Performance investigation on solar still with circular ...

Desalination 380 (2016) 66–74

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Performance investigation on solar still with circular and square fins in basin with CO2 mitigation and economic analysis T. Rajaseenivasan, K. Srithar ⁎ Department of Mechanical Engineering, Thiagarajar College of Engineering, Madurai 625015, Tamil Nadu, India

H I G H L I G H T S • • • •

Performance of solar still with circular and square fins is investigated. Theoretical and experimental analysis is carried out. CO2 mitigation and carbon credit analysis are studied. Embodied energy payback time decreases with increase in operational days.

a r t i c l e

i n f o

Article history: Received 22 July 2015 Received in revised form 23 November 2015 Accepted 24 November 2015 Available online xxxx Keywords: Solar still Circular fin Square fin Solar desalination CO2 mitigation Carbon credits

a b s t r a c t This paper discusses the experimental and theoretical performance of a solar still with circular and square fins integrated at the basin. A mild steel circular pipe (0.03 m dia × 0.07 m height) and a square hollow pipe (0.019 m side length × 0.07 m height) are used as fins in the modified still. Performance of the system is investigated by varying water depth (1 cm, 2 cm, 3 cm and 4 cm) in the basin and wick material covered over fins. The distillate attains a maximum (4.55 kg/m2 day) in the still with square fin and covering with wick, whereas the conventional still yields a maximum of 3.16 kg/m2 day. The carbon credit analysis result shows that the embodied energy payback time is less than one year for all cases and it further reduces with an increase in operational days of the solar still. Total CO2 emission mitigation is about 5.6 to 36.6 t with the life time variation of 5 to 30 years in wick covered square fin still. Economic analysis shows that the cost of distilled water reduces with an increase in operational days and life time of the solar still. Theoretical analysis results show good agreement with the experimental values. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Solar stills are simple devices used to produce distilled water from saline water and effluents. Performance of the still is affected by meteorological (solar intensity, ambient temperature and wind velocity) and operational parameters (exposure area, water depth, water–glass temperature, inlet temperature of water, cover inclination, basin material) [1]. Glass temperature affects the condensation rate and lower glass surface temperature increases the circulation of air inside the still in terms of enhancing convective and evaporative heat transfer between water and glass cover. Cover cooling results show that the use of film-cooling increases the still efficiency and wind velocity also has considerable effect on productivity. Productivity of the still improves with an increase in wind velocity due to higher convection heat transfer from the glass cover to the atmosphere [2,3]. ⁎ Corresponding author. E-mail address: [email protected] (K. Srithar).

http://dx.doi.org/10.1016/j.desal.2015.11.025 0011-9164/© 2015 Elsevier B.V. All rights reserved.

Water depth has a strong function on productivity and higher depth reduces the day time production and increases the nocturnal production. Many researchers concluded that, shallow basin still is better for higher water distillate at sunshine hours and deep basin stills for nonsunshine hours [4,5]. Black materials can absorb greater amounts of heat energy and release it during cloudy or night hours which enhance the distillate output. Wick material increases the exposure area which leads to an increase in evaporation rate. Glass, rubber, gravel, mild steel, asphalt, sponges, jute cloth, corrugated wick and waste cotton are some materials having these properties and resulted in better performance of the solar still [6–11]. Reflectors are used to increase the radiation receiving rate at the basin by reflecting the radiation into the basin. Internal and external mirrors increase the basin water temperature and lead to higher temperature and enhance the productivity. Reflector study shows that the mirrors are more useful in winter climatic condition rather than summer climatic condition [12,13]. Single basin solar stills with rectangular fins in a basin have been used to produce the distilled water from effluents and saline water

T. Rajaseenivasan, K. Srithar / Desalination 380 (2016) 66–74

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Fig. 1. Schematic view of solar stills. (a) Conventional still, (b) modified still.

which resulted in enhanced system performance [14,15]. Ethanol has been treated in the single basin solar with vertical fins in the basin and resulted in system performance increases with increasing number of fins [16]. Performance of the solar still has been investigated with extended porous fins and resulted in improved distillate output [17]. The effects of fin configuration on single basin solar stills have been theoretically and experimentally investigated [18]. The performance of solar stills with corrugated and vertical fins has been studied compared with conventional stills. The distillate output enhances by 21% and 40% higher than the vertical and corrugated finned still [19]. Pin finned wicks have been integrated and experimentally tested in solar stills to improve the evaporation rate and resulted in higher efficiency than the conventional solar still [20]. Multi basin stills are used to utilize the latent heat of condensation in glass cover for preheating the water in an upper basin. An analysis has been carried out to optimize the number of basins in solar stills and concluded that the double basin still has higher performance [21]. Double basin double slope solar stills with different wick and energy storing materials have been used in a lower basin to increase the performance [22]. Different methods used to improve the performance of the multi effect solar still have been reviewed and resulted in higher performance than conventional single basin solar stills [23]. The temperature difference between water in the basin and condensing glass cover has a direct effect on the performance of the still. Some external collectors are used to increase the basin water temperature by integrating it with the solar still. An evacuated tube collector has been integrated with the solar still and the water is circulated in forced circulation mode resulting in higher distillate than natural mode [24]. A single slope solar still has been integrated and tested with a flat plate solar collector, spraying unit, perforated tubes, external condenser and solar air collector. The result shows the performance of the system increases with an external condenser, solar water heater, and sprayed hot water and system performance decreases with a solar air collector

and it becomes more expensive and complex [25]. Work has been carried out to supply the preheated water to the still by integrating a solar flat plate collector within the basin of the still and resulted in better distillate output than the conventional solar still [26]. The solar still has been integrated with a solar parabolic dish concentrator and the preheated water supply is used to increase the distillate output in the system [27]. Dwivedi and Tiwari [28] carried out a carbon credit earned analysis on passive solar stills and reported that 9.33 t of CO2 can be obtained for 20 years life time. Sharon and Reddy [29] made an enviro-economic analysis on vertical solar distillation systems and concluded that 69.85 t of CO2 can be mitigated for the period of 20 years. Literature shows that the performance of the still is affected by the depth of water in the basin, water temperature, exposure area and water–glass temperature difference. Previous works carried out in the integration of fins in the basin plate of the solar still increases the basin exposure surface area and thus leads to higher heat transfer rate and higher evaporation rate. Rectangular, corrugated, vertical, porous fins and pin-fin wick fins have been used in the previous works [14–20]. Therefore in the present work, hollow circular and square fins are integrated in the basin plate and the performance is investigated. The presence of these fins increases the basin exposure area of the solar still. This study is carried out by varying the water depth (1 cm, 2 cm, 3 cm and 4 cm) in the basin and fins covered with wick material. 2. Experimental setup This work consists of two single slope–single basin solar stills namely conventional and modified still as shown in Fig. 1. A mild steel plate with a thickness of 1.4 mm is used to fabricate both solar stills. The size of the basin is 1 × 1 m2 and a height of 15 cm at one end and 32.6 cm at another end. It makes an inclination of 10° to the horizontal, which is the latitude of Madurai, India. 4 mm thickness window glass is

Fig. 2. (a) Square finned basin. (b) Circular finned basin.

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Fig. 3. Heat transfer mechanism in solar still.

used as a transparent cover in both stills. The outer side of the basin is insulated with 5 cm thermocole to reduce the basin heat loss. A collection trough is provided below the lower edge of the cover to collect the condensate. A distillate outlet is provided to drain the water through hoses and to store in jars. Provisions are made to supply raw water, drain the basin water and insert thermocouples. Circular and square fins are integrated in the two separate mild steel plates as shown n Fig. 2. These plates are used as a basin plate in the modified solar still. A mild steel circular pipe (0.03 m dia × 0.07 m height) and square hollow pipe (0.019 m length × 0.07 m height) are used as fins. A total of 64 fins with the same circumference area are welded in the basin plate at the same pitch ratio. A water storage tank with a capacity of 50 l is used to supply the saline water to the conventional and modified stills as shown in Fig. 1. Valves V1 and V2 are used to control the flow between the saline water storage tank and the conventional and modified stills respectively. Before starting the experiment, the required water level is maintained in the conventional and modified stills by opening these valves. As the water evaporates in the still, the level of the water is reduced and the makeup water is added in the conventional and modified stills for every thirty minutes. The temperatures are measured by the constantan thermocouples integrated with a temperature indicator and selector switch arrangement in the following locations: basin plate, water at the basin, vapor, and inner and outer glass temperatures. Solar radiation is measured with the help of a solarimeter and wind velocity by an anemometer.

A glass jar of 1 l capacity is used to measure the hourly yield and a vane type digital anemometer is used to measure the wind velocity. Observations (solar intensity, wind velocity, ambient temperature, yield and the temperatures at various parts of the stills) are recorded in an hourly basis from 9 AM to 6 PM. Experiments are simultaneously carried out in both the conventional and modified stills to compare the performance of the proposed system with the conventional system. In the first set of experiments, the performance of the systems is studied by varying water depth in the basin (1, 2, 3, 4 cm). In the second set of experiments, fins are covered with wick and 1 cm depth of water is maintained in both stills. All the experiments are performed in actual solar condition during the period of February–May 2014 and each test is repeated for a minimum of two times in a month depending upon the climatic condition to compare the performance of the systems in almost the same climatic condition. 3. Theoretical analysis The energy balance for the stills is carried out with the following assumptions for simplification: (a) no vapor leakage from the solar still; (b) neglecting the side heat loss from the solar still; and (c) water level in the basin of the solar still is kept constant. The heat transfer mechanism in the solar still is given in Fig. 3. Energy balance equation for basin liner [15],

Table 1 Accuracy of various measuring instruments. Sl. no.

Instrument

Accuracy

Range

Minimum value measured

% error

1 2 3 4 5

Thermometer Thermocouple Kipp–Zonen solarimeter Anemometer Measuring jar

+1 °C ±0.1 °C ±1 W/m2 ±0.1 m/s ±10 ml

0–100 °C 0–100 °C 0–2500 W/m2 0–15 m/s 0–1000 ml

30 30 40 1 100

3.33 0.33 2.5 10 10


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energy balance equation for water mass in the basin [15]. Energy available in the saline water (from solar and basin plate) is equal to the summation of energy transferred to the glass cover by convective, radiative and evaporative heat transfer from water and energy gained by the saline water. ðAw α w H s Þ þ Q c;b−w ¼ mw C pw

dT w þ Q c;w−g þ Q r;w−g dt

þ Q e;w−g ;

ð2Þ

energy balance equation for glass cover [15]. Energy gained by the upper glass cover (from solar radiation and heat transfer from water to glass) is equal to the summation of energy gained by the glass and energy lost to the sky by convective and radiative heat transfer. ðAg α g H s Þ þ Q c;w−g þ Q r;w−g þ Q e;w−g dT g þ Q r;g−sky þ Q c;g−sky ¼ mg C pg dt

Fig. 4. Daily efficiency variation with depth of water.

Energy received by the basin from the sun is equal to the summation of the energy gained by the basin plate, energy transferred to saline water and losses to the environment. Ab α b τ g H s ¼ mb C pb

dT b þ Q c;b−w þ Q b−atm ; dt

ð1Þ

ð3Þ

For the first iteration the temperature of the basin, water and glass are taken as actual ambient temperature at the time. The changes in basin (dTb), saline water (dTw) and glass temperature (dTg) are computed by solving Eqs. (1), (2) and (3), respectively for the time interval of 10 s. For evaluating, the above-mentioned temperatures in the simulation, the experimentally measured values of solar radiation and ambient temperature of the corresponding day and hour are used.

Fig. 5. Theoretical and experimental results of water temperature.

Fig. 6. Variation of productivity and water–glass temperature difference.

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5. Results and discussion

Fig. 7. Performance of solar still for fins covered with wick material.

The amount of distillate output of the still per unit basin area per unit time is expressed by, me ¼

Q e;w−g ΔT : hfg

ð4Þ

For the next time step, the parameter is redefined as T w ¼ T w þ dT w

ð5Þ

T g ¼ T g þ dT g

ð6Þ

T b ¼ T b þ dT b :

ð7Þ

The daily efficiency, ηd, is obtained by the summation of the hourly condensate production me, multiplied by the latent heat hfg, hence the result is divided by the daily average solar radiation Hs over the whole area Ab of the device: X ηd ¼

_ e hfg m X Ab Hs

ð8Þ

Fig. 4 shows the daily efficiency of conventional and finned solar stills with different depths of water in the basin. The overall performance shows the finned still is better than the conventional still at all depth conditions. A square finned still has a higher performance than a circular finned still. As expected, stills at lower depths give higher efficiency in all configurations. Thus a 1 cm depth of water is selected for further discussions. The efficiency of square and circular finned stills at a 1 cm depth of water is 15% and 13% higher than conventional solar still respectively. Fig. 5 shows the theoretical and experimental values of water temperature in conventional and finned stills. It shows that water temperature follows the same path of solar radiation and it reaches the maximum at noon. The water temperature of the solar still with fins is always higher than the conventional solar still due to a higher exposure area. This leads to higher absorption of solar radiation and transmits to water through the basin. Water temperature reaches the maximum value of 63, 61 and 56 °C for square finned, circular finned and conventional stills. Productivity variation and water–glass temperature difference in conventional and finned solar stills are given in Fig. 6. Condensation rate in the glass cover is directly proportional to the difference between the water and glass temperature. The mass of the circular finned still is higher than the square finned still which increases the thermal capacity of the still. It leads to a little drop in water temperature in the circular finned still compared to the square finned still and a higher evaporation rate in the square finned still. The highest water–glass temperature difference of 14, 12.5 and 8.5 °C and maximum experimental distillate of 0.6, 0.56 and 0.46 kg/m2/h is recorded in square finned, circular finned and conventional solar stills respectively. Hourly distillate yield of wick covered finned stills are presented in Fig. 7. The presence of fins increases the exposure area of the basin for solar radiation and resulted in increased water temperature whereas the wick material increases the exposure area of water by its capillary action and enhances the evaporation rate and distilled output. Thus, it leads to a higher condensation rate in the solar still than the fin alone. Day and night productivity of the conventional and modified stills is compared and presented in Table 2. The presence of wick material on square fins increases the day time productivity about 40%, whereas night time output is enhanced up to 82% more than the conventional still. This is due to the increase in exposure area and thermal capacity of the solar still. 6. Carbon dioxide mitigation and credit analysis

4. Error analysis Errors associated with the experimental measurements apparatus such as thermocouples, solarimeter, anemometer and measuring jar are calculated as given by Velmurugan et al. [30]. Table 1 shows the experimental errors of various instruments used in this work. Error ¼

Accuracy of instrument 100 Minimum value of the output measured

ð9Þ

This work provides the basic information about how much CO2 is mitigated from a solar still which reduces the releasing of harmful CO2 into the atmosphere. At present, there is no opportunity to sell the carbon credit from the solar still. However, it describes the amount of carbon that can be mitigated from a solar still and the value of carbon credit if it is sold. The solar still is fully operated by renewable energy and it does not pollute the environment. However the materials like steel, glass, iron sheet, insulation and paints used for this process are certainly

Table 2 Comparison of conventional still with modified solar still. S. no.

Modified still type

Productivity (kg/m2 day) Conventional still

1 2 3 4

Circular fin Square fin Circular fin with wick Square fin with wick

Productivity increase compared to the conventional solar still (%)

Modified still

Day

Night

Total

Day

Night

Total

2.75 2.73 2.71 2.72

0.41 0.38 0.43 0.4

3.16 3.11 3.14 3.12

3.47 3.71 3.66 3.81

0.52 0.54 0.61 0.74

3.99 4.25 4.27 4.55

26.3 36.7 36 45.8


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Table 3 Embodied energy of different components in solar still [28,29,31]. S. no.

Component

Materials

1 Basin 2 Stand 3 Transparent cover 4 Insulation 5 Absorber coating 6 Square fin 7 Circular fin Total embodied energy

Stainless steel Iron Glass Expanded polystyrene Black paint Iron Iron

Total weight (kg)

12 13.5 4 0.35 0.5 8.5 10

Embodied energy (MJ/kg)

56.7 25 15 88.6 90.4 25 25

manufactured by using the electricity generated by the conventional fuel. During this manufacturing process, a large amount of pollutants is released to the atmosphere and it resulted in environmental degradation. This analysis is used to evaluate the CO2 mitigated by the solar still on the environment during the operational period and energy payback time of the solar still. In the current Indian scenario, the average CO2 equivalent intensity for electricity generation from coal based power plants is approximately 0.98 kg of CO2 per kWh at the source. The transmission and distribution losses for the Indian condition are taken as 40% and domestic appliance losses are around 20%. By considering this the figure 0.98 is taken as 1.58 [28,29]. Thus Annual CO2 emission ¼

Ein 1:58 LT

CO2 mitigation ðkg of CO2 Þ per year ¼ Eout 1:58

Fig. 8. Energy payback time for solar still with different modifications.

Eout ¼

Circular finned still

(kWh)

(MJ)

(kWh)

(MJ)

(kWh)

680.4 337.5 60 31.01 45.2 – – 1154.11

189 93.75 16.67 8.61 12.56 – – 320.59

680.4 337.5 60 31.01 45.2 212.5 – 1366.61

189 93.75 16.67 8.61 12.56 59.03 – 379.62

680.4 337.5 60 31.01 45.2 – 250 1404.11

189 93.75 16.67 8.61 12.56 – 69.44 390.03

MY hfg : 3600

ð12Þ

The time taken to regain the embodied energy of the distillation unit is called the energy payback time (EPBT) and it is given in years as [29], EPBT ¼

Ein : Eout

ð13Þ

Therefore, total CO2 emission mitigated (TCEM) over the life time of the solar still is calculated by TCEM ¼

ð11Þ

Square finned still

(MJ)

where, Eout is the annual energy output from the solar still and it can be calculated by the yearly distillate yield obtained from the solar still multiplied by the latent heat of evaporation [29]

ð10Þ

where, Ein is the total embodied energy of the solar still and LT is the life time of the solar still. The embodied energy of the solar still can be calculated for the components used in the solar still by using the mass of each component and energy densities as given in Table 3. However in addition to initial investment, there is some maintenance needed in the solar still at a regular interval period. Maintenance of the solar still mainly consists of change of insulation and recoating of black paint (absorber plate) every year. Thus the energy required for this process is considered in the energy input for every year and multiplied with the life time of the solar still. The CO2 mitigation per year can be expressed as,

Total embodied energy Conventional still

ðEout LT Þ−Ein 1:58 : 1000

ð14Þ

Carbon credit earned analysis can be calculated by [28] CCE ¼ TCEM Cost of CO2 traded per ton

ð15Þ

Energy payback time on the solar still with different modifications is plotted in Fig. 8. Energy payback time reduces with an increase in the number of operational days which leads to higher annual distillate output. It causes higher regain of embodied energy from the solar still with less number of payback years. Variation of total CO2 emission mitigated and carbon credits earned in the life time of the solar still is displayed in Fig. 9. It is considered as the solar still is operated for 275 days in a year. TCEM and CCE increase with life time of the still and modifications of the solar still. This is due to the production of pure water from a renewable energy based system,

Fig. 9. Total CO2 emission mitigated and carbon credits with life time of solar still.

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Table 4 Initial investment on solar still with circular and square fins. S. no.

1 2 3 4 5 6 7 8 9 Total

Materials

Basin Stand Transparent cover Insulation Absorber coating Square fin Circular fin Fabrication cost Others

Cost (US$) Conventional still

Still with circular fin

Still with square fin

40 12.5 15.83 7.5 4.17

45 12.5 15.83 7.5 4.17 – 21.67 41.67 8.33 156.67

45 12.5 15.83 7.5 4.17 19.17 – 41.67 8.33 154.17

– – 33.33 8.33 121.66

which leads to an increase in mitigation of CO2 with a hike in life time of the solar still. Maximum TCEM and CCE is 36.63 t and 671.6 $ for the wick covered square finned solar still with the life time of 30 years. Fig. 11. Variation on cost of distilled water with operational days.

7. Economic analysis Economic analysis of a solar still with different configurations is presented in this section. Initial investment on solar stills and fins is presented in Table 4. Economic analysis is carried out to estimate the unit cost of distilled water in the present system using Eq. (15). TAC Cdw ¼ M

TAC ¼ FAC þ AMC–ASV

ð16Þ

FAC ¼ P ðCRFÞ:

ð17Þ

Capital cost (P) of the solar still with different modifications are given in Table 3. ið1 þ iÞn ð1 þ iÞn 1

ð18Þ

The interest per year (i) and the number of life years of the system (n) are assumed as 12% and life time (LT) of the solar still is varied from 5 to 30 years. AMC ¼ 0:15 FAC

ASV ¼ S SFF

ð20Þ

S ¼ 0:2 P

ð21Þ

ð15Þ

Total annualized cost (TAC) is calculated by using the fixed annual cost (FAC), annual maintenance cost (AMC) and annual salvage value (ASV) as follows,

CRF ¼

15% of the FAC is taken as annual maintenance cost (AMC).

ð19Þ

Here the salvage value of the system is taken as 20% of the capital cost (P) of the system. SFF ¼

i ð1 þ iÞn 1

ð22Þ

The cost of distilled water production and distilled water production per dollar from a solar still with different modifications is shown in Fig. 10. In this, the life time of the solar still is varied from 5 to 30 years and 275 operational days per year is considered. The cost of distilled water production decreases with an increase in life time of the system and it drops in a huge range up to 15 years and after that the drop is minimum. This causes an increase in salvage value of the system with years. Square finned still covered with wick material resulted in lower cost in the range of 0.049 to 0.029 $/kg for 5 to 30 years life span. The distilled water production rate varies in the range 20.42 to 34.48 kg/$ for 5 to 30 years life time.

Fig. 10. Economic analysis on solar stills with different modifications.


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Table 5 Performance comparison of solar still. S. no.

1 2

Author(s)

Velmurugan et al. [15] Srivastava & Agarwal [17]

3

Omara et al. [19]

4

Sakthivel et al. [32]

5

Present work

Modification

Rectangular fins in basin Porous fin Vertical finned still Corrugated still Still with jute cloth Square fins in basin Square fin with wick covered

Productivity (kg/m2/day) Conventional solar still

Modified solar still

1.88 6.5

2.8 7.5 4.55 3.95 4 4.25 4.55

3.25 3.35 3.11 3.12

Effect of operational days on cost of distilled water is analyzed in Fig. 11. It is noted that cost reduces with the number of operation days, which is the result of enhancing the total distillate output of the still. The increase in life time of the system more than 15 years does not result in considerable reduction in the cost of the solar still. It is difficult to operate the system beyond 10 or 15 years due to its exposure to the atmosphere which resulted in defects in the materials by corrosion and damage. Performance of present work is compared with previous works on solar stills with different fin configurations and presented in Table 5. 8. Conclusions Performance improvement on a single basin solar still with circular and square fins integrated in the basin is investigated in this work. Circular and square fins result in almost the same performance and there is a minimum difference in distillate output. The highest productivity of 4.55 and 3.16 kg/m2 day is obtained for the square fin covered with wick and conventional still respectively. Daily productivity of the still increases by 26.3 and 36.7% for circular and square finned stills and it changes to 36 and 45.8% for fins covered with wick materials. The embodied energy payback time is less than one year for all cases and it further reduces with an increase in operational days of the solar still. Economic analysis shows that the minimum cost of distilled water for 350 operational days and 30 years life time is about 0.024$/kg for square finned stills with wick material. Nomenclature A area, m2 CCE carbon credit earned, $ Conv conventional Cdw cost of distilled water, $/kg carbon dioxide CO2 specific heat capacity, J/kg °C Cp d difference, °C E embodied energy EPBT energy payback time solar intensity, W/m2 Hs LT life time, years yearly distillate, kg/year MY m mass, kg h heat transfer coefficient, W/m2 °C LT life time of solar still, years P partial pressure, N/m2 Q heat transfer rate, W/m2 T temperature, °C TCEM total CO2 emission mitigated, tons TH theoretical T time, s heat loss coefficient from basin to ambient, W/m2 °C Ub latent heat of water, J/kg hfg V wind velocity, m/s

Productivity increase compared to the conventional solar still (%) 48.9 16.9 40 21.5 19.4 36.7 45.8

Subscripts a ambient air atm atmosphere av. average b basin c convection e evaporation eff effective g glass in input loss side loss out output r radiation w water Greeks α ε σ Σ Δ

absorptivity emmisivity Stefan–Boltzmann constant (5.6697 × 10−8 W/m2 K4) algebraic sum change

Appendix The following equations are used for the theoretical calculation. Q c;b‐w ¼ hc;b‐w Ab ðTb −Tw Þ Q b‐atm ¼ Ub Ab ðTb −Ta Þ Q c;w‐g ¼ hc;w‐g Aw Tw −Tg " hc;wg ¼ 0:884

#1 Pw Pg ðTw þ 273:15Þ 3 Tw Tg þ 268:9 103 pw

Q r;w‐g ¼ hr;w‐g Aw Tw −Tg " hr;wg ¼ εeff σ

4 # ðTw þ 273Þ4 Tg þ 273 Tw Tg

Q e;w‐g ¼ he;w‐g Aw Tw −Tg he;wg ¼

Ma C pa

M w hfg pT hc;wg ðpT pw Þ pt pg

Q r;g‐sky ¼ σ εg Ag

h

i 4 Tg þ 273:15 −ðTa þ 267:15Þ4

Q c;g‐sky ¼ hc;g‐sky Ag Tg –Tsky hc;g‐sky ¼ 2:8 þ 3V

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