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Group:Dipta Majumder Ahmed Altaif
Experimental & Evaluation Procedure
Presentation & Description of Results
Presentation & Description of Evaluation
Comparison with Expectation
Discussion of result significance
Liquid Cooled Solar Thermal Collector
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Table of Contents
1. Introduction ... 3
2. Theoretical background ... 3
2.1 Basic working principle of a solar thermal collector ... 3
2.2. Hear Transfer Mechanisms ... 4
2.3 Energy balance of a solar collector ... 5
2.4 Efficiency of a solar thermal collector ... 6
3. Methodology ... 7
3.1 Experiment setup ... 7
3.2 Equipment used ... 8
3.3 Experiment procedure ... 10
4. Results ... 12
4.1 Measuring radiation intensity ... 12
4.2 Change in mass flow ... 12
4.3 Efficiency ... 13
5. Discussion... 15
5.1 Comparison with expectation: ... 15
5.2 Propagation of uncertainty ... 16
5.3 Observations on mass flow rate measurement ... 17
5.4 Observations on irradiance measurement ... 18
5.5 Negative efficiency ... 18
5.6 Relationship between mass flow rate and inlet and outlet temperatures ... 19
5.7 Stabilization time ... 19
6. Conclusion ... 19
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Energy from the sun is transferred to the earth through radiation. Heat from the transferred energy was one of the conditions which he
from the ancient times for various purposes e.g. cooking, comfort etc. Heat can also be transferred through other two mechanisms except radiation, known as conduction and convection.
With the advancement in science and technology, through solar thermal collectors.
thermal collectors . Capturing the radiation from the sun, the solar thermal collector absorbs the radiation & heats up. However, a
solar thermal collector. In order to investigate the
significance of all three heat transfer mechanisms
conducted as part of the course requirement of Postgraduate Programme Renewable Energy (PPRE), University of Oldenburg. A flat plate solar thermal collector was used as the heat absorber while the sun was simulated using four halogen floodlights.
The main objectives of this experiment
different operating conditions i.e. changing temperature and incoming i
relationship between efficiency and irradiance related temperature dependence. Analysis on the findings along with comparison with the expectations has also been done.
2. Theoretical background
2.1 Basic working principle ofIn a solar thermal collector, h
Collected heat is then transferred to the
reservoir. A glass panel is installed in front of the absorbing material to minimize convection and reflection from the absorber surface
Figure 1: Solar thermal collector working principle (Source:
Energy from the sun is transferred to the earth through radiation. Heat from the transferred energy was one of the conditions which helped life to grow on the earth. Heat has been used by the human beings from the ancient times for various purposes e.g. cooking, comfort etc. Heat can also be transferred through other two mechanisms except radiation, known as conduction and convection.
ith the advancement in science and technology, thermal energy from solar
through solar thermal collectors. Liquid cooled solar thermal collector is a commonly used type of solar Capturing the radiation from the sun, the solar thermal collector absorbs the . However, all the heat transfer mechanisms are relevant in case of a liquid
the characteristics of a liquid solar thermal collector and to understand e heat transfer mechanisms in this process, a laboratory experiment was conducted as part of the course requirement of Postgraduate Programme Renewable Energy (PPRE), A flat plate solar thermal collector was used as the heat absorber while the sun four halogen floodlights. Notably, water was the used liquid to transfer the heat.
of this experiment were to quantify efficiency of the solar thermal collector in different operating conditions i.e. changing temperature and incoming irradiance and to
relationship between efficiency and irradiance related temperature dependence. Analysis on the findings along with comparison with the expectations has also been done.
orking principle of a solar thermal collector
In a solar thermal collector, heat from the sunlight is absorbed by the flat plate of the collector. eat is then transferred to the fluid through conduction. Heat is
reservoir. A glass panel is installed in front of the absorbing material to minimize convection and reflection from the absorber surface. The glass would also need high trans
al collector working principle (Source: https://www.epa.gov/rhc/solar cooling-technologies)
Energy from the sun is transferred to the earth through radiation. Heat from the transferred energy was earth. Heat has been used by the human beings from the ancient times for various purposes e.g. cooking, comfort etc. Heat can also be transferred through other two mechanisms except radiation, known as conduction and convection.
thermal energy from solar has been used effectively Liquid cooled solar thermal collector is a commonly used type of solar Capturing the radiation from the sun, the solar thermal collector absorbs the e heat transfer mechanisms are relevant in case of a liquid cooled
a liquid solar thermal collector and to understand the , a laboratory experiment was conducted as part of the course requirement of Postgraduate Programme Renewable Energy (PPRE), A flat plate solar thermal collector was used as the heat absorber while the sun
liquid to transfer the heat. quantify efficiency of the solar thermal collector in
rradiance and to find out the relationship between efficiency and irradiance related temperature dependence. Analysis on the
eat from the sunlight is absorbed by the flat plate of the collector. eat is carried by the fluid to the reservoir. A glass panel is installed in front of the absorbing material to minimize heat losses due to . The glass would also need high transmissivity and
https://www.epa.gov/rhc/solar-heating-and-4 | P a g e
Efficiency of a solar thermal collector can be defined as the ratio of the usable heat and the irradiance on the thermal collector area. Efficiency characteristics can be explained with the use of the energy balance in a solar thermal collector. Basic working principle is shown graphically in figure 1 for a flat plate solar thermal collector. However, the involved heat losses have not been discussed till now. In the next section, relevant heat losses or transfer mechanisms are described.
2.2. Hear Transfer Mechanisms
Heat can be transferred in three ways i.e. radiation, convection and conduction. In order to explain the energy balance in a solar thermal collector, background of the abovementioned mechanisms will be needed. Necessary information on the mechanisms is as follows.
Radiation: A black body with a temperature T emits an electromagnetic radiation. Characteristics spectrum of this black body can be described by Planck’s Law. Radiation doesn’t need any carrier or medium to pass on the energy. ˙Two surfaces with areas A1 and A2 with temperatures T1 and T2 will have heat transfer through radiation. Heat transfer QE from the A1 to A2 will be opposed by the heat transfer from A2 to A1. Net heat transfer with respect to A1 can be calculated using the following formula.
Heat transfer, QE=σ. A1. F. (T14-T24) (1) Where, σ is Stefan Boltzmann constant1 and F is a form factor taking shape and geometry of the surfaces into account.
Conduction: In conduction, heat energy is transferred through diffusion due to temperature gradient. Continuous collision with nearby particles in solids, liquids or gases transfer energy until the equilibrium is reached. Heat transfer QE due to conduction from position x1 to x2 of a homogenous material of cross-sectional area A depends on the temperatures in two positions and thermal conductivity of the material. This can be calculated from the following equation.
Heat transfer, QE= . ( ) (2) Where, k depicts thermal conductivity and T1 and T2 are temperatures at positions x1and x2 respectively. Convection: Convection mechanism includes displacement of material (fluid) as medium to transfer the heat. This can originate naturally due to difference in temperature, a process known as “Natural convection”. Forced convection is also possible. Heat transfer (QE) from a surface area (A) with temperature T to the ambience with temperature (Ta) is given by the following:
Heat transfer, QE=h.A.(T-Ta) (3) Where, h is the heat transfer coefficient.
Stefan Boltzmann constant σ = 5.670367×10−8
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2.3 Energy balance of a solar collector
Having discussed the heat transfer mechanisms, the energy balance of a solar thermal collector can be derived. Information on the flow of energy is needed though to describe the process in a meaningful way. Heat transfer processes are described in the following part.
Step 1: Incoming power comes from the solar radiation power density (G). Amount of incident energy per second is thus the product of G and absorber area Aabs.
Step 2: As discussed earlier in section 2.1, a glass cover is installed before the absorber area. A portion of the radiation is reflected by the glass cover. Transmitted part of the energy is in what we are interested in. If τg, rg and αg are respectively the transmissivity, reflectivity and absorptivity of the glass cover, their summation will be equal to one. Assuming the absorptivity to be negligible, transmitted energy to the absorber area is τg. G.Aabs whereas (1-τg).G.Aabs will be lost due to the reflection by the glass cover.
Step 3: Absorber would take the transferred energy forward. However, it can only absorb based on its absorption factor (αabs). Hence, absorbed energy by the absorber is basically αabs.τg. G.Aabs with the assumption that the transmitted energy is transferred fully to the liquid (water). Water with inlet temperature of Ti and a specific mass flow ṁ, will heat up from the absorbed energy to an outlet temperature of To. Part of the heat will be lost through all three heat transfer mechanism. Total heat loss is depicted by QEL. The whole process is shown in Figure 2.
Figure 2: Energy balance in a solar thermal collector (Source: https://www.researchgate.net/file.PostFileLoader.html)
Considering all three steps described above, the energy balance equation can be written as the following.
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Where, Cp is the specific heat capacity of water (4.1813 Jg-1K-1). Notably, all heat going into the liquid can considered as positive while heat transferred out of the liquid as negative to have a balance at the end. ṁ.Cp.Ti and ṁCp.To in the equation represents the incoming and outgoing energy in the fluid.
2.4 Efficiency of a solar thermal collector
It has been stated in the introduction section that the main objective of this experiment was to find out the efficiency of a solar thermal collector at different operating conditions. Relationship between heat lost through the heat transfer mechanisms and temperature is non-linear. However, a first order approximation can be considered which will not be fully accurate. This approximation is valid only when the mean collector temperature Tm (average of inlet and outlet temperature) does not deviate from the ambient temperature Ta by a big margin. Heat loss QEL can be described as follows:
Heat loss, QEL=UL.Aabs. (Tm- Ta) (5) Where, UL is the overall heat loss coefficient. Usable energy (QEU) taken by the liquid is represented by the following equation.
Usable Energy, QEU= ṁ.Cp.To-ṁCp.Ti (6) Equation (4) can be rewritten as the difference between the incoming energy and loss.
Usable Energy, QEU = αabs.τg. G.Aabs- UL.Aabs. (Tm- Ta) (7) Efficiency (ɳ) is the ratio of the usable energy and the incoming energy from the sun. Combining
equations 5-7, ɳ can be derived from the following equation.
Efficiency, ɳ = QEU/ G.Aabs = ṁ. .. ṁ . = τg.αabs-UL( ) (8)
Transmissivity and absorptivity are constant in equation (7). Hence, theoretically efficiency depends linearly on irradiance related temperature difference, (Tm- Ta)/G. A typical efficiency characteristic of a flat plate solar thermal collector is shown in figure 3.
Figure 3: Solar thermal collector characteristics curve (Source: https://www.researchgate.net/file.PostFileLoader.html
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3.1 Experiment setup
Experimental set up for this experiment consisted of a light source, a solar thermal collector, intensity sensor to sense the irradiance from the light source, a water circulation system with a pump and temperature sensors to find out inlet, outlet and ambient temperatures. Schematic diagram of the set up is shown below in figure 4.
Figure 4: Experiment set-up schematic (Source: Authors).
Four halogen lights (each of 1000W) were used to simulate the sun. Pt-100 sensors were used to sense the temperatures at different points. With a view to measuring radiation intensity, a pyranometer was used as the radiation intensity sensor. Notably, the pyranometer was used only to check the irradiation and was removed from the set up instantly- not to disrupt the heat transfer process.
The collector set up on the other hand was set on a movable rack (see figure 5). In an experimental set up, it is difficult to change the light source to change the irradiation. A better approach is to change the distance for varying the irradiance which was done by the movable rack.
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Figure 5: Movable rack set up (Source: Authors)
A thermostat (with a pump) was part of the set up to heat up the water and to pump it to an upper reservoir. Surplus of water can return to the thermostat with available overflow pipe. In the used set-up, water runs into the system with an inlet valve. The water then runs through the collector and absorbs the heat from the thermal collector. Water runs to the outlet pipe and a flow control valve is there to get into a weighing vessel. During the mass flow determination (using the weighing vessel), available suction valve needs to be closed. After the mass flow measurement, suction valve need to be opened to give back the water and thus completing the fluid circuit.
3.2 Equipment used
The whole experiment was conducted with a ready set up as described in the above section. List of equipment used in this experiment is given below in Table 1. Measuring tools with available details are also given in Table 2.
Table 1: Equipment used for the experiment
Equipment Manufacturer Model Specification Accuracy
Change over switch Umschaltbox 116/99 - -
Weighting device Sartorius excellence - - ± 0.01 (g)
Pump and Thermostat HAAKE T52 0 - 100° C -
Weighting vessel - - Glass/ 200 ml -
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Connecting Cables - - Blue and Black -
Table 2: Measurement tools used for the experiment
Solar thermal collector set up described above is shown via a detailed schematic view below in figure 6. Instrument Manufacturer Type or S/N Specification Accuracy
2 Multimeters VOLTCRAFT® M-4650B Range: 200mV -
b/n: 840573 CG-501
Start /Stop 0.01 Second
x-t recorder BBC GoerzMetra watt / SE 120 Range: 100mV Speed: 30 cm/h - Pyranometer - CM5-860568 0.0169 mV/W/m2 - 2 Pt-100
Ambient Temp. Sensor ThiesGuttingen 2.1260.00 - -
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Figure 6: Solar collector setup with components (Source: Authors)
Components indicated in Figure 6 are 1) Solar simulator, 4 kW HMI-lamp, 2) Solar thermal collector, with optional glass cover and optional transparent isolation, 3) Inlet temperature measurement, Pt-100, 4)Vent valve (obsolete), 5) Outlet temperature measurement, Pt-100, 6)Ambient temperature measurement house, Pt-100, 7)Change-over switch, 8)Digital multimeter, range 0 – 200 mV and x-t recorder, 9)Valve in suction pipe to circulation pump, 10)Weighing vessel, 11)Flow control valve, 12)Circulation pump, 13)Thermostat, 14)Main cut-off valve (included in thermostat housing) and 15)Constant head tank, insulated with glass wool (60 mm).
3.3 Experiment procedure
Having the primary goal of finding out efficiency of solar thermal collector in mind, efficiency was calculated for different temperatures and irradiances. Based on the recommended procedure in Winter Laboratory Course Reader , the following steps were executed.
1) Pt-100 sensors were installed to measure temperatures at inlet and outlet point with ambient temperature. Pt-100 sensors were connected a constant current source of 1mA and the voltage drop were measured by a multimeter. Using Ohm’s law (Voltage= Current x Resistance), resistances were calculated. The electrical circuit of the equipment to measure the different temperatures was established and approved by the supervisor.
2) The area of the solar collector is measured by a ruler which is used to calculate the overall efficiency of the solar collector later.
3) The irradiance coming from the light source is measured on the collector plane at different points by using a pyranometer. Notably, calibration factor of the used pyranometer was 0.01169 mV/W/m2. 4) Radiation intensity of the light source used in this experiment varies over the area of the thermal
collector. It could have been better to use a source a uniform radiation source. Radiation intensity was measured at five different points on the collector plane which is shown in the following figure.
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Figure 7: Measuring radiation intensity at different points of collector (Source: Authors). Radiation intensity measured on the five points can be thought of measuring in different triangles taking each three points. Mean over a triangle will be the average intensity in a triangle. Four triangles could be formed. Average intensities of the triangles can then be measured as well. Simplifying the procedure, average intensity can be calculated using the following equation:
Average radiation intensity, G= (G1+G2+G3+G4+2G5)/6 (9) 5) The circulation pump was turned on to allow the fluid (water) to flow through the system. Controlling valves were checked in order to avoid overflow of the fluid from the weighing vessel. It was also observed that there were no bubbles in the system to be removed by vent valve which is located at the highest point.
6) Radiation source of 4 kW HMI-lamp was turned on.
7) Pt-100 sensors (thermo-resistors) were used to measure the inlet and outlet temperatures of the solar collector and the ambient temperature, these sensors were connected to a change-over switch to switch between the voltage readings by using a single digital multimeter. A x-t recorder with an offset of 100 mV and speed of 30 cm/h was connected to plot voltages related to inlet and outlet temperatures. It was basically used to confirm that the measured readings were stabilized. By using Ohm’s law, the resistance R was calculated. The formula to calculate the temperature is,
T=-244.037 °C + 2.3264 °C/Ω.R + 0.00113 °C/Ω2.R2 (10)
8) To measure the mass flow, the valve in suction pipe was closed while the valve to the weighing vessel was kept open. With the help of a stopwatch and a smart phone, one-minute-video was recorded. After taking data, suction valve was opened to allow the water to be circulated through the system.
9) Position of the solar collector rack was changed to vary the incoming irradiance. The higher values of light intensity were achieved by moving the solar collector towards the light source keeping in mind
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that the maximum radiation intensity of 1500 W/m2 should not be exceeded to protect the pyranometer.
10) Finally, in order to determine the efficiency of the solar collector and to cover the whole range of the linear graph of the collector efficiency, changes in parameters e.g. mass flow, the inlet temperature ( by adjusting the thermostat) and the irradiance at the solar collector were done. Efficiency for each case were calculated and plotted against irradiance related temperature difference to understand the solar thermal collector characteristics.
Following the procedure described in the earlier section, mass flow rate, radiation density and inlet temperatures were changed from time to time to find out the collector efficiency characteristics. The findings are summarized below.
4.1 Measuring radiation intensity
Based on the methodology described to change the radiation intensity, this parameter was changed four times during the experiment. Radiation intensities (G1 to G5) were measured at five points and the average radiation intensity (G) was calculated as per equation 9. Measured values are given in Table 3.
Table 3: Measured value of radiation intensity
Case 1 Case 2 Case 3 Case 4
SL V (mV) at sensor terminal Radiation intensity (W/m2) V (mV) at sensor terminal Radiation intensity (W/m2) V (mV) at sensor terminal Radiation intensity (W/m2) V (mV) at sensor terminal Radiation intensity (W/m2) G1 7.25±0.1 620.2±8.5 5.21±0.1 445.7±8.5 3.17±0.1 271.2±8.5 6.15±0.1 526.1±8.5 G2 7.60±0.1 650.1±8.5 5.60±0.1 479±8.5 3.40±0.1 290.9±8.5 6.10±0.1 521.8±8.5 G3 7.47±0.1 639±8.5 5.48±0.1 468.8±8.5 3.40±0.1 290.9±8.5 5.70±0.1 487.6±8.5 G4 7.22±0.1 617.6±8.5 5.07±0.1 433.7±8.5 3.13±0.1 267.8±8.5 5.94±0.1 508.1±8.5 G5 9.40±0.1 804.1±8.5 5.81±0.1 497±8.5 3.60±0.1 308±8.5 7.00±0.1 598.8±8.5 G 689.2±8.5 470.20±8.5 289.42±8.5 598.80±8.5
Light source used in the experiment could not provide uniform light intensity which was also prominent from the variation at different points in Table 3. Uncertainty in the measurement was introduced by the multimeter (0.05%) which also impacted the radiation intensity. The table also includes the associated uncertainty of the measured values of voltage and the corresponding radiation intensity.
4.2 Change in mass flow
Mass flow was changed five times during the experiment to change the operating point of the solar thermal collector and find out the corresponding efficiency. Mass flow rates were taken as mean of several data points. Average of several points was taken each time the mass flow rate was changed. The measured values with the deviation from the mean are shown in figure 8. Lower mass flow rate (5.95 g/s) has not been shown here for the sake of better resolution.
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Figure 8: Mass flow rate (g/s) with mean mass flow rate
In the figure above, the deviation from the mean value is clearly visible in four different mass flow rates. Considering the uncertainty of the weighing vessel is ±0.01g, figure 8 clearly indicates that the mass flow rate could not be kept totally constant.
Under different irradiance levels, mass flow adjustment and change in inlet temperatures, the efficiency of the solar thermal collector under test was calculated based on equation (7). The findings are shown in the following table.
Table 4: Efficiency with uncertainty and necessary information on operating conditions Mass flow rate (g/s) Standard error in mass flow rate Inlet T (0C) Outlet T (0C) Ambient T (0C) Mean T(0C) Irradiation (W/m2) Irradiance based on T difference Efficiency (%) Propagated uncertainty in efficiency2 ṁ σṁ Ti To Ta Tm G (Tm-Ta)/G ɳ σɳ(%) 19.48 2.02 62.54 62.75 25.64 62.65 289.42 0.13 18.06% 1.87% 19.48 2.02 53.04 53.48 25.26 53.26 289.42 0.10 38.26% 3.97% 19.48 2.02 40.41 41.60 24.82 41.00 470.20 0.03 63.46% 6.58% 19.70 0.20 27.39 29.48 24.18 28.44 689.19 0.01 76.75% 0.76% 19.93 0.44 29.84 31.31 24.36 30.58 470.20 0.01 80.16% 1.78% 2
Propagated uncertainty here is based on the uncertainty in mass flow. Uncertainty in other parameters has not been considered. 15 18 21 24 27 1 3 5 7 M as s fl o w r at e ( g/ s) Measurement point
Mass flow rate values with mean value
Mass flow 1 Mean mass flow 1 Mass flow 2 Mean mass flow 2 Mass flow 3 Mean mass flow 3
14 | P a g e 21.50 1.82 67.58 68.34 26.08 67.96 540.21 0.08 38.78% 3.28% 21.50 1.82 58.03 59.08 25.90 58.55 540.21 0.06 53.32% 4.51% 21.50 1.82 53.56 54.89 25.95 54.22 540.21 0.05 67.88% 5.74% 5.95 0.13 29.66 34.15 24.36 31.91 470.20 0.02 73.04% 1.59% 5.95 0.13 28.61 35.39 24.38 32.00 689.19 0.01 75.32% 1.64% 19.48 2.02 68.94 68.91 26.08 68.92 289.42 0.15 -2.26% -1.45%
In table 4, calculated efficiency with uncertainty and the parameters needed to compute efficiency were mentioned. An interesting finding of negative efficiency was highlighted. This unusual finding has been discussed in detail in section 5.5. Propagated uncertainty in efficiency ranges from 0.76% to 6.58% (barring the negative efficiency case).
The efficiency of the solar thermal collector with respect to the irradiance-related temperature difference changes linearly which was discussed in section 2.4. Relationship between efficiency and (Tm-Ta)/G is shown graphically in Figure 9. The propagated uncertainty is also shown as vertical bars.
Figure 9: Solar thermal characteristics ɳ as function of (Tm-Ta)/G
From figure above, it is clear that efficiency has a liner relationship with (Tm-Ta)/G which was expected from equation (8). Maximum efficiency of 80.16±1.78% was recorded. Linear fitting was done for the efficiency. The linear relation is as follows.
ɳ=0.8278-[4.8963 x (Tm-Ta)/G] (11) While, ɳ = τ.α-UL( ) y = -4.8963x + 0.8278 R² = 0.9478 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 0 0.05 0.1 0.15 ɳ(%) (Tm-Ta)/G [0C/W/m2] ɳ vs (Tm-Ta)/G
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Comparing the above equations, we can find effective optical efficiency (τg.αabs) from the linear fitting as 0.8278. Effective optical efficiency of 0.8278 represents that 82.78% of the incident energy has been transferred from the outside of the glass cover to the absorber material. This is known as optical energy capture. On the other hand heat loss coefficient UL is derived from the slope of the linear graph. Heat loss coefficient from the linear fit is 4.90 W/m2/0C. It is to be noted here that, the negative efficiency point has been omitted here from the graph.
Heat loss coefficient can be calculated in another way. Slope can also be obtained using two points. Slope from two points (x1,y1) and (x2,y2) is,
Slope , m= (12) In order to find the slope three points were taken from the figure and slopes were calculated for each pair.
Table 5: Heat loss coefficient from slope between two points
Points (Tm-Ta/G ,ɳ) Slope
(0.006, 76.75%) (0.011,75.32%) -2.86 (0.011,75.32%) (0.016,73.04%) -4.56 (0.006, 76.75%) (0.016,73.04%) -3.71
From table 5, varying slope thus the heat loss coefficient was observed. This can be attributed to the variation of heat loss coefficient with temperature. However, taking the slope of the fitted curve will give us an average value of heat loss coefficient.
In this discussion section, evaluation of the results is presented with possible significance of the analysis.
5.1 Comparison with expectation:
Based on the theoretical background, it was expected that the irradiance related temperature difference and collector efficiency have a linear relationship. This linear relationship is true if the mean collector temperature isn’t greater than the ambient temperature by a big margin. Linear relationship was observed between efficiency and (Tm-Ta)/G with coefficient of determination (R2)value of 0.95.
It was also expected that the outlet temperature (To) would be higher than inlet temperature (Ti). The difference depends largely on the irradiance and the water flow rate (mass flow rate). The higher the irradiance, the higher should be the outlet temperature. On the contrary, higher mass flow rate will not ensure proportional rise in the outlet temperature. The measurements and the calculations matched the
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expectation perfectly except for the negative efficiency which is a result of the negative (-) difference between the outlet and inlet temperatures (To- Ti< 0).
Higher efficiency is expected if mass flow is decreased keeping the irradiance same. This was also observed. On the other hand, it is expected that the efficiency will increase with increase in difference between outlet and inlet temperature. This can also be validated from the figure below.
Figure 10: Relationship between ɳ and temperature difference in outlet and inlet with linear fitting The figure above clearly indicates that higher efficiency is achieved when the difference between inlet and outlet is higher. During the experiment, maximum temperature difference was recorded to be 6.790C at an efficiency of 75.32%. However, higher efficiency was also achieved when the temperature difference is less than 6.790C. It can be concluded from here that, a solar collector operating at higher efficiency does not ensure that the hot water can be supplied for potential usage.
5.2 Propagation of uncertainty
Every experiment is done with measurements and with each measurement comes uncertainty. Error can occur in two ways i.e. statistical error and systematic error. Statistical error refers to the error when a measurement is done several times. If the average value of the measurements is used in calculating any other parameter, the error will also be propagated to the calculated one. This is known as propagation of error or propagation of uncertainty  . Uncertainty analysis helps to understand the significance of the measured data.
With respect to our experiment, mass flow rate was measured several times and the average value was used to find out the efficiency of the collector. Standard error of the mass flow rate was also calculated using the following equation. If a function F is dependent on independent variables X,Y,…. Standard deviation of the function is given by,
σF= √((∂F/∂x)2 . σx2 + (∂F/∂y)2 . σy2 + …… ) (13) -2.00 0.00 2.00 4.00 6.00 8.00 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% To -T i Efficiency
Collector temperature vs Efficiency
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Where, σf is the standard deviation of the function F. σx and σy are standard deviations of variables X and Y respectively.
This standard error was propagated when the mass flow rate was also used to calculate efficiency. It would have been more appropriate if the values of other parameters e.g. area, radiation intensity could also be measured several times to find out the standard error in those parameters. With a view to simplification, only standard error in measurement of mass flow was propagated to measure the error in efficiency.
From the solar collector characteristics, it was observed that the error increased when the collector was operating at comparatively high temperature difference related to change in irradiance. In case the (Tm-Ta)/G was very high, the error in efficiency dropped again. This behavior can be observed from the following figure.
Figure 11: Dependency of error in efficiency with temperature difference (including polynomial fit)
5.3 Observations on mass flow rate measurement
In order to decrease the uncertainty of the mass flow measurement, a smart phone along with a stopwatch were used to record a one-minute-video showing the increase in of weight (mass) in the weighing vessel and the corresponding time instantaneously. By playing and stopping the recorded video, the mass of water and the corresponding time were noted.
To calculate the mass flow rate, differences between mass and time were taken to find out the mass flow. The final flow rate was taken from the mean of the calculated values. It is noted that the, mass flow varies even within one minute of time frame. Hence, statistical error would occur if the mean mass flow is taken to calculate the efficiency. Standard deviation was used for the propagation of error as well. This deviation cannot happen from the inaccuracies of the equipment which would have resulted in the same deviation every time. If the valve controlling the flow rate of the water in the system is partially open, this may lead to turbulences and disturbed flow in the system which would result in
0.00% 2.00% 4.00% 6.00% 8.00% 0.000 0.050 0.100 0.150 P ro p ag at ed e rr o r in e ff ic ie n cy (Tm-Ta)/G [0C/W/m2] Error in efficiency vs (Tm-Ta)/G
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different flow rates. On the other hand, any presence of air bubbles in the piping system would also affect the performance of the pump and also lead to a disturbed flow through the system.
The Standard deviation of mass flow rates were calculated for the 5 sets of mass flow rate, the standard deviation error was in the range of 1 ~10 %. Due to this high deviation, statistical error was considered to analyze propagation of error.
5.4 Observations on irradiance measurement
In order to obtain a more accurate reading of the irradiation, a measurement in five spots was conducted. The average irradiance yielded by the solar simulator is determined by dividing the entire surface into four triangles.
Presumably, radiation measurement at the middle point (5) (Fig 4.2) showed the highest radiation since the light source was directed towards this point. The non-uniform distribution of the radiation over the collector surface would probably lead to some uncertainties in the estimation of the collector’s efficiency. Standard deviation in each of the irradiation is shown in the table below.
Table 6: Standard deviation in radiation intensity Mean radiation density (W/m2) Standard deviation(W/m2) Percentage of deviation 689.2 73.7 11% 470.2 23.4 5% 289.4 15.2 5% 540.2 39.4 7%
Considering the calibration factor of the pyranometer (0.01169 mV/W/m2) and uncertainty in the multimeter which was used to measure the voltage (0.01 mV), the uncertainty of the irradiance was (0.01169/0.01 = ±1.1 % W/m2) which is negligible compared with the statistical errors. To measure accurate and uniform values of measurement, high intensity xenon lamps could be used to simulate the sun.
5.5 Negative efficiency
Outlet temperature was recorded to be lower than the inlet temperature during the experiment under lowest possible irradiation with maximum mass flow rate while the inlet temperature was very high (68.940C). The only explanation of this behavior is that the fluid flowing inside the solar collector was not heated up from the heat exchange between the absorber and fluid. Due to low irradiance intensity and high mass flow, the heat transfer could not happen properly. Due to this fact, the outlet temperature was slightly lower than the inlet temperature, resulting in negative efficiency. This point wasn’t shown in the solar collector efficiency graph based on the uncertainties.
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By help of the negative efficiency, it was possible to interpolate and find out the ‘equilibrium temperature, Tm = 68.18° C (also called the stagnation temperature) which shows that the losses increase until η decreases to zero. The stagnation temperature gives an important guide to the range of possible applications of the collector. For example, a collector with a stagnation temperature of 60° C would be adequate for many domestic uses, but not for an industrial application that required boiling or near-boiling water.
5.6 Relationship between mass flow rate and inlet and outlet temperatures
In a solar thermal collector, difference between inlet and outlet temperatures is important to provide heat. However, if mass flow rate is higher, the outlet temperature will not rise. This is because the heat transfer could not take place due to very high flow rate. Mass flow was changed while keeping the irradiation intensity constant to check this behavior. The findings are as follows:
Table 7: Effect of changing mass flow rate with constant irradiation Irradiation intensity 470 W/m2
Mass flow rate (g/s) To-Ti (0C) Efficiency (%)
19.48 1.19 63.45%
5.95 4.49 73.04%
As per equation (7), under same irradiation capacity, if mass flow increased, efficiency should increase as well. However, change in mass flow rate also changes To-Ti (0C). From the above situation, it was observed that for increasing the mass flow 3.27 times, To-Ti (0C) decreased 3.77 times with respect to the initial situation. If other parameters are kept constant, theoretically the efficiency should decrease by 13.2% whereas measured efficiency was actually 13.1% lower from the initial situation.
5.7 Stabilization time
An x-t recorder was used to clearly understand if the voltages across Pt-100 sensors are stabilized or not. In order to find out the efficiency characteristics over a wide range of temperature, inlet temperature was increased. This was done by the thermostat. In case of heating, the temperature of inlet and outlet took comparatively longer time to stabilize. This can be attributed to the slowness of the thermal process both in case of heating and cooling.
The purpose of the experiment was to investigate the characteristics and the efficiency of a liquid cooled solar thermal collector. The solar thermal collector efficiency was determined by changing several parameters i.e. mass flow rate, inlet temperature and irradiation intensity. Effect of changing the parameters was analyzed. At the end, an efficiency curve was drawn for the solar thermal collector against irradiance related temperature difference. Maximum efficiency of 80.16% was recorded.
The relationship was found to fit a linear curve with R2value of 0.95. From the linear relationship, heat loss coefficient was found from the slope of the efficiency curve with a value of 4.90 W/m2/0C. In addition, optical efficiency was found 82.8 % from the linear fit.
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Uncertainty in mass flow was observed during the experiment. Standard deviation ranges from 1~10% in case of mass flow determination. This uncertainty was then propagated to the efficiency calculation. Uncertainty in efficiency varied from 0.76% to 6.58%.
Outlet temperature was expected to be found higher than the inlet temperature. However, in case of high flow rate and low irradiation intensity, the outlet temperature was lower than the inlet temperature resulting in negative efficiency. In addition, lower flow rate at the same irradiation intensity showed higher efficiency than higher flow rate. Relationship between the difference outlet and inlet temperature with efficiency was analyzed as well. It showed that the efficiency can be very high while the outlet temperature isn’t significantly higher than the inlet temperature.
In general, the findings from the experiment showed strong similarity with the theoretical background. The inaccuracies were taken into consideration for the validation of the measured data. It can be concluded that the experiment might be bettered by using the measurement devices with better accuracy and with improved equipment set up.
 Solar thermal collector n.d. https://en.wikipedia.org/wiki/Solar_thermal_collector (accessed January 8, 2017).
 Planck’s law n.d. https://en.wikipedia.org/wiki/Planck’s_law.
 PPRE stuff. Physical Principles of Renewable Energy Converters. WS 2016-17. 2016.
 Solar collectors n.d. http://www.powerfromthesun.net/Book/chapter05/chapter05.html#5.1.1 Optical Energy Capture (accessed January 16, 2017).
 Propagation of Uncertainty n.d. https://en.wikipedia.org/wiki/Propagation_of_uncertainty.  Stagnation Temperature n.d. https://en.wikipedia.org/wiki/Stagnation_temperature.