Experimental and Numerical Study on the Insulation Performance of a Photo-Thermal Roof in Hot Summer and Cold Winter Areas
Abstract
:1. Introduction
2. Methods
2.1. Experimental Model
2.2. Experimental Measurements
2.3. Mathematical Model
2.3.1. Heat Transfer Analysis
2.3.2. The Effective Thermal Conductivity of the Roof’s Insulation Material
2.4. Simulation Conditions
2.5. Simulation Verification
3. Results and Discussion
3.1. Experimental Results and Analysis
3.2. Effect of Water Saturation
3.3. Effect of the Thickness of Roof Insulation Materials
3.4. Variation in the Average Water Temperature of the Collectors
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
C | Specific heat capacity of materials (J/(kg·K)) |
D | Index of thermal inertia |
E | The total energy composed of thermodynamic and kinetic energy (J/kg) |
hg | Convective heat transfer coefficient of the glass cover (W/m2·K) |
hi,w | convective heat transfer coefficient of the inner surface of each material layer (W/m2·K) |
hj | Enthalpy of matter (kJ/kg) |
ho,w | convective heat transfer coefficient of the outer surface of each material layer (W/m2·K) |
I | Solar radiation intensity (W/m2) |
JJ | Diffusion flux (kg/(m2·s)) |
P | Pressure (Pa) |
qc,b | Heat convection between the collector’s back surface and the air (W/m2) |
qc,g | Heat convection between the glass cover and the external environment (W/m2) |
qc,in | Heat convection between the roof inner surface and the indoor air (W/m2) |
qc,out | Heat convection between the photo-thermal roof and the air (W/m2) |
qcond | Conductive heat flux (W/m2) |
Qw | Released heat by hot water (W) |
qr,b | Heat radiation of the collector’s back surface to the roof (W/m2) |
qr,g | Heat radiation of the glass cover to the external environment (W/m2) |
qr,in | Heat radiation of the roof inner surface to the indoor environment (W/m2) |
qr,out | Heat radiation of the roof to the collector’s back surface (W/m2) |
Si | Thermal effusivity of wall inner surface (W/m2·K) |
So | Thermal effusivity of wall outer surface (W/m2·K) |
Sh | Heat source (W/m3) |
Tb | Temperature of the back surface of the collector (℃) |
Tg | The temperature of the glass cover (℃) |
Tn | other surface temperatures in the room (℃) |
Tsky | Sky temperature (℃) |
Ti,a | The temperature of air in contact with the inner surface of the material layer (℃) |
To,a | The temperature of air in contact with the outer surface of the material layer (℃) |
Ti,w | The roof inner surface temperature (℃) |
To,w | The roof outer surface temperature (℃) |
αg | Absorptivity of the glass cover |
αp | Absorptivity of the absorber plate |
αw | Absorptivity of roof outer surface |
αi,w | Heat transfer coefficient of wall inner surface (W/m2·K) |
αo,w | Heat transfer coefficient of wall outer surface (W/m2·K) |
λa | Thermal conductivity of air (W/(m·k)) |
λe | Thermal conductivity of roof materials (W/(m·k)) |
λec | Effective thermal conductivity of porous media satisfying serial heat conduction model (W/(m·k)) |
λep | Effective thermal conductivity of porous media satisfying parallel heat conduction model (W/(m·k)) |
λl | Thermal conductivity of liquid phase in porous media (W/(m·k)) |
λp | Thermal conductivity of solar collectors (W/(m·k)) |
λs | Thermal conductivity of solid phase in porous media (W/(m·k)) |
εa | The volume percentage of the gas phase per unit volume (%) |
εb | Emissivity of the collector rear cover |
εg | Emissivity of the glass cover |
εi,w | Emissivity of the roof inner surface |
εo,w | Emissivity of the roof outer surface |
τ | Unit time |
τg | Transmissivity of the glass cover |
φ | Water saturation (%) |
σ | The Boltzmann constant, σ = 5.67 × 10−8 W/(m2·K4) |
ϕ | Time lag |
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Test Parameters | Test Instrument | Type | Accuracy |
---|---|---|---|
Solar radiation intensity | Solar pyrometer | TBQ-2 | ≤0.2% |
Temperature | Thermocouple | Ni-Cr and Ni-Si | ±0.5 °C |
Data acquisition unit | XSR-70A | ≤0.2% |
Material Layers | Size | Density (kg/m3) | Specific Heat Capacity (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
---|---|---|---|---|
x × y × z (mm3) | ||||
Glass cover | 1000 × 2000 × 4.5 | 2500 | 840 | 0.76 |
Air layer in collector | 1000 × 2000 × 45 | 1.205 | 1005 | 0.026 |
Absorber plate | 1000 × 2000 × 1.5 | 2719 | 871 | 202.4 |
Copper pipe | 8 × 2000 × 8 | 8978 | 381 | 387.6 |
Insulation in collector | 1000 × 2000 × 55 | 50 | 1380 | 0.04 |
Air layer | 4000 × 5000 × 100 | 1.205 | 1005 | 0.026 |
Reinforced concrete layer | 1000 × 2000 × 160 | 2500 | 860 | 1.73 |
Insulation layer | 1000 × 2000 × δ | 120 | 750 | 0.04 |
Cement mortar layer | 1000 × 2000 × 40 | 2000 | 840 | 0.87 |
Boundary | Type | Value | Remarks |
---|---|---|---|
Glass cover | Convective heat transfer surface | αg = 0.12 τg = 0.8 | Introduction of solar radiation from the solar ray tracing model. |
Absorber plate | Coupling surface | αp = 0.95 | - |
Copper pipe | Temperature surface/Coupling surface | 50 °C/- | The temperature of the pipe was kept constant by adjusting the water flow. |
Insulation in collector | Coupling surface | - | - |
Outside surface of the photo-thermal roof | Coupling surface | - | - |
Outside surface of the ordinary roof | Mixed | αw = 0.6 | - |
Inner surface of roofs | Coupling surface | - | - |
Contact surface between air-conditioned area and non-air-conditioned area | Coupling surface | - | - |
Solar Radiation Intensity (W/m2) | Ambient Temperature (°C) | Wind Speed (m/s) | Sky Temperature (K) |
---|---|---|---|
1000 | 35.8 | 2.6 | 296 |
Comparison of Simulation and Experimental Results | Ordinary Roof Outer Surface Temperature | Ordinary Roof Inner Surface Temperature | Photo-Thermal Roof Outer Surface Temperature | Photo-Thermal Roof Inner Surface Temperature |
---|---|---|---|---|
Experimental values | 53.0 | 43.2 | 37.0 | 36.8 |
Simulation values | 51.3 | 39.7 | 33.5 | 32.7 |
RE (%) | 3.2% | 8.1% | 9.5% | 11.1% |
RMSE | 3.3 |
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Zhang, Y.; Sun, H.; Long, J.; Zeng, L.; Shen, X. Experimental and Numerical Study on the Insulation Performance of a Photo-Thermal Roof in Hot Summer and Cold Winter Areas. Buildings 2022, 12, 410. https://doi.org/10.3390/buildings12040410
Zhang Y, Sun H, Long J, Zeng L, Shen X. Experimental and Numerical Study on the Insulation Performance of a Photo-Thermal Roof in Hot Summer and Cold Winter Areas. Buildings. 2022; 12(4):410. https://doi.org/10.3390/buildings12040410
Chicago/Turabian StyleZhang, Ying, Hongfa Sun, Jibo Long, Li Zeng, and Xiaohang Shen. 2022. "Experimental and Numerical Study on the Insulation Performance of a Photo-Thermal Roof in Hot Summer and Cold Winter Areas" Buildings 12, no. 4: 410. https://doi.org/10.3390/buildings12040410