/T system to investigate the influence of the distance between them on the photo‑thermal efficiency. Using typical meteorological data for Tianjin, we calculated the heat dissipation and photo‑thermal efficiency for various distances at two fixed solar panel temperatures. The following conclusions are drawn:
- As the distance between the glass cover plate and the solar panel increases, the photo‑thermal efficiency first increases rapidly, reaches a maximum, then decreases slightly, and finally stabilizes with minor oscillations. The heat dissipation from the solar panel exhibits the opposite trend.
- For the two solar panel temperatures analyzed (40 °C and 50 °C), the optimal distance decreases as the temperature of the solar panel increases. At 40 °C, the optimal distance is 6 cm; at 50 °C, the optimal distance is 5 cm.
- The improvement in photo‑thermal efficiency at the optimal gap relative to a narrow gap (1 cm) is 6.1% for 40 °C and 13.0% for 50 °C, demonstrating the practical significance of selecting an appropriate gap.
- The variation of heat dissipation with solar irradiance throughout the day confirms that the optimum gap reduces heat loss and enhances thermal output under varying radiation conditions.
Because adjusting the distance between the glass cover plate and the solar panel is easy to implement, choosing a suitable gap is a valuable and cost‑effective measure to improve the photo‑thermal performance of PV/T systems.