TOTAL HEAT ABSORBED BY A SOLAR COLLECTOR
A solar collector is a device that collects and/or concentrates solar radiation from the Sun. These devices are primarily used for active solar heating and allow for the heating of water for personal use. In this blog, we will have compiled the formulae to find out the useful heat and efficiency of a flat plate solar collector.
Solar flat plate collectors, which utilizes sunrays to produce energy, are commonly used for domestic and industrial purposes and have the largest commercial application amongst the various solar collectors. This is mainly due to simple design as well as low maintenance cost. An attempt is made to analyse the heat absorbed solar collector. We tried to study the heat absorbed by the collector and its efficiency. In this blog, you’ll find the solidworks model of the same as well as pictures of the hand calculations done by us. A problem explaining how to find the area of a solar collector for required input and output temperatures is also solved
Flat plate solar collector
A typical flat-plate collector is a metal box with a glass or plastic cover (called glazing) on top and a dark-coloured absorber plate on the bottom. The sides and bottom of the collector are usually insulated to minimize heat loss. Sunlight passes through the glazing and strikes the absorber plate, which heats up, changing solar energy into heat energy. The heat is transferred to liquid passing through pipes attached to the absorber plate. Absorber plates are commonly painted with “selective coatings,” which absorb and retain heat better than ordinary black paint. Absorber plates are usually made of metal — typically copper or aluminium — because the metal is a good heat conductor. Copper is more expensive, but is a better conductor and less prone to corrosion than aluminium. In locations with average available solar energy, flat plate collectors are sized approximately one-half- to one-square foot per gallon of one day’s hot water use.
The solar energy is the energy received from the sun that sustains life on earth. It is an important source of renewable energy and its technologies are broadly characterized as either passive solar or active solar depending on how they capture and distribute solar energy or convert it into solar power. Active solar techniques include the use of photovoltaic systems, concentrated solar power and solar water heating to harness the energy. Passive solar techniques include orienting a building to the Sun, selecting materials with favourable thermal mass or light-dispersing properties. In this age, a power-hungry India is locking towards a renewable energy for its need. Extensive researches are going on in this field. Therefore, it would be ideal to invest in solar collectors as well as photovoltaic cells. The Earth receives 174 petawatts (PW) of incoming solar radiation (insolation) at the upper atmosphere. Approximately 30% is reflected back to space while clouds, oceans and landmasses absorb the rest.
Solidworks model
The above screenshots are of a flat plate solar collector which were modelled in solidworks. Then calculations were performed to find out the useful heat and efficiency.
For that three cases were considered. Keeping the diameter constant, mass flow rate was varied to calculate the useful heat and efficiency
Efficiency
The equation of efficiency and the useful heat is given below with the nomenclature of its terms
Cases
Case 1:
- ṁ = 0.025 kg/s
- Cp = 4182 J/kg
- T0 = 313.702 K
- Ti = 308.6 K
- Ac = 0.8 * 0.8
For the above values,
Useful heat= Qu = 533.414
Efficiency= η = 63.294%
Case 2:
- ṁ = 0.05 kg/s
- T0 = 311.093 K
- Ti = 308.6 K
- Ac = 0.8 * 0.8
For the above values,
Useful heat= Qu = 521.286
Efficiency= η = 61.855%
Case 3:
- ṁ = 0.075 kg/s
- T0 = 310.10 K
- Ti = 308.6 K
- Ac = 0.8*0.8
For the above values,
Useful heat= Qu = 470.475
Efficiency= η = 55.826%
Result table
Now to find the area of the collector for given inlet and outlet temperature, we need to find out QU. To understand it in a better way, we solved an example.
Problem:
A solar thermal collector will be installed for hot water production in a house in Morocco. You are now hired as a consultant to advise which collector type should be purchased for a design outlet temperature of 65°C and a design total irradiance on the collector of 835W/m2 . Your research on solar collectors for solar thermal applications has yielded the following information:
Both collectors can be considered perfectly insulated (adiabatic) at the sides and the ambient temperature equal 20°C.
The fluid inlet temperature to the collector can be assumed to be 25°C For both collectors determine:
• The collector area required to achieve the design outlet temperature of 65°C.
• Which collector would you recommend to buy? Explain why
Solution
Heat balance of the fluid flowing through the collector:
𝑄𝑢𝑠𝑒 = 𝑀̇ ∙ 𝑐𝑝 ∙ (𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)
Heat balance on the collector
𝑄𝑢𝑠𝑒 = (𝑄𝑎𝑏𝑠𝑜𝑏 − 𝑄𝑙𝑜𝑠𝑠𝑒𝑠) ∙ 𝐹 ′ = 𝐼𝑡 ∙ 𝐴 ∙ 𝐹 ′ ∙ [(𝜏𝐺 ∗ ∙ 𝛼𝐴 ∗ ) − 𝑈𝑡 ∙ (𝑇𝑓𝑙,𝑚 − 𝑇𝑎𝑚𝑏)/ 𝐼𝑡]
𝑏𝑒𝑖𝑛𝑔 𝑈𝑡 = 𝑈𝑓𝑟𝑜𝑛𝑡 + 𝑈𝑏𝑎𝑐𝑘
𝑎𝑛𝑑 𝑇𝑓𝑙,𝑚 = (𝑇𝑜𝑢𝑡 + 𝑇𝑖𝑛)/2
Combining the formulas and isolating A:
𝐴 = 𝑀̇ ∙ 𝑐𝑝 ∙ (𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛) / (𝐹′ ∙ [𝐼𝑡 ∙ 𝜏𝐺 ∗ ∙ 𝛼𝐴 ∗ − 𝑈𝑡 ∙ ((𝑇𝑜𝑢𝑡 + 𝑇𝑖𝑛/ 2) − 𝑇𝑎𝑚𝑏)])
Substituting the above values in the equation, we get
𝐴𝑢𝑛𝑐𝑜𝑣𝑒𝑟𝑒𝑑 = 33.7383 𝑚2
𝐴𝑐𝑜𝑣𝑒𝑟𝑒𝑑 = 21.3257 𝑚²
The costs can easily be calculated as the product of the specific costs (€/m²) and the collector area
𝐶𝑢𝑛𝑐𝑜𝑣𝑒𝑟𝑒𝑑 = 3373.83 €
𝐶𝑐𝑜𝑣𝑒𝑟𝑒𝑑 = 3625.36 €
Recommendation
If cost is the main driver, the uncovered collector would be the most suitable. Nonetheless, if the available space is an issue, the flat plate collector could become a suitable choice. In both the cases, useful heat is equal as inlet and outlet temperatures as well as mass flow rate is considered same.
Conclusion
In this assignment we studied how the solar collector absorbs solar irradiation from the sun and in turn its heat is used for some applications like solar water heaters. We calculated the heat absorbed by the collector and its efficiency. We solved a problem wherein we varied the mass flow rate and calculated the parameters. Then we observed that, the one with the lowest mass flow rate( 0.025 kg/sec) made the highest efficiency of around 61.29%We also solved a numerical to find out the area of a solar collector and we concluded that for uncovered solar collectors, their surface area is more and vice versa.
Thereby a study on the solar collectors were made.
References
- CFD Analysis of forced convection through flat plate solar collectors by Elias Babu, G Prasanth, Joseph Paul, Mathews Jose, Prof. Sabu Kurian A
- https://www.eurostar-solar.com/solar-collectors.html
- Thermal Analysis of Solar Flat Plate Collector Using CFD by Mohammed Abdul Junaid, Mohammed Nazimuddin, Mohd Arifuddin, Mohammed Faisal
- https://www.eurostar-solar.com/solar-collectors.html
- Problems for the seminar 7, MJ2411 HT17 by Royal Institute of Technology
By: Atharva Chitnis, Dharmesh Chowdhary, Rohit Daithankar
