A Realistic Approach of the Maximum Work Extraction from Solar Thermal Collectors
Abstract
:1. Introduction
2. Review up Today
2.1. Maximum Work Extraction from Solar Energy
2.2. Maximum Work Extraction Using Solar Collectors
3. Suggested Model
3.1. General Description
- -
- The optical efficiency of the collector (ηopt), which is the product of the receiver absorbance, the cover transmittance, the concentrator reflectance; it also includes the impact of the incident angle.
- -
- The radiation thermal losses of the receiver are taken into account using the emittance of the receiver (εr). This parameter usually takes low values (close to 0.05~0.10) for high-quality collectors. It has been assumed the collector exchanges irradiation with the ambient and not with the sky.
- -
- The solar irradiation is considered as heat and not irradiation in the model, something that is not performed in similar studies [13].
- -
- The convection losses are neglected because by using vacuum between glass cover and absorber (in parabolic trough collectors, for instance), these thermal losses become negligible. This assumption is reasonable because the present work aims to determine the maximum work extraction using a real concentrating solar collector. So, this assumption corresponds to a high quality concentrating collector. In any case, an increase in the emittance (about 0.1) can be performed in order to take into account the convection thermal losses.
3.2. Mathematical Description
3.2.1. Energy Balance in the Receiver
3.2.2. Energy Balance in the Thermal Engine
3.2.3. Total System Energy Balance
3.2.4. Optimum Operation Temperature
4. Results—Discussion
4.1. Solution of the Optimization Polynomial
4.2. Impact of Design Parameters in the System Performance
4.3. The Application of the Model in a Real Solar Collector
4.4. Discussion
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
A | Area, m2 |
C | Concentration ratio, - |
f | Geometric factor, - |
G | Solar irradiation, W/m2 |
p | Efficiency parameter, - |
q | Polynomial parameter, - |
Q | Heat or radiant energy, W |
T | Temperature, K |
UL | Thermal loss coefficient, W/m2 K |
W | Work, W |
X | Ratio of receiver temperature to ambient temperature, - |
Z | Collector quality parameter, - |
Greek symbols | |
α | Absorbance, - |
γ | Intercept factor, - |
δ | Cone half-angle, ° |
ε | Emittance, - |
η | Efficiency, - |
θ | Incident angle, ° |
ρ | Reflectance, - |
σ | Stefan–Boltzmann constant, [=5.67 × 10−8 W/m2 K4] |
τ | Transmittance, - |
Subscripts and Superscripts | |
a | Aperture |
amb | Ambient |
carnot | Carnot cycle |
coll | Collector |
ex | exergy |
loss | Thermal losses |
max | Maximum |
opt | Optimum |
out | Output heat |
r | Receiver |
r,opt | Optimum receiver |
solar | Solar energy |
sun | Sun |
sys | System |
th | Thermal |
u | Useful |
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Collector | C | ηopt | εr | Tr,opt (K) | ηsys |
---|---|---|---|---|---|
Flat plate collector | 1 | 0.8 | 0.25 | 401 | 0.1449 |
Evacuated tube collector | 1 | 0.7 | 0.10 | 451 | 0.1777 |
Compound parabolic collector | 3 | 0.6 | 0.10 | 527 | 0.2079 |
Parabolic trough collector | 30 | 0.75 | 0.10 | 884 | 0.4400 |
Solar dish collector | 100 | 0.75 | 0.10 | 1110 | 0.5011 |
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Bellos, E.; Tzivanidis, C. A Realistic Approach of the Maximum Work Extraction from Solar Thermal Collectors. Appl. Syst. Innov. 2018, 1, 6. https://doi.org/10.3390/asi1010006
Bellos E, Tzivanidis C. A Realistic Approach of the Maximum Work Extraction from Solar Thermal Collectors. Applied System Innovation. 2018; 1(1):6. https://doi.org/10.3390/asi1010006
Chicago/Turabian StyleBellos, Evangelos, and Christos Tzivanidis. 2018. "A Realistic Approach of the Maximum Work Extraction from Solar Thermal Collectors" Applied System Innovation 1, no. 1: 6. https://doi.org/10.3390/asi1010006